Review on pneumatic operations in centrifugal microfluidics

J. F. Hess a, S. Zehnle b, P. Juelg b, T. Hutzenlaub ab, R. Zengerle ab and N. Paust *ab
aLaboratory for MEMS Applications, Department of Microsystems Engineering – IMTEK, University of Freiburg, Georges-Koehler-Allee 103, 79110 Freiburg, Germany
bHahn-Schickard, Georges-Koehler-Allee 103, 79110 Freiburg, Germany. E-mail: Nils.Paust@Hahn-Schickard.de

Received 10th May 2019 , Accepted 21st September 2019

First published on 27th September 2019


Centrifugal microfluidics allows for miniaturization, automation and parallelization of laboratory workflows. The fact that centrifugal forces are always directed radially outwards has been considered a main drawback for the implementation of complex workflows leading to the requirement of additional actuation forces for pumping, valving and switching. In this work, we review and discuss the combination of centrifugal with pneumatic forces which enables transport of even complex liquids in any direction on centrifugal systems, provides actuation for valving and switching, offers alternatives for mixing and enables accurate and precise metering and aliquoting. In addition, pneumatics can be employed for timing to carry out any of the above listed unit operations in a sequential and cascaded manner. Firstly, different methods to generate pneumatic pressures are discussed. Then, unit operations and applications that employ pneumatics are reviewed. Finally, a tutorial section discusses two examples to provide insight into the design process. The first tutorial explains a comparatively simple implementation of a pneumatic siphon valve and provides a workflow to derive optimum design parameters. The second tutorial discusses cascaded pneumatic operations consisting of temperature change rate actuated valving and subsequent pneumatic pumping. In conclusion, combining pneumatic actuation with centrifugal microfluidics allows for the design of robust fluidic networks with simple fluidic structures that are implemented in a monolithic fashion. No coatings are required and the overall demands on manufacturing are comparatively low. We see the combination of centrifugal forces with pneumatic actuation as a key enabling technology to facilitate compact and robust automation of biochemical analysis.


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Jacob Friedrich Hess

Jacob Friedrich Hess studied mechanical engineering at the Karlsruhe Institute of Technology and the Institut National des Sciences Appliquées of Lyon with a focus on fluid mechanics and thermal turbomachinery, where he received his master’s degree in 2015. He currently works as an R&D engineer and PhD candidate with the laboratory of MEMS Applications at the University of Freiburg. His research focuses on the system and assay integration of laboratory workflows on centrifugal microfluidic cartridges.

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Steffen Zehnle

Dr. Steffen Zehnle earned a Bachelor and a Master degree in Microsystems Engineering. In 2012, he joined Hahn-Schickard to focus on the research in centrifugal microfluidics for lab-on-a-chip applications. In 2019, he received a doctoral degree from the University of Freiburg for his work entitled “Pneumatic operations in centrifugal microfluidics – An enabling technology for assay automation”. Since 2018, Dr. Zehnle works as R&D System Engineer at TrueDyne Sensors AG, an Endress+Hauser company, located in Reinach, Switzerland. In this function, he drives the development of MEMS-based density and viscosity sensors for liquids and gases for the use in in-line process applications.

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Peter Juelg

Peter Juelg studied Mechanical and Biomedical Engineering at the Technical University of Berlin and the Instituto Superior Técnico in Lisbon. He finished his studies in 2014 with a thesis on laser micro structuring of medical fibers at the Fraunhofer IZM. After his studies, he developed fluid mechanical components at the W.O.M. GmbH, a Berlin based company for minimally invasive surgery. In 2016, he joined the Hahn-Schickard division for microfluidic platforms in Freiburg. As PhD candidate at the University of Freiburg his current research focus is the application of Lab-on-a-Chip techniques for cancer monitoring.

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Tobias Hutzenlaub

Tobias Hutzenlaub studied Environmental Process Engineering (degree: Diploma) and Energy Conversion and Management (degree: Master of Science) at Offenburg University of Applied Sciences. In autumn 2008 Mr. Hutzenlaub started his PhD work on fuel cells and batteries at the Laboratory for MEMS Applications (Prof. Zengerle) and finished it in 2014, subsequently changing his focus to Lab-on-a-Chip and centrifugal microfluidic system integration. Currently he is head of the group Layout and Simulation at Hahn-Schickard in Freiburg.

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Roland Zengerle

Dr. Zengerle is full professor at the Department of Microsystems Engineering at the University of Freiburg, Germany, and director of the “Hahn-Schickard-Institut für Mikroanalysesysteme”. His research is focused on Microfluidics, Lab-on-a-Chip as well as Electrochemical Energy Systems. Dr. Zengerle co-authored more than 380 papers and chaired several leading international conferences such as IEEE MEMS (2006) and MicroTAS (2013). He was editor in chief of the Springer Journal of Microfluidics and Nanofluidics and currently is Advisory Board Member of the journal “Lab on a Chip”. Since 2011 he is a member of the National Academy of Science, Leopoldina.

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Nils Paust

Dr. Nils Paust studied energy and process engineering at the Technical University of Berlin with a focus on fluid mechanics, thermodynamics and control engineering (degree: diploma). He received his Ph.D. with the dissertation entitled “Passive and self-regulating fuel supply in direct methanol fuel cells” at the University of Freiburg in 2010. Since 2010, Nils works for Hahn-Schickard, first as a group leader and nowadays as the head of the division “Microfluidics Platforms”. Main research interest of Nils Paust is the centrifugal microfluidic system integration. This comprises new microfluidic functionalities, the interface between fluidics and scalable cost-efficient mass fabrication and the implementation of complete laboratory workflows on centrifugal microfluidic cartridges.


1. Introduction

Centrifugal microfluidic propulsion offers major advantages when compared to other actuation principles.1–10 The propulsion simply by centrifugation allows for a closed fluidic system, devoid of any interfaces to external pumps. Enclosed gas volumes within the liquid that may disturb the analysis are removed by employing buoyancy in the artificial gravity field. Main advantage of centrifugal microfluidics is that the actuation forces can easily be scaled by adjusting the rotational frequency, which allows for well-defined and controlled liquid handling from the nanoliter to hundreds of microliter domain even for highly wetting liquids. On the downside, centrifugal forces are always directed radially outwards and additional actuation forces are required for liquid manipulation.

Capillary,11–18 Coriolis19–24 and Euler25–32 forces have been widely used in combination with centrifugal forces to enable mixing, valving or metering on centrifugal microfluidic platforms. Still, even at moderate rotational frequencies, these forces are mostly orders of magnitudes lower than centrifugal forces, making them effective in small operating ranges, only. This fact helps to develop robust automation of complex workflows, where unintentional transport of liquids at lower frequencies can lead to system failure. Valving, pumping or metering principles based on form closure, such as membranes33–43 or wax,44–48 can also be integrated on centrifugal microfluidic platforms, but require more sophisticated devices or more complex cartridge designs for the implementation, which may result in higher manufacturing costs. In the past decade, robust solutions for liquid manipulation have been found by making use of the air that is intrinsically available in practically all microfluidic platforms to generate pneumatic forces. Pneumatic forces are typically in the same order of magnitude as centrifugal forces, which makes them particular suitable for liquid manipulation by the interplay of both forces. The usability of pneumatic forces as means of liquid control and propulsion has been proven on other microfluidic platforms in the past. Microfluidic chips that are supplied with liquids by additional pumps use pneumatically actuated membrane valves for flow control. In this way, “normally-closed” check valves as well as “normally-open” valves have been realized with silicon and polydimethylsiloxane (PDMS) as membrane material, integrated even in a large scale.49–53 Other approaches use electric power to heat up gas bubbles on-chip that thermally expand and drive pumping or valving mechanisms.54 Hong et al. even used electric heating to melt a pre-defined breaking point to release on-chip pressurized gas that in turn is used for pumping liquids.55

Whereas excellent overviews on existing centrifugal microfluidic unit operations and applications in general can be found in the respective reviews,1,2,16,18,24,32 in this work, we focus on the unique combination of centrifugal microfluidics with pneumatic actuation. From our perspective this combination significantly broadens the degree of freedom for the design, enhances flow control and improves the robustness compared to centrifugal microfluidic systems as known from the early days.8,9 We start with the theoretical background and continue with an overview and classification of different unit operations making use of pneumatic actuation. Applications enabled by pneumatics are presented and discussed thereafter. The second part of this review is a tutorial to provide detailed insight in the design process. We attempt to discuss all parameters that are relevant. Starting from the generation of pneumatic pressure by compressing the air, we consider the influence of additional capacities of flexible cartridge materials such as sealing foils and the effect of vapour pressure. Furthermore, the influence of manufacturing tolerances are evaluated. Whereas the design of the first tutorial is based on analytical equations only, the second tutorial teaches a more sophisticated design technique using network simulation.

2. Pneumatic liquid manipulation

Pneumatic liquid manipulation in microfluidics follows the same principle in which the pressure of a gas pid is changed according to Boyle–Mariotte's law for ideal gases given by
 
pid = (nRT)/V(1)
where n is the amount of substance, R is the Boltzmann constant, T is the absolute temperature and V is the volume of the gas. The induced pressure change leads to a change in volume that is used to displace liquid. According to eqn (1), pneumatic pressures can be induced by changing three different parameters as illustrated in Fig. 1:

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Fig. 1 Principles of the generation of pneumatic pressure. A-Initial condition at rest with the liquid in the inlet chamber. B-Intrinsically generated pressure by change of volume. When increasing the frequency, the liquid enters the pneumatic chamber positioned radially outwards and compresses the volume of the air. Consequently, the ideal gas pressure equals to the centrifugal pressure induced by the liquid column. By reducing the rotational frequency, the pneumatic pressure is released and can be used for the execution of unit operations. C-Pressure increase by additional temperature change. In addition to configuration B, the chamber is now heated and the pneumatic pressure increases while still being balanced by centrifugal pressure. Release of the pressure can either be realized by reducing the temperature or by reducing the rotational frequency. Notice that the cases presented in B and C are not completely independent of pressure generated by amount of substance. The partial vapour pressure in the pneumatic chamber rises, as soon as liquid enters it and leads to an increasing pneumatic pressure. When increasing the temperature in case C, additional liquid evaporates and the pressure change by evaporation can even be greater than the pressure generation by temperature change. Substances can also be added by additional means such as chemical reactions or external pumps.

1) Volume of gas.

2) Temperature.

3) Amount of substance.

Before examining the different parameters in detail, it should be mentioned that pneumatic pressures are rarely generated by one of the three parameters alone, but by a combination. Fig. 1C represents the influence of all parameters in a single chamber. Compressed volume combined with temperature increase and varying amount of substance due to evaporation match the centrifugal pressure. This fact can be described by a total pressure ptot resulting from partial pressures

 
ptot = pid + ϕpvap(T)(2)
where ϕ is the relative humidity of the liquid in the air and pvap the saturated vapour pressure of the liquid at a defined temperature. Due to the low volume to surface ratio, equilibrium is reached rather quickly and thus, in many cases, saturation conditions can be assumed as soon as the liquid enters the pneumatic chamber. When heating the air, both partial pressures increase and often, the change in vapour pressure becomes the driving force for liquid manipulation.

2.1. Generation of pneumatic pressures by change of volume V

Inherently, microfluidic chips contain liquid that can be used for compression/expansion of entrapped gas thereby changing the gas volume and building up a pneumatic over- or underpressure, as depicted exemplary in Fig. 1B. In contrary to changing n or T, the gas compression/expansion is characterized by a pressure-dependent fluidic capacity C, defined as
 
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assuming isothermal condition for the constant amount of substance n. Using liquid for air compression/expansion in microfluidic chips is the most common approach, but deforming materials may also be possible.56,57

2.2. Generation of pneumatic pressures by change of temperature T

The existing molecules can be accelerated or slowed down by externally induced temperature changes. In centrifugal microfluidics, this is done by heating/cooling of the microfluidic chip that in turn transmits the temperature changes to the air volume used for pneumatic actuation. This heating/cooling action is realized by exchange of cold or hot air within the processing device, by contact heating/cooling of the chip, by absorption of radiation or via exo-/endothermal chemical reactions.58,59

2.3. Generation of pneumatic pressures by change of amount of substance n

Changing the number of gas molecules in a confined space with constant volume and temperature translates to a proportional pressure change. The technical implementation is done either by on-chip gas production via chemicals reactions or evaporation/condensation of liquids. Another straightforward approach to change the number of gas molecules on-chip is the use of additional pumps for gas supply or evacuation, whereby the latter is referred to as externally generated pneumatic pressure.60,61

3. Unit operations utilizing pneumatics in centrifugal microfluidics

Apart from the physical classification based on the ideal gas law, another reasonable categorization shall be considered for pneumatic operations, namely pneumatic actuation using centrifugation, only and pneumatic actuation using additional means.

Pneumatic actuation principles using centrifugation only set relatively low demands on the processing device. Basically, a rotary motor that can be run with a pre-defined programmed rotational protocol is sufficient. With the rotational protocol as the only control parameter, however, complex workflows require complex fluidic designs to achieve full assay automation.

Pneumatic actuation principles using additional means set higher demands on the processing device that is used not only for centripetal acceleration of the microfluidic chip, but also for electrical concatenation and thermal or pneumatic actuation. These additional means grant additional degrees of freedom to enable fluidic unit operations while keeping fluidic designs simple.

In the following, pneumatic unit operations realized on centrifugal microfluidic platforms are presented and classified according to the use of additional means.

3.1. Pneumatic liquid transport

Automation of fluidic workflows is practically always based on transport of liquid between at least two chambers, e.g. from inlet to reaction chamber or from reaction chamber to waste. While centrifugal microfluidic platforms by definition enable pumping of liquid towards the outer rim, the challenge of pumping the liquid back towards the centre of rotation is inseparably linked with it, and has already been extensively discussed in literature.
3.1.1. Pneumatic liquid transport actuated by additional means. A natural choice for liquid transport on a microfluidic chip in any direction – in particular radially inwards – is to stop the chip and connect pneumatic tubes so that externally applied pressure gradients move the liquid along a desired path, as suggested in a patent by Lee et al.62 This purely pressure-driven transport mechanism, however, encounters challenges such as bubble entrapment that are characteristic for pressure-driven microfluidics and actually would be solved by centrifugation.

A combination of pneumatic actuation via tubes and centrifugation was presented by Clime et al. (Fig. 2) who built a rotating platform for processing microfluidic chips that are continuously connected to pneumatic tubing. At an applied pneumatic pressure of 340 mbar, pump rates of up to 40 μl s−1 were demonstrated over a radial distance of around 33 mm and all liquid could be transferred. Due to the continuous rotation at 10 Hz, liquid/air interfaces are kept stable and thus, bubble entrapment is prevented. Not only liquid transport, but also other unit operations such as mixing and valving can be realized on this platform with comparatively simple fluidic structures, as discussed in the following chapters. The downside of this approach is the need for a complex rotor with an integrated pressure source, manifolds and tubings which in turn involves a certain contamination risk when interfaced to the microfluidic chip.1,63,64


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Fig. 2 Combination of centrifugal and pressure-driven microfluidics reproduced from Clime et al.63 with permission from The Royal Society of Chemistry, 2015. All relevant components, such as the microfluidic device, control technology and pneumatic tubing, are integrated on a rotor. The integrated pressure-driven system allows the integration of many pneumatic operations, such as liquid transport or mixing.

A similar device/chip interface challenge emerges in the approach presented by Noroozi et al. using integrated electrodes for electrolysis of water to hydrogen and oxygen. These gases are entrapped in a chamber that is connected to a radial inner end of a liquid reservoir. As hydrolysis proceeds, the amount of gas molecules increases and a pneumatic pressure builds up. As a consequence, the pressurized liquid in the reservoir starts moving through the radial outer outlet of the reservoir and can be completely transferred into any other chamber on the microfluidic platform. In this work, pump rates of up to 9 μl s−1 over a radial distance of around 34 mm were reported, with applied currents at 90 mA.65

The solid connection between the microfluidic chip and external energy sources is omitted in the approach used by Kong and Salin. Instead, pressurized air is released from an external compressed-gas container and directed towards openings in the rotating platform, so that the impact pressure of the released gas propels the liquid inside the microfluidic chip. While this approach is simple and effective, a considerable contamination risk by liquid and aerosols that escape through the chip openings has to be taken into account.60 The same principle is also used by Kazarine et al.66 for recirculation pumping.

Strategies to omit any mechanical interface between external energy sources and the on-chip fluidics based on radiation are presented by Abi-Samra et al. In this approach, an infra-red lamp is employed to irradiate a rotating polymer disk. The absorbed energy heats up the disk material and the entrapped air which leads to a volume increase. This volume expansion is used to drive all of the liquid from a radially outer to a radially inner chamber with up to 17.6 μl min−1 over radial distances of up to 32 mm.67

Alternatively, a temperature increase can also be induced by convective heat transport or heat conductance. In this case, the surrounding of the microfluidic chip – be it the air or rotor – is heated up until the inside of the chip reaches the desired temperature. Depending on the application, either of the heating concepts may be favoured. IR heating of a particular compartment on-chip can be relatively fast, provided that the radiation of the particular wavelength is absorbed by the medium. On the other hand, heating of the surrounding is only limited by the heat transfer characteristics of the disk material. In analogy to pneumatic actuation by heating, similar results can be achieved by cooling of the centrifugal microfluidic platforms.68

3.1.2. Pneumatic liquid transport without additional means. Heating and cooling elements are featured in many centrifugal processing devices due to their need in biological applications. However, if heating, cooling and other external elements can be omitted entirely, costs can be saved. Apart from that, the use of actuation principles with and without additional means maximizes the number of independent processing parameters so that each unit operation can be designed with possibly higher robustness.

Pneumatic liquid transport without any additional auxiliary means has been presented by Zehnle et al. In this principle, the sample fluid is first centrifugally pumped into a dead end (pneumatic) chamber where air is entrapped and compressed. Subsequently, the rotational frequency is reduced so that the entrapped air expands again (Fig. 3). Since the pneumatic chamber is devised with a narrow inlet (high fluidic resistance) and a wide outlet (low fluidic resistance), the liquid is largely pumped through the outlet and transferred to any arbitrary location on the platform. Intrinsically, a transfer efficiency of 100% is not possible, although more than 90% is common given that the inlet channel can be designed with small diameters (e.g. <100 μm) and the processing device provides decent deceleration rates (>10 Hz s−1). Typical flow rates depend on the viscosity of the fluid and in case of water, up to 40 μl s−1 over a radial distance of 40 mm are reported.56


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Fig. 3 Passive pneumatic inward pumping reproduced from Zehnle et al.56 with permission from The Royal Society of Chemistry, 2012. At the start, the liquid is only in the inlet chamber and the system is at rest (A). When increasing the rotational frequency, most of the liquid is transported into the compression chamber where the entrapped air is compressed (B and C). Small amounts remain in the inlet and outlet channels providing the centrifugal counterpressure. A fast deceleration leads to the expansion of the entrapped air and the liquid is transferred into the inlet and collection chamber (D). Due to the low resistance of the outlet channel in comparison to the high resistance of the inlet channel, most of the liquid flows into the collection chamber as illustrated in (E).

In a different approach, Kong et al. and Soroori et al. set lower demands on channel dimensions and on the rotational protocol for pneumatic liquid transport without additional means. An ancillary fluid is used to compress or expand an air pouch between the ancillary fluid and the sample fluid, so that the resulting pneumatic pressure pushes or pulls the sample fluid from the radial outer chamber to the radial inner destination chamber.69,70

3.2. Pneumatic valving and switching

In contrast to liquid transport, the unit operation “valving” requires temporary pressure pulses, only, to initiate the liquid transfer process by centrifugation. Due to simple monolithic integration and high robustness, pneumatically actuated valves on centrifugal microfluidic platforms are mostly implemented as siphon valves. They always follow the same principle:

1) A pneumatic pressure pulse is used to displace a small amount of the sample fluid from a chamber into an adjacent siphon.

2) Once the siphon is filled up to the critical fill level on the descending side of the siphon, the entire sample fluid is transferred through the siphon to downstream elements.

Basically, any pneumatic liquid transport mechanism presented so far can be used for pneumatic siphon valving. However, the counterplay between pneumatic pressures on the one side and centrifugal pressures and viscous dissipation on the other side offers much more valving and switching solutions, as discussed in the following.

3.2.1. Pneumatic valving and switching actuated by additional means. A selection of combined pumping, siphon valving and switching operations by thermo-pneumatic actuation is given by Thio et al. These “push–pull-microfluidics” are powered with a hot air gun to selectively heat up pneumatic chambers so that thermal air expansion or contraction leads to siphon priming or complete liquid transfer into receiving chambers.68 Similarly, Aeinehvand et al. used the hot air gun for thermo-pneumatic actuation of a latex membrane to open and close a fluidic path.71 Keller et al. used the global convective heating in a RotorGene Q for thermal expansion of an entrapped gas volume to prime a siphon.72 Analogously, a sample fluid can be sucked into a siphon by cooling-induced air volume reduction in the receiving chamber. This process requires either a closed receiving chamber or an open receiving chamber with a venting path with high fluidic resistance and a fast cooling rate. The latter approach is based on the effect that the high resistance venting channel delays the air supply from the ambience while the fast air contraction in the receiving chamber enforces siphon priming.59

A combination of liquid pre-storage and thermo-pneumatic siphon valving is presented by Kong et al. using paraffin wax on-chip. Liquid pre-storage is realized between two solid wax layers that separate the sample liquid from the environment. In a first heating step during centrifugation, the wax is molten and concentrates due to its lower density radially inward of the sample liquid. At low rotational frequency, the molten wax creeps into an adjacent venting channel by capillary action. Subsequent cooling solidifies the wax again, thereby closing the vent, so that in following heating steps, an overpressure is built up and pushes the sample liquid over a siphon crest.45

Inherently, microfluidic platforms are designed for liquid processing, which is why the use of ancillary liquids is an obvious way to realize fluidic valves. Al Faqueri et al. introduced an ancillary fluid to close the air vents of either the sample reservoir or the receiving chamber that is connected to the sample reservoir via an overflow siphon. For both configurations, it holds that at low rotational frequency, the sample fluid remains in the sample reservoir due to the closed air vent. At high rotational frequency, the moving sample fluid builds up either a vacuum in the sample reservoir or an overpressure in the receiving chamber. At a certain threshold frequency, the overflow siphon is primed so that the entire liquid volume is transferred into the receiving chamber.73

Gorkin et al. used the suction effect generated within a channel when an ancillary liquid is pumped through it to prime a siphon.74 A different, but effective approach is to use an ancillary liquid in a chemical reaction to produce gas that builds up a pneumatic pressure and triggers the valving process. This is presented by Kinahan et al. who dissolved baking powder in water to generate carbon dioxide that in turn pressurized the sample liquid. In this implementation, the sample liquid is pushed against a dissolvable patch that serves as valve. However, it appears obvious that the generated gas pressure may also be used for further liquid transport.75

Based on the dissolvable film technology presented by Gorkin et al.,76 Kinahan et al. presented the combination of ancillary fluids and dissolvable films to create conditional microfluidic circuits with Boolean functions (see Fig. 4). In essence, fluid paths are interrupted by dissolvable films. With a plurality of siphons, the fluidic design ensures that sample fluids and dissolvable films remain separated by compressed air pouches. When the ancillary liquids dissolve distinct dissolvable films, air vents are opened so that the air pouches are no longer compressed and the sample fluids proceed.77


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Fig. 4 Dissolvable film reproduced from Gorkin et al.76 with permission from The Royal Society of Chemistry, 2012. The valve consists of two components: a dissolvable film and a pressure sensitive adhesive. At the start, the pneumatic pressure prevents the liquid from getting in contact with the dissolvable film. When increasing the centrifugal pressure, liquid enters the chamber and the dissolving process starts. Duration of dissolving depends on the film components.
3.2.2. Pneumatic valving and switching without additional means. Pneumatic siphon valving without additional means and even without capillary forces goes back to the principle presented by Gorkin et al. as illustrated in Fig. 5. First, the centrifugal pressure of a sample fluid is used to compress a defined air volume, and second, with the stored pneumatic energy, a siphon is primed at low rotational frequency.78 This valving mechanism has later been complemented by Zehnle et al. with three more pneumatic siphon valving principles that use compression or vacuum. Additionally, they use the hydrodynamic priming of siphons by tuning of fluidic resistances. In total, four different pneumatic siphon valves are distinguished that are triggered either at high or low rotational frequency or at high rotational acceleration or high rotational deceleration. In the same work, the combination of two of the valves is used as a siphon switch that routes liquid through a first siphon or through a second siphon, depending on the applied rotational deceleration.79
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Fig. 5 Pneumatic siphon valving adapted by permission from Springer Nature Customer Service Centre GmbH: Springer Nature, Microchimica Acta, Pneumatic pumping in centrifugal microfluidic platform, Gorkin et al.,78 2010. At the start (a), all liquid is in the radially inward positioned inlet chamber and the system is at rest. When increasing the rotational frequency, the entire liquid volume is transported into a closed chamber, where the entrapped air is compressed, and into the adjacent channels (b–d). The liquid remains in this chamber until the rotational frequency is decreased below a certain value (e). At this point, the radially inward position of the liquid meniscus needs to be smaller than the radially inward position of the siphon to compensate the pneumatic pressure. Thus, the liquid primes the siphon and is transported into the outlet chamber (f).

Another embodiment of pneumatic siphon valving is presented by Schwemmer et al., splitting the pneumatic chamber into two sub-chambers that are connected via a channel with high fluidic resistance. In this way, the release of pneumatic pressure is strongly delayed so that the valving can be performed with a defined time shift as schematically depicted in Fig. 6. A combination of four of such microfluidic timers was proven to enable valving on demand, in which the valving sequence of the four valves could be altered in any desired fashion, determined solely by the rotational protocol.80


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Fig. 6 Principle of a microfluidic timer reproduced from Schwemmer et al.80 with permission from The Royal Society of Chemistry, 2015. Liquid enters the divided pneumatic chamber (chamber 1 and 2) at a high rotational frequency and compresses the air (A). When decreasing the rotational frequency, the liquid is transported at a low flow rate radially inward due to the high fluidic resistance of the timing channel (B). As soon as chamber 2 and the timing channel are empty (C), the liquid is transported at a high flow rate. This change in flow rate allows siphon priming at a defined point of time and independently of the acceleration rate.

Although siphons have proven to be a highly suitable tool for valving and switching elements, in some applications, alternative solutions may be even simpler to implement. Kim et al. presented a switch consisting of a main channel with radial orientation and one narrow side branch, each of which terminating in separate collection chambers. In operation, a first liquid is always routed through the main channel into the first collection chamber until the fill level in this first collection chamber is high enough to protrude into the main channel. As a consequence, an air pouch is entrapped between the first liquid and the following second liquid, so that the second liquid cannot flow into the first collection chamber, but is routed through the side branch into the second collection chamber.81

Mark et al. presented a pneumatic switch, which is based on a similar principle. A radially outward positioned pneumatic chamber is filled with the first liquid and pneumatic pressure is generated. This pressure prevents the second liquid to move into the pneumatic chamber and is transferred via a siphon channel into a second chamber.82

Conversely, Burger et al. used a mechanism called centrifugo-pneumatic gating which generates a liquid plug to close the venting path between the radial inner inlet reservoir and the radial outer receiving chamber. In doing so, a pneumatic pressure difference between both chambers was maintained so that the sample fluid requires a certain burst pressure to enter the receiving chamber.83

3.3. Pneumatic mixing

Unit operations for mixing by pneumatics require similar premises as liquid transport or valving and switching. Either a pressure is generated to generate bubbles moving through the separated liquids or repetitive pressure generation can mix fluids by reciprocation.
3.3.1. Pneumatic mixing actuated by additional means. Recent developments use pressurized gas to generate gas bubbles that are transported through the liquids to be mixed by buoyancy. Gas production and compression can be done either off-chip in close analogy to the pumping approaches by Clime et al.63 (Fig. 7) and Kong et al.,84 or on-chip by heating a gas volume (Hin et al.58) or in a chemical reaction, as presented by Burger et al.61
image file: c9lc00441f-f7.tif
Fig. 7 Bubble mixing with combined centrifugal and pressure-driven microfluidic system reproduced from Clime et al.63 with permission from The Royal Society of Chemistry, 2015. At the start (1.), two liquids are in two layers in the same chamber. When increasing the pressure in the channel on the right hand side (2.), air bubbles are formed and move against the centrifugal force field. This results in a fast and homogeneous mixing procedure (3.).

The on-chip gas production uses the catalytic decomposition of hydrogen peroxide at manganese dioxide to water and oxygen. Instead of hazardous hydrogen peroxide, other chemicals can be used for gas generation and bubble mixing. In particular, Kinahan et al. used baking powder that was dissolved in water to build up pneumatic pressures by release of CO2 gas, as described in the previous chapter.75 The implementation of CO2 producing reactions is convenient because the reagents are non-toxic, easy to pre-store and the reactions are well-controllable. Carbon dioxide, however, turns the sample liquid acidic during the mixing process. Such pH shift has to be taken into account, as it may not be compatible to the target assay. Hin et al.58 developed a mixing principle generating the required pressure by temperature increase only. This method is advantageous to the previously mentioned methods, as no other reagents are required for the mixing process. Moreover, no additional means are required besides temperature control which was needed any way for the considered application of nucleic acid analysis. It should be considered that Hin et al. used global heating for actuation for which assay compatibility with temperature changes has to be considered. A processing device providing the capability of local heating would solve this issue.

3.3.2. Pneumatic mixing without additional means. A multitude of the pneumatic pumping and valving principles are based on the alternating compression and expansion of entrapped air by the sample fluid.56,78,79,86 Although this mechanism lends itself for well-defined fluid control, it inevitably also leads to the mixing of the sample fluid. In particular, repetitive flow reciprocation between a reservoir and a pneumatic chamber implies at least four mixing mechanisms, namely mixing in channels by Taylor dispersion and by Coriolis force, and mixing in chambers by Euler force and by re-arrangement of fluid layers with different densities. Furthermore, mixing is supported by vortices that are generated at the channel/chamber orifices. This mixing method has been quantified by Noroozi et al. measuring the distribution of fluorescently labelled polystyrene particles during the mixing process. The microfluidic structure features two parallel inlet reservoirs, one is loaded with the particle suspension (8 μl), the other with the same volume of sample fluid, but without particles. After three load/discharge cycles, the particles were distributed homogeneously.87 Schwarz et al. examined mixing by reciprocation based on network simulation tools to optimize mixing efficiency.88 Flow reciprocation mixing does not require any additional means, but it still requires alternation of the rotational frequency, while mixing purely relies on intrinsic hydrodynamic effects.

3.4. Pneumatic metering and aliquoting

Metering and aliquoting are unit operations that are often used in combination. Since aliquots require certain volume accuracy for quantitative analysis, metering of each aliquot is mostly indispensable. As outlined in the introduction, the pneumatic pressure can easily be set high enough so that it counteracts the centrifugal pressure in the same order of magnitude. At high rotational frequencies, in turn, surface forces become increasingly suppressed, which means that liquid menisci take on a perfect isoradial shape and are easy to predict. Based on this knowledge, pneumatic aliquoting as presented by Schwemmer et al. is designed for the supply of two different liquids into one collection chamber as illustrated in Fig. 8. In this work, metering was accomplished in a pneumatic chamber that contained a defined overflow for the sample liquid. Hence, the metered volume was defined at high rotational frequency by the volume within the pneumatic chamber below the overflow, in addition to the volume within the inlet and outlet channels of the pneumatic chamber. Subsequent reduction of the rotational frequency released the metered liquid volume through the outlet channel that can be realized as a siphon in order to extract the entire liquid volume. With this method, 5 μl-aliquots could be realized with coefficients of variations of less than 1.2% for a wide range of different liquids. However, the high accuracy and high robustness had to be paid with a relatively large footprint of the fluidic structure.85
image file: c9lc00441f-f8.tif
Fig. 8 Metering and aliquoting principle reproduced from Schwemmer et al.85 with permission from The Royal Society of Chemistry, 2015. When increasing the rotational frequency (A), liquid starts entering the metering chamber. All additional volume is transferred into an overflow chamber that is connected with the metering chamber via a channel (B). After reducing the rotational frequency, only the volume in the metering chamber is transported to the collection chamber, whereas the surplus liquid remains in the pneumatic chamber (C and D).

A major advantage of the structure presented by Schwemmer et al. is that the metering and aliquoting can be performed simultaneously for two liquids that are subsequently transported into a common reaction chamber. The structure can thus be used to supply two liquids in a highly accurate manner to start a chemical reaction, for example an enzyme substrate reaction to measure the concentration of analytes.

Space efficient alternatives for aliquoting of one liquid into dead-end chambers were presented by Mark et al. and Nwankire et al. In both approaches, the sample liquid is routed from an isoradial supply channel into radial outer metering fingers with terminal cavities at the radial outer end. All metering fingers are filled by the sample liquid at low rotational frequency, demanding a stable liquid/air interface between the metering fingers and the terminal cavities. At subsequent high rotational speed, the metered liquid volumes are transferred into the terminal cavities. In the structure presented by Mark et al., these cavities are dead-end chambers that are predominantly used as optical read-out cavities.89 Nwankire et al. closed these cavities with a dissolvable film so that first air entrapment is granted, and second, after aliquoting, a fluidic downstream connection is realized.90

3.5. Pneumatic particle handling

Microparticles have become a standard tool for affinity based separation. Still, the use in centrifugal microfluidic platforms is limited, possibly for the reason that centrifugation leads to fast particle sedimentation at the radial outer end, while resuspension is difficult. Approaches that are known so far use shake-mode mixing to resuspend particles, and external magnets to move magnetic particles, both at low or zero rotational frequency. Timed pneumatic actuation, as presented in the chapter Pneumatic valving and switching without additional means also enables fluid control at rest or at slow rotation, while the pneumatic pressure is released slowly. This effect was used by Zhao et al. for particle resuspension by shake-mode mixing. Due to the pneumatic actuation, the sedimentation/resuspension structure could be coupled to two siphons that are used selectively to either extract the supernatant into a waste chamber or into a detection chamber with very small particles losses.91

4. Applications utilizing pneumatics in centrifugal microfluidics

Due to their high robustness, pneumatic unit operations have made their way into many applications on centrifugal platforms, already. For better clarity, we differentiate between applications in nucleic acid analysis, protein analysis and clinical chemistry.

4.1. Nucleic acid analysis

Nucleic acid analysis is a highly useful tool in diagnostics. The most established and widespread approach is the amplification of specific sequences of DNA or RNA, for example by polymerase chain reaction (PCR) or isothermal amplification methods with subsequent detection of fluorescent labels. Consequently, this approach has also found its way into centrifugal microfluidics.58,92–101

Nucleic acid analysis often requires specific sample preparation, such as extraction with bind-wash-elution steps. Brassard et al. showed this concept on a cartridge with integrated solid-phase extraction matrix. The complete workflow requires pneumatic operations for liquid transfer and for bubble mixing. Comparison with commercial kits prove that the centrifugal microfluidic cartridge is compatible and leads to high nucleic acid extractions yields.64

For fully automated applications, reactions are mostly performed in specific chambers often containing prestored primers and probes. The implementation of entire detection panels with a plurality of reaction chambers often requires geometric multiplexing, i.e. metering and aliquoting. In this context, centrifugo-pneumatic aliquoting has been used for detection of the bacteria Staphyloccocus aureus and its antibiotic resistance gene mec A, Staphylococcus warneri, Streptococcus agalactiae, Escherichia coli and Haemophilus influenza in foil disks made of cyclic olefin polymer (COP) as represented exemplary in Fig. 9.92,93,95 Czilwik et al. additionally combined the on-disk detection module with a bead based sample preparation module that provides the purified DNA in an elution chamber. Since this elution chamber is located radially outward of the PCR module, pneumatic pumping is used for radial inward transfer.95


image file: c9lc00441f-f9.tif
Fig. 9 Centrifugo-pneumatic valve used for nucleic acid analysis reproduced from Lutz et al.92 with permission from The Royal Society of Chemistry, 2010. At the start the glass capillary (A) has to be broken (B i). RPA buffer and lyophilisate are then mixed in a chamber (B ii) before the siphon channel is primed by capillary forces (B iii). The mixture then enters the aliquoting structure, where closed reaction chamber generate a pneumatic pressure allowing an exact metering of the liquid (B iv and B v).

In continuation with this work, Stumpf et al. integrated liquid reagent prestorage in stick-packs on-disk for sample-to-answer detection of influenza A H3N2 virus on a COP foil disk, processed in a LabDisk player. In this work, the sample preparation module was also linked with the detection module via pneumatic pumping that in turn was loaded via a temperature change rate actuated valve.59 It is a good example of cascaded pneumatic operations that affect each other, so that robust processing requires the optimization of design parameters. For this reason, this application is investigated in more detail in the second tutorial section of this paper.96

A prominent example of combining pneumatics with centrifugal microfluidic for nucleic acid analysis is the implementation of a nested PCR. Such nested PCRs are typically implemented for two reasons: on the one hand, the sensitivity of the subsequent geometric multiplexing is enhanced,93 on the other hand, the first PCR can handle DNA mixes with less purity than the second specific PCRs. In a centrifugal microfluidic platform, a major advantage is that the high copy numbers after the first PCR are handled in a closed chip and are not exposed to the laboratory environment which significantly reduces the risk of contamination.

The workflow as introduced by Czilwik et al. comprises a first PCR reaction inside a pressurized pneumatic chamber (Fig. 10). After the first PCR is completed, the frequency is reduced and the liquid is pumped radially inwards for further processing as described by Zehnle et al.56 In this context, the challenge of the combination of pneumatics with PCR is that the amount of gas n is increased by heating up the pneumatic chamber which can lead to comparatively high overpressures of up to 100 kPa due to evaporation. The sealing foil must be capable of withstanding such overpressure, but more importantly, a liquid column must be provided so that centrifugal pressure can compensate the pneumatic pressure. To reduce the generated overpressure, Czilwik et al.94 implemented a narrow channel as diffusion barrier for vapor, thereby limiting the amount of vapor that is produced from the processed liquid. By employing this vapor diffusion barrier (VDP), the overpressure in the closed pneumatic chamber in which the first PCR is performed could be limited to 35 kPa while the temperature was raised from 23 °C to 95 °C, compared to 80 kPA without the VDP. The biological functionality was proven in a PCR, amplifying the PAL gene region of Escherichia coli in 20 thermocycles and later within the sample to answer workflow for “Rapid and fully automated bacterial pathogen detection on a centrifugal-microfluidic LabDisk using highly sensitive nested PCR with integrated sample preparation”. Beside the vapour diffusion barrier, the microfluidic cartridge includes four additional pneumatic unit operations (Fig. 10) and is thus a prime example for the importance of pneumatic operations in centrifugal microfluidics.


image file: c9lc00441f-f10.tif
Fig. 10 Fully automated sample to answer on single microfluidic chip developed by Czilwik et al.95 with permission from The Royal Society of Chemistry, 2015. The workflow (b) includes a complete DNA extraction from serum sample (c–f), a pre-amplification (g) and thirteen real-time PCRs (j) and requires rotational frequency, magnets as well as temperature as control parameters (a). In total, five different pneumatic operations are utilized. Before the binding step, a pneumatic siphon valve needs to be primed with help of a temperature increase to transport the binding buffer into the following chamber (d). After the DNA extraction, the elution buffer is transported into the pre-amplification zone at a high frequency (g). A vapour diffusion barrier helps to reduce the generated pressure and allows to perform the pre-amplification. When reducing the frequency, centrifugo-dynamic pumping transports the liquid into the subsequent chamber (h). Temperature change rate actuated valving allows the liquid to be transported into the next structure, where pneumatic aliquoting ensures precise metering of volumes for all thirteen PCRs (i). A total number of five unit operation based on pneumatics underline the importance of pneumatics for automation of complex workflows.

Oh et al. developed a system that fully automates a colorimetric pathogen detection protocol from milk samples. Their workflow includes a silica bead based washing and elution step and five parallel loop-mediated isothermal amplifications afterwards. Pneumatic aliquoting permits to obtain precise and equal volumes for each amplification.102

4.2. Protein analysis

Proteins are biomarkers in numerous diseases. Consequently, their detection and quantification is of high importance. Protein analysis in centrifugal microfluidics is mostly performed by immunoassays.103–110 Full automation of immunoassays on centrifugal microfluidic platforms faces the challenge to sequentially release liquid reagents (i.e. sample, washing buffers, blocking buffers, secondary antibody solution) and to perform all mixing and valving steps with each buffer while other buffers are kept in their chambers. Thio et al. used their push–pull pumping approach to automate the entire fluidic workflow for an immunoassay. This includes the sequential loading of a functionalized reaction chamber with the sample fluid, washing buffer (2×), blocking buffer, again washing buffer, buffer with secondary antibody and again washing buffer.104

In order to investigate the efficiency of binding reactions in immunoassays on a centrifugal microfluidic platform, Noroozi et al. used pneumatic reciprocation mixing combined with pneumatic siphon valving (Fig. 11). A microarray with Burkholderia antigens spotted on a nitro cellulose membrane was implemented in a microfluidic disk. In a semi-automated way, the serum samples and the assay reagents were loaded manually into the disk, whereas mixing of the fluids on the microarray and valving into the waste chamber was done with the centrifugal protocol. As a result, similar signal intensities for manual and centrifugal processing could be obtained, while sample volume and time could be reduced in the centrifugal setup by one order of magnitude.111


image file: c9lc00441f-f11.tif
Fig. 11 Fluidic for a multiplexed immunoassay reproduced from Noroozi, Z. et al. (2011). A multiplexed immunoassay system based upon reciprocating centrifugal microfluidics. Review of Scientific Instruments, 82(6).111 with permission of AIP Publishing. Reagents are loaded manually in the loading chamber. The subsequent rotational frequency protocol includes mixing by reciprocation between the pressure and the upper chamber and pneumatic siphon valving.

An immunoglobulin G assay was completely automated by Miyazaki et al. on a disk covering the plasma extraction and aliquoting of whole blood. Several films are used for valving at high frequencies and a centrifugo-pneumatic siphon valve is implemented to remove plasma and washing buffer.112

Uddin et al. developed a cartridge, which combines the detection of C-reactive protein with peripheral blood mononuclear cell quantification. Whole blood is the starting material and after the blood plasma separation, a centrifugo-pneumatic siphon valve is used to allow liquid transport into the following chamber.113

Schwemmer et al. used pneumatic reciprocation mixing of the flow in a microfluidic foil disk for protein structure analysis by small-angle x-ray scattering (SAXS). The disk featured the aliquoting of a protein solution and two further reagents to generate sub-μl-aliquots with different protein concentrations. Since mixing of such small volumes is particularly challenging and difficult to achieve by shake-mode, reciprocation mixing was implemented in this application.114

Zhao et al. demonstrated a fully automated CRP Immunoassay based on centrifugo-pneumatic particle handling. All reagents were pre-stored on the disk. Sequential supply of two washing steps and supply of substrate was realized by pneumatic pumping including a timer for timed release. Eventually, the reaction mix was transported via pneumatic valving to a detection chamber with a stopping solution for termination of the enzyme substrate reaction and subsequent read-out.103

4.3. Clinical chemistry

Assay automation is the major goal in centrifugal microfluidics and many applications aim towards point-of-care analysis. Hence, clinical chemistry and in particular blood analysis are of highest relevance for centrifugal microfluidics.90,109,115–122

In particular, for blood plasma separation, which is an essential unit operation for many applications, the combination of centrifugal and pneumatic forces provides unique advantages. Obviously, plasma can be separated by centrifugation. Using pneumatic pressure for valving allows to remove the plasma under constant rotation, which avoids resuspension of the red blood cells and consequently enables very good separation efficiency in combination with a high yield. A guideline on how such blood plasma separation based on pneumatic valving can be optimized using network simulations has been presented by Zehnle et al.86

Godino et al. employed a cascade of pneumatic operations to automate colorimetric nitrite and nitrate detection from whole blood in a microfluidic disk. By cascading pneumatic siphon valves, first, 40 μl of plasma was extracted from 100 μl of whole blood, then, the extracted plasma was mixed with 60 μl of an enzyme solution and finally, the plasma/enzyme solution was mixed with 100 μl of colorimetric reagents. A spectrophotometer was used to measure the absorbance of the product in order to determine the nitrite or nitrate concentration, which could be performed for the entire healthy human range (Fig. 12).115


image file: c9lc00441f-f12.tif
Fig. 12 Automated NO colorimetric detection reproduced from Godino et al.115 with permission from The Royal Society of Chemistry, 2013. At the start, blood and enzyme are pipetted in two radially inward positioned chambers. A blood plasma separation takes place at a high rotational frequency (A) and only the blood plasma is transported via a pneumatic valving siphon at a lower frequency in the subsequent chamber, where it is metered by the disk design (B). After all reagents are incubated in a chamber at a high frequency (C), a pneumatic valving siphon empties the liquids into the colorimetric reaction chamber (D).

While the ability to cascade single unit operations is significantly boosted by pneumatics, the unique strength of centrifugal microfluidics in general is the parallelization by means of aliquoting operations. Both, the parallelization and the cascading of the single assay steps was used by Nwankire et al.90 in an assay panel to test whole blood samples for the liver function relevant parameters total bilirubin, albumin, alkaline phosphatase, γ-glutamyltransferase and direct bilirubin. In short, plasma separation from whole blood is cascaded with pneumatic plasma aliquoting using the dissolvable film valves. Downstream of the aliquoting, the plasma aliquots are collected in reaction chambers that contain assay specific reagents, already. Depending on the liver parameter tested, parallel fluidic paths are used to add further reagents into the reaction chambers via dissolvable film valves.90 Kong and Salin used their platform based on the external air stream that is directed on openings in the centrifugal disk to implement the parallel and cascaded pumping of aqueous liquids. In this work, an assay for detection of aqueous sulfide was automated. As in the previous applications, detection was based on a colorimetric assay with subsequent spectrophotometric measurement.116

Krauss et al. implemented radially inward pumping for an automation of a colorimetric drug detection by mixing prestored sodium bicarbonate with sulphuric acid to generate pneumatic pressure.123

5. Introduction to tutorial section

The importance of pneumatic operations in centrifugal microfluidics is evident considering the number of unit operations and applications described in the previous chapters. This tutorial section addresses the fluidic engineer who wants to employ pneumatic in combination with centrifugal forces for the design of robust unit operations. Within two examples, physical effects relevant for the design are discussed. The first example addresses a comparatively simple layout strategy based on analytical equations for a pneumatic valve. The second example discusses a more sophisticated layout strategy using network simulations to design cascaded pneumatic operations. Within both examples, challenges and risks are discussed in detail.

To understand the limitations of the design of pneumatic operations we start by briefly reflecting on the boundary conditions of fluidic design in general. The starting point of any automation consideration is usually the assay. Depending on the workflow and the complexity of the assay, suitable unit operations need to be chosen for automation. Limitations for pneumatic operations mainly occur on two levels: the processing device and the manufacturing technique. If the assay is rather simple and designed for low-cost applications, the processing device must usually also be low-cost, limiting its functionality (e.g. no temperature control) and reducing available unit operations to intrinsic pressure generation. A complex assay workflow in turn requires high integration densities and space on the microfluidic chip may be limited. Processing devices with additional means for pneumatic actuation are often more suitable for such an automation. Both scenarios, one where no additional means are available and one with temperature as a second independent actuation parameter, are discussed in Tutorial I and II, respectively.

Cost considerations are usually also the reason for choosing specific manufacturing techniques that are suitable for mass production of single use cartridges such as injection moulding or thermoforming. Tolerances are inherent and result in differences between the designed with the manufactured geometry. In both tutorials, a robustness analysis is performed to underline the importance of tolerances.

Even though in the two tutorial examples we make use of intrinsically generated pneumatic pressure, we would like to emphasize that the design guideline and the discussed pneumatic effects are largely independent from how the pneumatic actuation is supplied. If a simple valve with no accurate timing is required, the pneumatic pressure just needs to be sufficiently high to trigger the valve. If, however, accurate flow control, precise metering or exact timing is needed, additional effects such as capacitances caused by flexible cartridge materials, the influence of vapour pressure or the influence of manufacturing tolerances need to be taken into account. The combination of these effects can be complex, and we suggest to employ network simulation to access the interplay of the different phenomena which is detailed in the second tutorial.

6. Tutorial I: design guidelines for the implementation of a centrifugo-pneumatic siphon valve

This first tutorial examines a simple and robust unit operation, which can be designed using analytical methods only. The principle was first described by Gorkin et al.78 The valve opens at a threshold frequency fth at which the equilibrium liquid level in the siphon is at the crest point. When operating the microfluidic system above this frequency, the valve remains closed, independent of acceleration or deceleration rates. Only if operated below the threshold frequency, the siphon primes and liquid is transported into the collection chamber. Thus, this valve is a low-pass valve with respect to rotational frequency.

6.1. Working principle

The five phases of operation are depicted in Fig. 13.
image file: c9lc00441f-f13.tif
Fig. 13 Fluidic working principle of a siphon valve triggered by the release of pneumatic energy as first introduced by Gorkin et al.78 Subfigures A–E show all relevant fluidic steps including the important parameters: initial phase (A), loading phase (B), compression phase (C), priming phase (D) and transfer phase (E). The first scheme on the left hand side includes the description of all elements and defines all geometric parameters. All dynamic parameters required for the calculation are presented in the picture of phase B. On the bottom of the figure, a schematic rotational frequency protocol (blue line) is presented. The compression frequency fcomp, the threshold frequency fth, and the transfer frequency ftrans are marked by horizontal dashed line. The threshold frequency is defined by the equilibrium liquid level in the siphon at the crest point.

A-Initial state: the entire sample fluid is in the reservoir while the microfluidic platform is at rest.

B-Loading phase: at increasing rotational frequency, the sample fluid is transferred from the reservoir into the pneumatic chamber. The rotational frequency exceeds the threshold frequency fth.

C-Compression phase: the compression frequency fcomp > fth is reached. After a certain time, the liquid levels are in equilibrium.

D-Priming phase: the rotational frequency is decreased to smaller than fth. At fth, the liquid level in the siphon reaches the crest. Subsequently, the siphon is primed.

E-Transfer phase: the sample fluid is transferred from the pneumatic chamber and the reservoir to the collection chamber.

6.2. Design guidelines

In a first step, the geometric boundary conditions must be specified, starting with the definition of the radial positions of the reservoir and collection chamber, with the pneumatic chamber located radially in between and the required volumes for the reservoir and collection chambers. These constraints, as mentioned in the previous section, usually result from the implementation of the entire assay workflow in a centrifugal platform with pre-defined geometric constraints. The chamber geometry is additionally influenced by the fabrication technology that determines e.g. maximum chamber depths and aspect ratios as well as minimum draft angles.

In a second step, a channel diameter for the siphon must be chosen. On the one hand, it should be as large as possible to reduce unwanted capillary forces; on the other hand, it should be small enough to ensure that the meniscus remains stable while the liquid moves through the siphon during priming. Typically, numerical values range between 100–500 μm in both channel width and depth.

In a third step, the siphon crest position has to be defined. A good starting point is the radial position of the outlet of the reservoir. If the crest is located further radially inwards, priming of the siphon may not be possible. If located further radially outwards, one would have to ensure that the siphon is not primed during the loading phase. For fine-tuning of the crest position, capillary forces need to be considered in both cases.

In a fourth step, the rotational frequencies for the compression phase fcomp, the threshold frequency fth and the transfer frequency ftrans must be defined. At low fth for example, capillary forces become more dominant and may hinder siphon priming. Higher fth in turn bear the risk of meniscus instability during siphon priming. Typical numerical values for fth range between 15–50 Hz.

Once all geometric parameters, liquid properties and the operating frequencies are defined, the pressure balance

 
Δpcent + Δppneu + Δpcap = 0(4)
can be established for siphon priming (Fig. 13D) where Δpcent is the centrifugal pressure difference between the siphon crest and the fill level in the pneumatic chamber, Δppneu describes the overpressure in the pneumatic chamber and Δpcap the capillary pressure difference in the siphon. The required volume of the pneumatic chamber, V0, can be described by
 
V0 = Vliq(1 − p0/(2π2fth2ρ(rcrest2rp,min2) + Δpcap)).(5)

Typical values for this scenario are rcrest = 20 mm, rp,min = 35 mm with a selected threshold frequency of fth = 30 Hz. Using 100 μl of water (ρ ≈ 1 g cm−3 at room temperature) at sea level (p0 ≈ 1013 mbar), we obtain V0 ≈ 791 μl. In this calculation, the capillary pressure is neglected (Δpcap = 0 Pa), which is a good assumption, as in this tutorial example, the computed V0 would differ by less than ±5% for the entire range of contact angles 0° < θ < 180° in a siphon with a cross section of 250 μm × 250 μm.

In a fifth step, the system has to be checked for premature siphon priming by verifying the fill level in the siphon during the loading phase. Premature priming in this context means that the siphon is primed during the filling process of the pneumatic chamber. This has to be considered because at the start of centrifugation, the system accelerates and it takes time until the equilibrium frequency that safely avoids priming is reached. Hence, acceleration must be sufficiently fast. Alternatively, at a given acceleration, the pressure that builds up in the pneumatic chamber must be sufficiently low so that the liquid level in the siphon does not reach the crest point.

The time dependent fill levels in the pneumatic chamber rp (t) and in the reservoir rr (t) are described by the following equations

 
rp(t) = rp0Vliq(t)/(ap,dap,w),(6)
 
rr(t) = rr0 − (Vliq(t = 0) − Vliq(t)/(ar,dar,w))(7)
where ap,d, ap,w, ar,d and ar,w are the depth and width of the pneumatic and reservoir chamber, respectively, rp0 and rr0 are the initial fill levels in both chambers and Vliq is the liquid volume in the pneumatic chamber. The fill level in the siphon rs can be determined by solving eqn (4) considering the gas pressure in the pneumatic chamber and the centrifugal pressure induced by the fill level difference between siphon channel and pneumatic chamber. It is thus given by
 
image file: c9lc00441f-t2.tif(8)

The time dependent liquid volume in the pneumatic chamber can be determined by the pressure balance along the inlet channel

 
Δpcent + Δppneu = Δpvisc(9)

The pressure difference between reservoir chamber and pneumatic chamber results in flow into the pneumatic chamber which causes a viscous pressure drop along the channel. Assuming laminar flow with a Poiseuille profile, the pressure balance can be written as

 
1/2ρ(2πf(t))2(rp2rr2) − p0(1/(1 − Vliq(t)/V0) − 1) = R[V with combining dot above]liq(t).(10)

The fluidic resistance R of the inlet channel for a channel with a square cross section can be calculated by

 
R = 28.4ηL/ac4(11)
where L is the length of the channel, η the viscosity of the fluid and ac the width and depth of the channel. The factor in the fluidic resistance equation is a function of channel geometry and only valid for a square channel. Rotational frequency is assumed to increase linearly with help of a constant acceleration coefficient ca by
 
f = cat.(12)

The linear differential equation can easily be solved for the fill levels in the relevant elements. Typical values for the calculation are ap,d = ap,w = ar,d = ar,w = 3 mm, rp0 = 45 mm, rr0 = 10 mm, η = 1 mPa s, L = 45 mm and ca = 5 Hz s−1 resulting in the graphs depicted in Fig. 14. At the start, the siphon channel is quickly filled and with increasing frequency, the volume flow into the pneumatic chamber rises. In order to avoid premature siphon priming, one needs to track the fill level in the siphon channel, which in the studied configuration always remains further radially outwards compared to the radial position of the siphon crest.


image file: c9lc00441f-f14.tif
Fig. 14 Calculated radial position of the fill levels in the relevant elements. Blue lines indicate the fill levels of the designed unit operation. Red lines define a robustness corridor originating from geometrical tolerances of up to 10%. These tolerances lead to variation in the pneumatic chamber volume from 712 to 870 μl and channel widths and depths of 225 to 275 μm. Maximal channel width is combined with minimal pneumatic chamber volume describing the worst-case scenario. This case is depicted by the dashed line. The dotted lines present the other case of maximal pneumatic chamber volume and minimal channel width. Left: The radial position of the fill level in the pneumatic chamber decreases at the start, as the liquid level increases in the pneumatic chamber. Middle: The radial position of the fill level in the reservoir increases until the chamber is empty. Right: The radial position of the fill level in the siphon channel decreases rapidly at the start and the fluidic resistance of the channel slows the subsequent filling procedure. The minimal radial position of the fill level in the siphon is rs ≈ 24 mm and is thus sufficiently large for a robust microfluidic system.

In a sixth step, the emptying of reservoir and pneumatic chamber has to be examined to ensure a defined volume transfer. In this context, it is important to consider from which fluidic path air is drawn into the siphon first, which interrupts the transfer to the collection chamber. If air is drawn in from the pneumatic chamber, there may be liquid remaining in the reservoir that is not transferred. Alternatively, if air is drawn in from the inlet reservoir, the remaining liquid in the pneumatic chamber needs to be taken into account. We designed the structure in this tutorial so that the air enters into the siphon channel from the reservoir by adding an inverted siphon next to the pneumatic chamber. Pressure is thus applied on the pneumatic chamber, as long as the crest position of the inverted siphon rh is positioned further radially outward than the radial position of the siphon outlet into the collection chamber. In order to obtain a robust system, it is important to verify that the centrifugal pressure of this liquid column is greater than the vapour pressure in the pneumatic chamber. The liquid volume remaining in the inverted siphon after transfer is calculated to be approximately 1 μl and is thus negligible in comparison to the total volume transferred from the reservoir to the collection chamber. If rh = 55 mm, r0 = 50 mm and fcoll = 20 Hz, a maximal centrifugal pressure of 42 mbar is working against a vapour pressure of 12 mbar when assuming a relative humidity change from 60% (ambient condition) to 100%.

Additionally, the pressure at the siphon crest should be examined during the transfer phase. Underpressure can result in outgassing, which is a risk for flow separation at the siphon crest. As long as the siphon crest remains below the inlet chamber, flow separation due to outgassing of the liquid can only occur at a state, when most of the liquid has already been transported.

Finally, a robustness analysis is performed in order to avoid problems based on manufacturing tolerances, liquid property variations or varying pipetting volumes. Commonly, manufacturing tolerances should lead to geometry variations below ±10%. Here, we discuss ±10% as a worst case for which the channel dimensions result in variation from 225 μm to 275 μm and pneumatic chamber volumes from 712 to 870 μl. The only worst-case scenario that needs to be examined in this study is the largest channel dimensions in combination with the smallest pneumatic volume, because this could lead to premature siphon priming. With the given values, the minimal radial position of the liquid meniscus in the siphon during pneumatic chamber loading is rs ≈ 24 mm and thus, a siphon crest on the radius of rcrest = 20 mm is sufficient for a robust design. The contact angle θ can be varied between 0° and 180° which does not lead to significant capillary pressures as the maximal capillary pressure for 225 μm is 13 mbar. The ambient pressure can be evaluated from 900 mbar to 1013 mbar corresponding to the pressure at 1000 m above sea level and the pressure at sea level, respectively. The microfluidic system is robust against these changes because only higher pressures could lead to premature siphon priming and the dimensioning is done with the highest realistic pressure. Density changes arising from this pressure difference can be neglected when using fluids resembling to water. Liquid volume variations of ±5% do not lead to premature siphon priming and do not influence the pumping efficiency.

6.3. Discussion

In general, the simple design and dimensioning of this concept is a convincing benefit. The demands on the processing device are very low and the valve can be applied in standard laboratory centrifuges. Drawback of this design approach is the required real estate, as all liquid volume needs to be stored in the pneumatic chamber. Real-estate saving alternatives are siphon priming principles utilize dynamic frequency changes. Dynamic priming concepts are based on a flow divider principle of the inlet channel and the siphon. As the frequency is reduced to release pneumatic energy, the design must ensure that at a specific deceleration rate, a critical filling of the siphon is reached for priming. In equilibrium, most of the liquid remains in the inlet chamber and the pneumatic chamber needs to accommodate only a small amount of liquid, which is sufficient to prime the siphon. To avoid premature priming, the siphon crest has to be positioned more radially inward than the inlet chamber. Since the total volume of the pneumatic chamber can be reduced significantly, a higher degree of integration can be achieved. A detailed description of the different pneumatic siphon priming concepts is discussed by Zehnle et al.79 The saving of real estate comes along with a little more effort for calculations. The use of calculation tools, such as network simulation, is recommended for dimensioning. Further details on using network simulations for the design of centrifugal microfluidic disks are discussed by Schwarz et al.88 and in Tutorial II.

Alternatively, the use of external pressure for siphon priming can also save real-estate on the disk and simplifies the design as detailed by Clime et al.63 with the downside of a more complex processing device to supply the pneumatic energy.

Another important aspect is that the siphon valve discussed in the first tutorial is dimensioned without considering any interplay with other unit operations. However, unit operations are often a part of a larger automation protocol and it is thus important to consider their functionality in a larger context. In principle, it is beneficial to decouple the unit operations as much as possible and to implement such independent unit operations as discussed in Tutorial I to keep the complexity as low as possible. In some cases and in particular if a high degree of integration is required, these simple design approaches are not sufficient. For that reason, in the next tutorial, we investigate cascaded pneumatic operations that highly depend on each other and we discuss microfluidic design enabled by simulations.

7. Tutorial II: design guidelines for the implementation of combined pneumatic temperature change actuated valving and pumping

For this tutorial, we explain in detail the dimensioning of a part of the fluidics of a LabDisk for detection of respiratory pathogens96 and present possible improvement steps regarding the protocol and design. The examined LabDisk represented in Fig. 15 only requires one manual handling step at the start and provides eight different reaction cavities for pathogen detection via PCR. Main differences to the previous example are the serial operation of two pneumatic operations that highly depend on each other, namely temperature change rate actuated valving59 with subsequent pneumatic pumping56 and the use of temperature beside the frequency as additional means.
image file: c9lc00441f-f15.tif
Fig. 15 Overview of all fluidic elements on the LabDisk for detection of respiratory pathogens.96 The first step is a bead-based sample preparation including lysis, binding, washing (twice) and elution steps. All required fluidic elements are encircled by a green line. For the pathogen detection, the eluate has to be transported to the PCR region, which is marked by a dashed red line. Two pneumatic operations are used for that transfer: temperature change rate actuated valving and subsequent pneumatic pumping. The required structures for these operations are encircled with a dotted blue line. In this tutorial, dimensioning of the blue structure is discussed, which includes the following main elements: pneumatic chamber 1 (vertical lines), pneumatic chamber 2 (horizontal lines), reservoir (points) and collection chamber (diagonal lines) The fluidic operation is illustrated in Fig. 16.

image file: c9lc00441f-f16.tif
Fig. 16 Fluidic working principle of the two cascaded pneumatic operations, namely temperature change rate actuated valving and pneumatic pumping, used for transferring the eluate from the sample preparation module to the detection module of the examined LabDisk.96 In the top, all relevant elements of the transfer structure are depicted and the five operation states are presented. The black rectangles mark fluidic resistances relevant for the layout. Valving step (A–C): initial phase (A), preparation phase (B), priming phase (C). Pneumatic pumping step (D and E): loading phase (D) and transfer phase (E). In the bottom, the frequency (blue) and temperature (red) protocols are illustrated. The two variants of the temperature protocols in phase D and E describe pneumatic pumping with and without additional thermal induced pressure increase during the loading phase.

7.1. Working principle

The fluidic concept depicted in Fig. 16 is divided in five phases to illustrate the two combined operations: temperature change rate actuated valving (A–C) and pneumatic pumping (C and D):

A-Initial state: the entire sample fluid is in the reservoir while the microfluidic LabDisk is at rest.

B-Preparation phase: the rotation frequency is increased to 50 Hz. Then, the temperature is changed from 30 to 60 °C. A temporary overpressure builds up in the downstream part of the LabDisk and the gas flows through the venting channel until atmospheric pressure is reached.

C-Priming phase: the frequency is lowered to 5 Hz and subsequently, the temperature is decreased rapidly to 30 °C. The quick temperature reduction induces an underpressure in the downstream part of the LabDisk which primes the siphon. A capillary restriction at the inlet channel of the pumping structure stops the flow of liquid into the pneumatic chambers 1 and 2 during thermal actuation. The liquid is transferred at 30 °C as the frequency increases in the following loading phase.

D-Loading phase: when 30 °C temperature is reached, the frequency is increased to 50 Hz. The liquid fills the pneumatic chamber 1 until equilibrium is reached. No liquid enters pneumatic chamber 2. In the first case of this Tutorial II, the temperature is held at room temperature, whereas the second case includes a temperature increase to 60 °C after loading the pneumatic chamber 1 and 2. The temperature rise increases the overpressure in the pneumatic chambers 1 and 2, which improves the pumping efficiency.

E-Transfer phase: the frequency is reduced to 5 Hz at a deceleration of 30 Hz s−1 and the liquid is pumped inwards into the collection chamber. The restriction in the inlet channel of the pumping structure comprises a high fluidic resistance ensuring that only very little volume is transferred back into the reservoir.

A table with the detailed protocol steps can be found in the ESI. Assuming that important parameters such as the radial pumping distance and the volume of liquids are fixed by specifications, robust performance of the cascaded operations depends mainly on three parameters:

1) Fluidic resistance of the venting channel.

2) Fluidic resistance of the inlet channel of the pumping structure.

3) Total volume of the collection chamber.

In order to understand the influence of these parameters, it is important to discuss their impact on each unit operation separately.

7.2. Temperature change rate actuated valving

A temperature change rate actuated valve (Fig. 16A–C) uses thermally induced underpressure by cooling down a heated air volume. In this example, the relevant air volume is given by the collection chamber including the aliquoting structure and its adjacent chambers, which are marked by diagonal lines in Fig. 15. These chambers are only connected to the environment by the venting channel with a high fluidic resistance.

Global cooling of the air can lead to two different events depending on the venting channel. First, slow cooling or high centrifugal counterpressures allows for a sufficient amount of air to flow through the venting channel and the siphon is not primed. Secondly, when rapidly cooling down at low centrifugal counterpressure, the thermally induced underpressure builds up temporarily because viscous dissipation of the air flow slows down pressure compensation and this underpressure sucks the liquid over the siphon. Hence, the higher the resistance of the venting channel, the less dependent is the valving procedure on cooling rates.

For the valving step, the fluidic resistance of the inlet channel of the pumping structure has to be considered only if it is very large in comparison to the resistance of the venting channel because then it may hinder temperature change rate actuated valving. The viscous dissipation of the displacement of air present in the siphon through the inlet channel of the pumping structure may cause a pressure drop that compensates the temperature change rate induced underpressure. Consequently, the siphon would not be primed and the temperature change rate actuated valve would not be functional.

The volume of the collection chamber should be as large as possible. This helps to obtain a robust design in two ways. First, the generated underpressure in the collection chamber leads to an air flow from the environment into the collection chamber. The larger the volume of the collection chamber, the more air volume needs to be transferred into the chamber until equilibrium is reached. Consequently, a higher amount of air has to be transported through the venting channel and the underpressure is applied for a longer time on the fluid. Secondly, when liquid is transferred in the direction of the collection chamber, it compresses the air volume, which reduces the underpressure. The latter can be neglected if the volume transported during siphon priming is small compared to the total gas volume of the collection chamber.

7.3. Pneumatic pumping

The principle of pneumatic pumping is based on the ratio between the fluidic resistances starting from the T-junction in direction of the reservoir and in direction of the collection chamber.

When working with high venting resistances to improve robustness of valving, during pumping, the collection chamber behaves at small time scales like a pneumatic chamber. The critical part is that the volume flow into the collection chamber is not only defined by the viscous resistance of the outlet channel of the pumping structure connecting the collection with the pneumatic chamber, but also by the overpressure generated due to gas compression in the collection chamber. Hence, for pumping, the fluidic resistance of the venting channel should be as small as possible to allow the air to leave the collection chamber quickly so that only a minor counterpressure builds up.

Opposite to the resistance of the venting channel, the resistance of the inlet channel of the pumping structure should be as large as possible. The smaller the resistance of the inlet channel of the pumping structure, the more liquid is transferred back into the inlet chamber and is thus not available for the consecutive PCR.

As for the valving unit operation, the air volume of the collection chamber should be as large as possible in order to reduce the maximal counterpressure generated during pneumatic pumping.

7.4. Cascaded operation

When now comparing both unit operations, temperature change rate actuated valving and pneumatic pumping, similar and different demands can be determined and need to be considered. Both unit operations require a large collection chamber volume and this parameter does not lead to any contradictions. The volume of the collection chamber is limited by the available real estate on the disk. The fluidic resistances of the pumping and venting channels however need to be dimensioned carefully. High fluidic resistance of the inlet channel of the pumping structure allows for highly efficient liquid transfer, but could ultimately lead to a non-functional temperature change rate actuated valve. An increase of the resistance of the inlet channel may also require an increase of the resistance of the venting channel in order to keep the temperature change rate actuated valve functional. As often in microfluidics, it is the task of the designer to determine a convincing combination of real estate requirements and robust design.

7.5. Simulation supported design

The presented system is too complex to be dimensioned with analytical equations leading to the necessity for more sophisticated calculation techniques. Network simulations88 allow for modelling fluidic networks with a much higher degree of complexity than analytical approaches at a reduced effort. These network simulations are similar to electrical networks and each fluidic element, such as channels and chambers, is represented by a lumped model with a specific transfer function defining the relation between through and across variable. In case of microfluidic networks, the across variable is a pressure difference and the through variable is a volume flow. The transfer of the fluidic design into a fluidic network model is depicted in Fig. 17.
image file: c9lc00441f-f17.tif
Fig. 17 2D design of transfer structure (left) and fluidic network model of the LabDisk (right). The system includes radial (RC) and isoradial (IC) channels, vented chambers (VC), pneumatic chambers (PC), two-port chambers (TC) and a T-junction (TJ). All elements are connected (lines) and dimensions are specified in the ESI.

Parameters of all elements are defined in the ESI. Note that for simplicity, the whole aliquoting structure including the adjacent chambers is replaced by a single vented two-port chamber. It is important to mention that capillary forces are not considered in this simulation, but should not be forgotten. In the examined system, capillary forces could be of importance during the temperature change rate actuated valving by generating a counterpressure that prevents the priming of the siphon. However, the width and depth of the channel of the siphon are rather large with 600 μm and result in capillary pressures in the order of ∼1 mbar. For robust temperature change rate actuated valves, the generated underpressure should be considerably larger.

The physical principles and dependencies explained in the previous sections need to be implemented into such a model. Table 1 presents all relevant elements and the considered physical effects. The following discussion focuses on the pneumatic pressure and how to include all relevant influence factors for this specific design. Further effects are discussed by Schwarz et al.88 According to eqn (2) and Table 1, two partial pressures have to be examined in detail:

Table 1 Relevant physical effects considered in different network elements. More details on the implementation are depicted by Schwarz et al.88
Model Considered effects
Vented chamber • Centrifugal pressure• Viscous dissipation of the air flow
Pneumatic chamber • Total pneumatic pressure resulting from partial pressures according to ○ Change of temperature, substance or volume

 ○ Vapour pressure depending on temperature and relative humidity

Two-port chamber • Centrifugal pressure• Pneumatic pressure with partial pressures of

 ○ Change of temperature, substance or volume

 ○ Vapour pressure depending on temperature and relative humidity

• Viscous dissipation of the air flow

Radial channel • Centrifugal pressure• Inertial pressure

• Viscous dissipation

Isoradial channel • Euler pressure• Inertial pressure

• Viscous dissipation

T-junction • Connection of three fluidic elements, no physical effect is considered


1) Partial pressure of evaporated liquid in air.

2) Partial pressure of air (ideal gas).

7.6. Partial pressure of evaporated liquid

The pneumatic chamber is split into two chambers called pneumatic chamber 1 and 2 which are connected by a small channel (Fig. 15). Only the pneumatic chamber 1 is filled with liquid during the pneumatic operation, whereas the pneumatic chamber 2 always remains filled with air. In general, air in microfluidic systems is immediately saturated when liquid enters the relevant chamber due to the small volume to surface ratio. When connecting chambers by narrow channels, the time to reach saturation increases significantly.94 We assume that only little vapour flows from the filled pneumatic chamber 1 into the empty pneumatic chamber 2 due to the channel in between working as a diffusion barrier. The total amount of vapour in the pneumatic chamber 2 thus remains almost constant. This results in a constant water vapour partial pressure during operation. According to eqn (2), it can be stated that
 
psat = ϕsatpvap(T) = ϕ0pvap,0 = const.,(13)
where φ0 and pvap,0 are the relative humidity and the vapour pressure at room temperature. When simulating the case of constant temperature, this can be modelled by simply keeping the relative humidity constant at 60%, which represents the humidity level of the air. In case of transfer at elevated temperature, the saturation pressure increases significantly whereas the relative humidity decreases due to a higher possible liquid content in the air. Due to the diffusion barrier, only little additional vapour is generated and we assume constant partial pressure of the vapour. At the start, the relative humidity is assumed to be 60% and the saturated vapour pressure is 42.5 mbar at room temperature resulting in a vapour pressure of 25.5 mbar. When now increasing the temperature to 60 °C, the saturated vapour pressure increases to 199.3 mbar, but assuming a constant amount of vapour, the relative humidity has to decrease to 13%. In the considered configuration, the additional pressure increase when working with temperatures only occurs due to thermal expansion and not due to evaporation.

7.7. Partial pressure of ideal gas

After the loading phase of pneumatic pumping is completed, the partial pressure after compression p2 in pneumatic chamber 2 is given by
 
p2 = p1V1T2/(T1(V1Vl)),(14)
if we assume rigid chambers. Here, p1 is the pressure at the start of the compression procedure, V1 the starting air volume in the pneumatic chamber and Vl the volume of liquid that entered the pneumatic chamber. However, thin foils are susceptible to deformation at relatively low pressures. Consequently, the pressure calculation has to be changed to correspond to reality by adding a volume Vd that represents the foil deformation volume.
 
p2 = p1V1T2/(T1(V1Vl + Vd))(15)

The additional volume results in a lower pressure and thus allows more liquid to enter the pneumatic chamber. In this tutorial, the examined LabDisk consists of a structured foil made of cyclic-olefin polymer (COP) and an adhesive composite sealing foil (polypropylene and pressure sensitive adhesive) with a total thickness of 100 μm (50 μm polypropylene, 50 μm pressure sensitive adhesive). All details of the manufacturing process are described by Stumpf et al.96

The small thickness of the polypropylene layer leads to significant deformation even at low pressures and consequently, foil deformation has to be taken into account. FEM-simulations are performed in order to obtain realistic values for the volume change due to deformation, which can be found in the ESI. The total volume change due to deformation depends on the pressure inside the examined chamber and the material properties of the foil. If different temperatures occur during processing, two additional effects need to be considered. First, temperature increase leads to a rising pressure and thus a stronger foil deformation. Secondly, material properties often depend on temperature and for polypropylene (PP), Young's modulus decreases with higher temperatures.124–126 Therefore, two FEM simulations have to be executed. The first simulation covers the material properties at room temperature and the pressure level originating from the compressed volume and vapour pressure only. The second simulation considers material properties at elevated temperatures and higher pressure levels due to the additional pressure increase by temperature change. At room temperature, for a total volume of the pneumatic chamber of 402 μl, the deformation volume is 18.8 μl at a pressure of 278 mbar. At 60 °C, the foil deformation leads to a volume change of 23.9 μl at a pressure of 303 mbar. The pressure values were determined in the experiments described in the next section.

Besides foil deformation, it is also important to consider the relaxation process of the foil. The examined PP-foil shows viscoelastic behaviour resulting in a time dependent relaxation process. It was observed experimentally (see ESI) that the relaxation takes longer than the pumping process and it is assumed that no energy of the foil deformation can thus be recovered for pumping. In the simulation, the compressing of the air is delayed until the liquid volume in the pneumatic chamber exceeds Vd. Influence of the partial pressure of ideal gas can thus be approximated similar to plastic deformation by the following equation:

 
image file: c9lc00441f-t3.tif(16)

Notice that the dynamic filling procedure of the pneumatic chamber is not correctly represented, as the deformation volume is kept constant in simulation, but changes continuously with increasing pressure in reality. Important for the pneumatic operation is the pressure when all liquid is transported to the pneumatic chamber.

7.8. Experimental and simulation results

For the experiments, every protocol was performed three times in a prototype LabDisk player (Qiagen Lake Constance GmbH, Germany) with 120 μl of DI water as liquid. All transferred volumes were determined by evaluating the fill levels in the aliquoting structure with help of a stroboscopic image acquisition system by Biofluidix GmbH, Germany. The results including the standard deviation of the experiments are presented in Table 2. Numerical and experimental data are in good agreement. The pumping efficiency can be significantly improved by increasing the temperature of the system. However, it is important to remember that not all biological liquids (in other potential applications) are resistant to heat and that the maximal applicable temperature is defined by the disk materials as well as by the used reagents.
Table 2 Numerical and experimental volume in aliquoting structure. Standard deviation and average are based on three experiments. Simulation considers the discussed effects, namely the low saturation pressure and foil deformation. Further details on the simulation are presented in the ESI
Without temperature increase With temperature increase
Experiment 71.3 ± 1.3 μl 100.4 ± 2.1 μl
Simulation 69.4 μl 104.9 μl
Relative error 2.7% 4.5%


7.9. Design guidelines

The network simulation tool allows for development of robust cascaded pneumatic operations. As discussed previously, the collection chamber volume has to be as large as possible. For this study, we assume that there is no more real estate left and the collection chamber volume is already as large as possible. Hence, for optimizing the system, two parameters have to be considered: the fluidic resistances of the venting and the inlet channel of the pumping structure. In order to simplify required design changes, channel lengths are kept constant and only width and depth of the channels are varied. To simplify further for this tutorial, we keep the resistance of the inlet channel of the pumping structure fixed and evaluate only the influence of the venting channel on the pumping efficiency (Fig. 18). Two boundaries have to be considered to understand the influence of this resistor. First, if the venting resistance is very large, the collection chamber works as a pneumatic chamber and liquid entering the collection chamber generates a pneumatic counterpressure. The pumping efficiency would thus be very low. Secondly, if there is no fluidic resistance at all, the collection chamber remains at atmospheric pressure during liquid transfer. The pumping efficiency would be quite high, but the temperature change rate actuated valving would not work. It is now important to design the disk in a way that disturbing parameters, such as manufacturing tolerances, do not influence the total performance of the disks.
image file: c9lc00441f-f18.tif
Fig. 18 Pumping efficiency in dependence of venting channel dimension. The red colored line depicts the efficiency of the temperature supported step and the blue line presents the results without additional heating during loading. Dimensions of the venting channel with square cross section are given by w. The pumping efficiency strongly depends on the dimensions and thus the fluidic resistance. On the one hand, the venting resistance must be low to achieve sufficiently high pumping efficiencies to transport at least 80 μl of liquid to the aliquoting structure for the following PCR. On the other hand, the venting resistance must be sufficiently high to still allow temperature change rate actuated siphon priming. For very small dimensions of the venting channel, the pumping efficiency of the temperature supported pneumatic pumping is lower than for the pumping process at room temperature. Notice that the frequency and temperature protocol remain unchanged. Additionally, efficiency improvements can also be obtained by increasing the deceleration rate or increasing the frequency.

With a channel width and depth of 100 μm, tolerances from manufacturing of about 10% do not lead to a relevant drop in pumping efficiency as illustrated in Fig. 18, if the loading phase is supported by temperature. If the venting resistance was much higher with a channel dimension for example of about 45 μm in width and depth, the system would be much more susceptible to tolerances. An imprecision of 5 μm and a consequent change of the channel width from 45 to 40 μm would already result in a pumping efficiency drop from 87.5% to 73.5%.

7.10. Discussion

The second tutorial demonstrates that even cascaded pneumatic operations can be modelled with available numerical tools. However, it is important to consider all effects, such as the design of pneumatic chambers as single or split elements or the manufacturing technique of the microfluidic disk. The layout of the cascaded operation may seem quite complex. However, if the relative influence of the different centrifugal microfluidic phenomena are adequately considered, robust networks can be designed with a large degree of freedom. The network based simulations allow for a fast assessment and quantification of the different influence parameters, so that design of even complex centrifugal networks becomes fast and simple. Of course it would be beneficial to reduce complexity and this should be done wherever possible. One easy method, for example, would be to avoid volume variations due to deformation of the foil by changing the manufacturing process of the microfluidic chips. Thicker foils are an attractive option but then, in particular for the considered application, one would have to evaluate if such thicker foils are compatible to thermocycling for the PCR application, as the desired fast heat transfer is slowed down.

In summary, we would encourage to use cascaded operations in order to realize highly integrated fully automated centrifugal automation. The assessment of all relevant effects including a network simulation set-up is from our point of view worth the effort because employing pneumatics is a key element to provide highly integrated robust and cost efficient automation with centrifugal microfluidics.

8. Conclusions

Pneumatic operations in centrifugal microfluidics allow for automation of laboratory processes in a wide range of applications. Pneumatic forces provide large propelling pressures that are of the same magnitude as centrifugal forces and typically a magnitude larger than capillary forces, at least for dimensions relevant for biochemical analysis. Thus, varying liquid properties such as wettability of samples and reagents play a minor role and the unique combination of centrifugal and pneumatic pressure significantly enhances robustness and controllability.

The challenge of the centrifugal forces being directed radially outwards is mastered. Adding additional actuation forces such as temperature changes is beneficial but not mandatory. Such additional actuation would be used in particular if it is needed anyhow for controlling the assay. The diverse methods can be used to valve, transfer, mix fluids, even handle micro-particles, and to realize basically all fluidic operations required for the automation, miniaturization and parallelization of laboratory workflows. For implementation, only a fundamental understanding of physics is required. Disks can be manufactured in a monolithic fashion using scalable fabrication methods such as injection moulding or thermoforming. Depending on the complexity, analytical or numerical models permit the analysis and dimensioning of pneumatic operations in microfluidic networks. The robustness against change of dimensions due to manufacturing tolerances can be considered. It depends on the specific use-case, if pneumatic actuation should be realized with external means by pressure connections or with liquids processed on the disk. External sources require interfaces, bear the risk of contamination and require more complex processing devices. Their benefit is that the microfluidic disk design and manufacturing is simpler.

No matter how pneumatic pressures are realized, the usefulness of the combination of centrifugal and pneumatic actuation has been successfully demonstrated in numerous applications. From our perspective using pneumatics is indispensable for modern centrifugal microfluidic automation of laboratory workflows.

We hope that with this review we could provide a good overview of the different demonstrated implementations and with the tutorials provide detailed insights into the design process of pneumatic operations in centrifugal microfluidics.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

Financial support by the German Research Foundation (DFG) within the project CentriMix (Grant No. ZE 527/10-1), by the Federal Ministry of Education and Research (BMBF) within the project TB-Tube (Project No. 13N13457) and within the project IRMA-4-ALL (Project No. 01EK1508D) is gratefully acknowledged.

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Footnote

Electronic supplementary information (ESI) available. See DOI: 10.1039/c9lc00441f

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