Capillary pumps for autonomous capillary systems

Abstract

Autonomous capillary systems (CSs), where liquids are displaced by means of capillarity, are efficient, fast and convenient platforms for many bioanalytical applications. The proper functioning of these microfluidic devices requires displacing accurate volumes of liquids with precise flow rates. In this work, we show how to design capillary pumps for controlling the flow properties of CSs. The capillary pumps comprise microstructures of various shapes with dimensions from 15–250 µm, which are positioned in the capillary pumps to encode a desired capillary pressure. The capillary pumps are designed to have a small flow resistance and are preceded by a constricted microchannel, which acts as a flow resistance. Therefore, both the capillary pump and the flow resistance define the flow rate in the CS, and flow rates from 0.2–3.7 nL s⁻¹ were achieved. The placement and the shape of the microstructures in the capillary pumps are used to tailor the filling front of liquids in the capillary pumps to obtain a reliable filling behaviour and to minimize the risk of entrapping air. The filling front can, for example, be oriented vertically or tilted to the main axis of the capillary pump. We also show how capillary pumps having different hydrodynamic properties can be connected to program a sequence of slow and fast flow rates in a CS.

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Introduction

Microfluidic devices are promising for applications that require precise displacement of small amounts of liquids or that can benefit from peculiar behaviours that liquids and chemical reactions exhibit at the micrometre length scale.¹ At small scale, for example, diffusion times of reactants and analytes are short, surface-to-volume ratios are large, and surface tension forces dominate gravitation forces.^2,3 Accurate control of the flow of liquids in microfluidics is key to their proper functioning and can be achieved with either actuated or passive microfluidics. In actuated microfluidics, the flow is controlled using an external power source or pump and is driven mostly by displacement, centrifugal, electric-field or magnetic-field pumping mechanisms.⁴ Actuated microfluidics are most powerful in pumping on demand milli- and microlitres of liquids for a long time and with a high flow rate. In passive microfluidics, flow rates are encoded in the design of the microfluidics. Typical driving forces for propelling liquids in passive microfluidics are, for example, chemical gradients on surfaces, osmotic pressure, degassed PDMS,⁵ permeation in PDMS⁶ or capillary forces.^7,8 Such microfluidics fill spontaneously and are appealing owing to their portability, low dead volume and small power consumption. A combination of actuated and passive control for moving liquids in microfluidics has also been demonstrated.⁹ There, pressurised gas chambers embedded in a plastic chip were separated from a liquid via thin membranes. Opening these membranes irreversibly using a thermal actuator caused the liquid to be pushed through hydrophobic microfluidic channels at flow rates defined by the geometry of the channels.

We are mainly interested in developing passive microfluidics driven by capillary forces for use in bioanalytics and for patterning biomolecules on surfaces.¹⁰ We call such microfluidics capillary systems (CSs).¹¹ Passive microfluidics have also been used for micromoulding in capillaries to study the dynamics of wetting of liquid prepolymers in rectangular capillaries¹² or to deposit locally enzymes within capillaries.¹³ Passive microfluidics which require the displacement of large volumes of liquid or very low flow rates can be enhanced by peripheral equipment.¹⁴ As the flow rate of a liquid in passive microfluidics is predefined, minor device variations can compromise their operation. For this reason, modelling the filling dynamics^15,16 of liquids in capillaries is desirable, but for capillary-force-driven microfluidics the computational fluid dynamic methods require extremely high grid resolution or adaptive grid refinement algorithms to track the movement of the liquid filling front.^17,18 Therefore, a high computational effort is necessary to apply these methods. An alternative method is to use a constraint energy minimization approach, but such a method cannot describe the dynamics of filling.¹⁹

In this paper we are interested in extending the performance of CSs by understanding and governing the filling dynamics of liquids in CSs better. We therefore designed, fabricated and tested a range of CSs, and compared their experimental filling behaviour with a simple analytical model. We use CSs that are microfabricated into silicon chips and sealed with PDMS. The CSs comprise a loading pad, a capillary retention valve (CRV) and a reaction chamber, in which an immunoassay can be performed, as well as a flow resistance and a capillary pump with a vent, see Fig. 1. Surface-immunoassays can be performed directly on the sealed chip by patterning receptors for analytes on the PDMS layer.²⁰ Given the importance of capillary pumps on the hydrodynamic performance of CSs, we focus on designing and implementing new types of capillary pumps in this work. As will be shown below, a flow resistance in front of the capillary pump can also be used to modulate the filling behaviour of liquids in capillary pumps. The flow rate Q of a liquid in a CS is determined by the wettability of the CS, the viscosity of the liquid, the total flow resistance and the capillary pressure in the capillary pump, and can be expressed as

where η is the viscosity of the liquid, ΔP the difference in pressure inside and in front of the liquid, and R_F the total resistance to flow of the flow path. In CSs such as that shown in Fig. 1a, a microchannel of variable length dominates the flow resistance. The resulting capillary pressure P_c of a liquid–air meniscus in such a rectangular microchannel iswhere γ is the surface tension of the liquid, α_b,t,l,r are the contact angles of the liquid on the bottom, top, left, and right wall, respectively, and a and b are the depth and width of the microchannel, respectively.

Fig. 1 Encoding flow rates of a liquid in a CS using a capillary pump. (a) The capillary pump is the principal structure determining the flow rate of the liquid in the CS and can therefore be designed to program this flow rate. A chip having one or several CSs has a typical area of 1 cm². The capillary retention valve (CRV) prevents the reaction chamber from drying out. (b) The pumping power of a capillary pump depends on the contact angles of the filling liquid with its walls and the characteristic dimensions of its structures. The various parts in the scheme are not to scale.

The flow resistance of such microchannels is a geometric term with a Fourier series and can be approximated by a linear term²¹

satisfying the condition a < b. Here L is the length of the microchannel and R_H is the hydraulic radius of the microchannel,
with P being the perimeter and A the area of the cross section of the microchannel.

The flow in a microchannel can thus be estimated by the capillary pressure divided by the flow resistance that continually increases as the channel is being filled. In the case of capillary filling, spontaneous filling of a liquid inside a microstructure results from the interaction between the surface tension of the liquid and the chemistry and geometry of the surfaces of the microstructure. In the following sections, we review how to design capillary pumps for CSs and show how the capillary pumps enable advanced flow control in CSs.

Experimental

The CSs were fabricated in silicon using photolithography and dry etching. Briefly, photoplotted polymer masks²² (Selba S.A., Versoix, Switzerland) with a resolution of 25400 dpi were used to pattern a photoresist on silicon wafers. The CSs were etched 30 µm deep into the silicon using a deep reactive ion etcher (STS ICP, Surface Technology Systems plc, Newport, UK). On some CSs the flow resistor was then coated by hand with resist and the remainder of the CS was etched to a total depth of 60 and 90 µm. Unless otherwise noted, we will discuss the 30 µm CSs in detail. After removal of the photoresist, the wafers were coated with Ti (10 nm) and Au (150 nm), and then diced to produce individual CSs.

The Au surface of the CSs was cleaned in a UV-ozone chamber (UV-Ozone Photoreactor PR-100, Ultra-Violet Products, Upland, CA) for at least 20 min. The CSs were then immersed for 30 s in a 2 mM ethanolic solution of thiolated poly(ethylene glycol) (HS-PEG 12750-4, Rapp Polymere, Tübingen, Germany) to make the Au surface hydrophilic. The CSs were rinsed with ethanol and dried under a stream of N₂. The resulting Au surface had an advancing contact angle of 40° with deionised water, to which a food colorant was added (Food Colour bordeaux, Werna W. Schweizer AG, Wollerau, Switzerland). Contact angles were measured using the sessile drop method on flat surfaces. A few millimetres thick layer of cured PDMS (Sylgard-184, Dow Corning, Midland, MI) was used to seal the CSs from the capillary retention valve to the vent. The advancing contact angle of deionised water with PDMS was 115°. All surface treatment and sealing steps were executed in a laminar flow box.

The CSs were used within 5 to 45 min after derivatization of its surface and sealing. Coloured deionised water was used as a model liquid in the experiments for this paper. The CSs showed comparable filling characteristics when other liquids having similar contact angles and viscosities as water were used (data not shown). To prevent evaporation of liquid from the loading pads, the sealed CSs were placed on a Peltier stage in a closed chamber and maintained at a temperature of 1 K above dew point (∼10 °C). The chamber was briefly opened to pipette liquid into the loading pads. The flow rate was determined based on the time it required to fill a capillary pump completely. This time ranged from 45 s to a few minutes. The filling of liquids in the CSs was observed using a stereomicroscope (Wild Heerbrugg, Switzerland) equipped with a digital camera (Coolpix E990, Nikon).

Results and discussion

Designing advanced capillary pumps

A CS starts filling upon pipetting a liquid into its loading pad. After the liquid has filled the capillary retention valve, the reaction chamber and the flow resistor, the liquid front reaches the capillary pump. The total volume of the elements in a CS located before the capillary pump is generally negligible compared with the volume of the capillary pump. The capillary pump therefore dictates the flow conditions of the largest volume fraction of liquids pipetted in the loading pad. Ideally, capillary pumps should be able to generate a smooth flow of liquid in a CS, to induce flow rates ranging from micro- to picolitres per second and to fill the CS entirely without entrapping air. In practice, these requirements can be difficult to meet. This is the case for CSs that are used to miniaturize surface immunoassays and in which the long (up to 10 mm) and narrow (cross section ≤ 30 × 30 µm²) reaction chambers possess a significant flow resistance and thus required capillary pumps having low flow resistance and high capillary pressure. A large flow resistance can also build up in a capillary pump that has a large volume capacity. If capillary pumps having different characteristics are to be connected, it is important to fill the first capillary pump completely before the liquid proceeds to the next one. Control over the filling front of a liquid in a capillary pump is therefore desirable and may also be advantageous if some of the liquid present in the capillary pump must be retrieved for further analysis or processing.

Fig. 2 shows different implementations of capillary pumps. The simplest possible capillary pump is a microchannel having a sufficient volume to accommodate the volume of liquid that needs to be displaced. The next simplest capillary pump is a cavity, which can have supporting posts to prevent collapse of the soft PDMS sealing cover (“Posts” capillary pump in Fig. 2a).²³ Capillary pressure in the capillary pump can be increased by splitting the capillary pump into smaller parallel microchannels (“Tree lines a” in Fig. 2a).¹¹ We previously used such capillary pumps to encode a high capillary pressure in autonomous CSs.¹¹ The total flow resistance of such capillary pumps, however, can significantly increase when the microchannels in the capillary pump are long. An alternative design is to place microstructures, such as hexagons, at regular intervals inside the capillary pump. These capillary pumps have a comparatively lower flow resistance because of the large number of parallel flow paths. They can thus be used when larger volumes of liquid must be pumped at constant flow rate.²⁰

Fig. 2 Examples of capillary pumps. (a) The characteristic dimensions of the structures generating capillary pressure in a capillary pump can be varied by changing the density (“Posts”), shape (“Hexagons”), relative positioning, and continuity (“Tree lines”) of these structures. (b) Examples of capillary pumps described in depth in this work. All capillary pumps are shown with a filling direction from left to right.

Advanced capillary pumping structures as shown in Fig. 2b can further enhance the pumping capabilities of CSs. Elongated microstructures can be used to control the filling front of a liquid by imposing various time constants for the progression of a liquid along different directions of the capillary pump. A straight filling front can be achieved by using lines, as shown in Fig. 2b. Changing the width (u) of the structures compared with their spacing (v) affects the progression rates of the liquid in the vertical and horizontal directions: the liquid moves quickly in between two parallel lines, whereas it spreads more slowly elsewhere. The areas separating microstructures act as pinning sites, which can delay the progression of the filling front for considerable amounts of time. It is preferable to have microstructures with a round periphery to minimize the occurrence of pinning of the liquid. Reducing the width of the microstructures in the region where they run parallel (“Balled lines” in Fig. 2b) increases the storage capacity of a capillary pump.

It is important to connect the capillary pump correctly to the remainder of the CS to ensure that the capillary pressure is sufficiently high everywhere in the connecting region to draw liquid efficiently from the CS to the capillary pump. This can be done by gradually expanding the lateral dimension of the capillary pump and centring one microstructure in the connecting channel at the entrance of the capillary pump. Interlocked structures, such as the rounded hexagons in Fig. 2b, reduce the time needed for a liquid to move along the sidewalls of the microstructures and to bridge them. Moreover, the edges of the capillary pump can be made long and similar to the microstructure lattice to minimize the risk of having the liquid shortcutting the capillary pump by rapidly wetting its edges. The last type of capillary pump shown in Fig. 2b (“Tree lines b”) has branched filling regions, which, once filled, become disconnected from the central flow path. With this type of geometry, capillary pumps can be programmed to have zones that generate different capillary pressures and that can be filled one after the other without continuously adding flow resistance to the CS.

From the set of capillary pumps described in Fig. 2, we implemented the most promising ones into CSs using various characteristic dimensions, measured their flow rate and characterized their filling behaviour, Table 1. We chose characteristic dimensions to obtain flow rates of a few nanolitres per second. Such flow rates are typical for high-sensitivity and low-volume assays.²⁰Table 1 summarizes the findings for CSs, in which the capillary pumps have characteristic dimensions of 15–250 µm and which draw liquid with rates from ∼2 to 4 nL s⁻¹. As expected, the fastest CSs have capillary pumps with the smallest characteristic dimensions. The “symmetric line”-type capillary pump with a typical dimension of 15 µm, however, has a smaller flow rate than expected from the calculations. A reason is probably the high number of sites in which the meniscus at the liquid front is pinned. A liquid filling this capillary pump exhibits a random filling front—similar to a liquid filling a porous medium²⁴—but this random filling front can be changed to a straight one by rotating the microstructures in the capillary pump by 90°. “Symmetric line”-type capillary pumps having larger characteristic dimensions, and “asymmetric line”-type capillary pumps have a straight filling front, which is oriented perpendicular to the main axis of the capillary pump. Liquid that fills “hexagon”-type capillary pumps sometimes runs preferentially along the capillary edges, which is typical for most capillaries.²⁵ Flow rates in “rounded hexagon”-type capillary pumps are very uniform, because the microstructures are interlocked so that liquid is less pinned. A reproducible filling front can be observed in the tree-line capillary pump: Liquid in this capillary pump fills the individual branches one after the other. All capillary pumps have an absorption capacity (filling factor) of ∼60 to 75% of their total volume and can accommodate ∼0.02 µL mm⁻² of liquid for a depth of 30 µm. In our experiments, the capillary pumps typically had a total volume of 0.3 µL on an area of 15 mm². From the analytical model based on eqn (1)–(3), we estimated a flow rate of 1.7–8.7 nL s⁻¹ for the “symmetric line”-type capillary pumps. The capillary pumps were modeled as networks of parallel and serial resistors, each resistor representing a small channel of the capillary pump. The total resistance was derived using the equivalent network approach and Ohm's Law. We assumed a flow resistance of 3.6 × 10⁻¹⁴ m⁻³, which includes the exit channel of the loading pad, three parallel, 10 µm-wide capillary retention valves, the reaction chamber, and a 30 µm-wide and 1 cm-long flow resistor. In eqn (3) we used a corrected width of , which we observed from the experiments as the typical width of the moving meniscus in the “symmetric line”-type capillary pumps. We will now discuss the influence of the flow resistance in front of the capillary pump on the flow rate and compare the experimental with the estimated flow rates.

Table 1 Characteristics of advanced capillary pumps

Capillary pumping structure	Characteristic dimensions/µm	Experimental flow rate^a/nL s^−1	Calculated flow rate/nL s^−1	Filling factor (%)	Volume^b/µL mm^−2	Comments
a for a total flow resistance of 3.6 × 10^14 m^−3; b volume for a uniform depth of 30 µm; c without the distributing triangle.
Hexagons	u = 60	2.1	—	59 (71)^c	0.018 (0.021)^c	Good filling, risk of shortcutting along the edges of the pump
Sym. line	u = v = 15	3.7	6.2	65	0.020	Random filling front
Sym. line	u = v = 80	2.6	2.7	63	0.019	Straight filling front, straighter with smaller flow resistance
Sym. line	u = v = 150	2.0	2	62	0.019	Straight filling front, straighter with smaller flow resistance
Sym. line	u = v = 250	2.0	1.7	65	0.020	Straight filling front, straighter with smaller flow resistance
Asym. line	u = 40, v = 80	2.4	—	74	0.022	Good filling, like for sym. line pumps
Balled line	u = 20, v = 80	2.1	—	75	0.023	Preferred filling from the side
Rounded hexa.	u = 60, v = 30	2.6	—	60^c	0.018	Filling front moves continuously
Rounded hexa.	u = 30, v = 15	3.0	—	60^c	0.018	Filling front moves continuously
Sym. line	u = v = 15, 90°	3.6	—	65^c	0.020	Straight filling front, tilted by 45°
Tree line b	u = 30	3.2	—	61	0.018	Subsequent filling of the branches

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Connecting capillary pumps using microchannels of different lengths

It is convenient to change the flow rate of a CS without changing the design of the capillary pump by simply varying the flow resistance in front of the capillary pump. For example, we varied the flow resistance in CSs using “symmetric line”-type capillary pumps. The flow rates for these CSs are displayed in Fig. 3 for four different total flow resistances. A capillary pump has a maximal flow resistance when it is almost fully filled. This resistance can however be neglected as it is very small and at least 2–3 orders of magnitude smaller than the total flow resistance of the CS. The predominating flow resistors used here precede the capillary pump and had lengths of 1, 5, 9 and 13 cm and are abbreviated R1, R5, R9 and R13, respectively. For these CSs, experimental flow rates varied by a factor of ∼18 and ranged from 0.2–3.7 nL s⁻¹. Flow rates were determined with an accuracy of ±0.1 nL s⁻¹ or better. In the CSs with the smallest flow resistance (R1), the liquid filled the capillary pumps with the largest flow rate, namely 2.0–3.7 nL s⁻¹. A larger flow resistance (R5) slowed down the flow rate to 0.6–0.7 nL s⁻¹. By further increasing the flow resistance (R9, R13), flow rates down to 0.2–0.4 nL s⁻¹ could be achieved. Irrespective of the preceding flow resistor, the capillary pump with the smallest characteristic dimension of 15 µm exhibits an experimental flow rate that is significantly smaller than expected from the calculations. For the other CSs, experimental results fit the predicted flow rates with a deviation of ∼10%. Large flow resistances (R9, R13) can predominate the flow rate, whereas the capillary pump determines the flow rate when flow resistances are small (R1), see CS 15_R1 and CS 250_R1 in Fig. 3. Although the internal structure of the capillary pump seems to be less important for the flow rate than the flow resistance, it can be relevant to ensure a proper filling, as we will show next.

Fig. 3 Calculated and experimental flow rates of water in “Symmetric line”-type capillary pumps. For each type of CS, the first number refers to the spacing (in µm) between the microstructures of the capillary pump and the last number indicates the length (in cm) of a flow resistor having a cross section of 30 × 30 µm² and placed before the capillary pump. The insets are optical micrographs showing the relative size of the microstructures in the capillary pumps. The scale bars are 50 µm.

Time series of typical filling fronts of coloured water in various types of CSs are shown in Fig. 4. The liquid fills the capillary pumps from the left to the right. The exact shape of the filling front depends on the total flow resistance and the type of capillary pump. A low flow resistance (R1, R5) in front of a “symmetric line”-type capillary pump results in a filling front that is parallel to the microstructures, Fig. 4a. The liquid spreads preferably along the edge of the capillary pump into the next row of microstructures and is then drawn by the slightly higher capillary pressure into the space between two parallel lines, and fills the entire width of the capillary pump. This overall straight filling front moves consistently along the main axis of the capillary pump. In Fig. 4b the capillary pump has the same capillary pressure as in Fig. 4a but the flow resistance is larger (R13), which reduces the flow rate and changes the filling behaviour. Here, spreading of liquid along the edge of the capillary pump predominates. In the case of a sealed capillary pump, such a filling behaviour increases the risk of incomplete filling and enclosing air. This risk is minimized when using the “symmetric line”-type of capillary pumps in which two filling fronts of liquid converge from the edges of the capillary pump toward its centre without entrapping air. For small characteristic dimensions (15 µm) in the capillary pump, Fig. 4c, the filling line is rotated by 45° compare with the large structures in Fig. 4a. The capillary pump shown in Fig. 4c has two main parts, namely, of a triangular entrance and a rectangular main body. Spreading of liquid along the edges of the capillary pump is slowed down in the entrance of the capillary pump because the entrance sidewalls are indented. In the rectangular part of the capillary pump, the microstructures are parallel to the sidewalls and these walls are therefore not indented. Accordingly, the microstructures vicinal to the sidewalls are placed 25 µm instead of 15 µm away from the walls to reduce the capillary pressure in this region and to prevent undesired spreading of liquid along the peripheral walls.

Fig. 4 Time series of optical micrographs showing the typical filling fronts of coloured water in various types of capillary pumps. Liquid flows from left to right. (a) Flat filling front in a capillary pump that is preceded by a low-flow resistor and corresponding scheme showing how the water menisci (plain lines) progress from structure to structure (dashed arrows). (b) Capillary pump preceded by a high-flow resistor that has a meandering filling front. Such a capillary pump is designed to minimize the risk of entrapping air. (c) Example of a capillary pump designed to control the shape and orientation of the filling fronts in the capillary pump. The scale bars are 500 µm. The videos of these results are available as ESI.†

Serial connection of capillary pumps

Biological assays typically comprise multiple incubation and rinsing steps, which can differ in duration. Because liquids in CSs flow in a laminar manner, a brief rinsing step can be an efficient way to remove a preceding liquid from a reaction chamber.¹¹ In contrast, the time needed to capture antigens from solution or to bind detection antibodies to a surface-immobilized antigen may amount to some minutes.²⁰ Matching the flow rates during an assay to the optimal durations of individual steps is desirable to shorten the time to result when using microfluidic systems.^20,26

A sequence of steps can be optimized using a capillary pump with multiple zones, each generating a slightly different flow rate. It is easy to design a CS in which a first capillary pump is followed by a second, slower one because the high flow resistance of the second capillary pump does not affect the filling of the first capillary pump. The reverse case is more challenging for two reasons. First, the filling behaviour of the liquid in the capillary pumps must be carefully controlled to prevent the first (slow) capillary pump from being bypassed. The second challenge for accelerating a liquid in a CS using serial capillary pumps is the additive effect of flow resistances of serial microfluidic elements. Bypassing, as has been shown above, occurs preferentially along the peripheral edges of the capillary pump and might lead to an only partial filling of the first capillary pump. The risk of bypassing can be greatly reduced by selecting a capillary pump having indented peripheral walls, Fig. 5. In addition, the liquid at the end of the first capillary pump can gradually be directed to a single connexion channel using a series of hierarchical bridges, Fig. 5a. Here, the capillary pressure in the successive bridges diminishes (in absolute value) and favours the complete filling of the small bridges over that of the larger ones. The geometry of the junction between smaller and larger bridges also helps pinning a liquid that fills a bridge from only one side until the liquid has also filled the second branch. We found such hierarchical structures to be very efficient for the CSs designed here. In addition, these structures have a relatively small footprint. The increase in resistance of serial capillary pumps can be compensated by augmenting the capillary pressure in the second capillary pump compared with that in the first one. The serial capillary pumps shown in Fig. 5b are connected via hierarchical bridges, do not entrap air, are not bypassed by the spreading of liquid along the capillary pump edges, and the second capillary pump generates a flow rate that is about twice as fast as the first one.

Fig. 5 Optical micrographs showing (a) the consolidation of liquid streams at the end of a capillary pump to prevent entrapping air or incomplete filling of a capillary pump, and (b) a liquid moving from a completely filled, slow pump to a second faster pump. The inset shows the same region observed a few seconds later when liquid starts filling the second pump. The scale bars are 500 µm.

Conclusions

The work presented here enhances the capabilities of autonomous CSs by showing how to program their filling properties. The possibility of slowing down or even temporarily stopping the flow of liquid in a CS makes it possible, for example, to fill a reaction chamber, perform an incubation step or enzymatic assay, and flush the reactants and products for a next test in the same CS. Enzyme-linked immunosorbent assays as well as other types of assay could in principle be implemented on CSs using appropriate types of capillary pumps. These CSs would certainly lead to sensitive and versatile platforms for point-of-care testing.²⁷ Here, we studied capillary pumps in combination with flow resistances, in which the capillary pressure was defined solely by the geometry. Such CSs can also have tailored surface chemistry²⁸ to further enhance their flow behaviour or to add new functionalities such as hydrophobic valves and metering channels. Other functions that can be added to CSs are filters for cells or particles, mixers, chambers with immobilized cells, and surface-immobilized binding sites for analytes. The small form factor of CSs, their simplicity in term of utilization, and the possibility of tailoring their hydrodynamic properties using advanced capillary pumps may help to promote their use for a large number of applications in which miniaturization provides a benefit to performing biological assays.

Acknowledgements

We thank U. Drechsler and R. Stutz for their help with the fabrication of the CSs, D. Juncker for helpful discussions, and W. Riess and P. Seidler for their continuous support. M. Z. acknowledges support from H.-J. Guentherodt and financial support from the Swiss Commission for Technology and Innovation.

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Footnotes

† Electronic supplementary information (ESI) available: The time series of Fig. 4 as real time videos. See DOI: 10.1039/b609813d

‡ The HTML version of this paper has been enhanced with colour images.

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