An integratible acoustic micropump based on the resonance of on-substrate sharp-edge micropillar arrays

Abstract

There is a growing demand for reliable, efficient, and easily integrated micropumps for microfluidics. Despite the demonstrated potential of acoustic wave-driven devices for on-chip pumping, current prototypes lack the practicality and integratability for deployment in microfluidic systems. This study presents an acoustic micropump based on the resonance of arrays of on-substrate sharp-edge micropillars prepared in a fluid-filled channel and driven by a piston ultrasonic transducer. At an operating frequency of 80.5 kHz and a driving voltage of 54 V_p–p, a flow rate of 16.2 μL min⁻¹ is achieved in a downstream straight channel with dimensions 12(L) × 0.6(W) × 0.2(H) mm³. The corresponding pumping pressure exceeds 1.3 kPa, more than an order of magnitude higher than its predecessors. In experimental demonstrations, two micropumps are employed as feeding units for an acoustofluidic particle separation device based on tilted-angle standing surface acoustic waves (TaSSAWs). The current micropump exhibits advantages of high pumping pressure, fast response time, and high reliability, making it a promising pumping unit for lab-on-a-chip systems.

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1 Introduction

While microfluidic devices are widely applied in various fields, fluid flows therein are typically driven via external mechanical pumps such as syringe,^1–4 peristaltic,^5,6 and pressure pumps.⁷ The integration of microfluidic devices and the realisation of lab-on-a-chip systems are hindered by the bulky nature of the equipment currently in use. In order to address this issue, a number of on-chip micropumps have been developed, employing a variety of techniques, including optical,^8,9 thermal,^10,11 piezoelectric,^12,13 electromagnetic,^14,15 and acoustic.^16–30 Among these, acoustic micropumps have attracted significant attention due to their simplicity of fabrication, biocompatibility, independence of fluid properties, and fast response time.

Acoustic micropumps can be grouped into two categories, i.e., those driven with Lamb waves (LWs)¹⁶ or surface acoustic waves (SAWs)^17–20 which can be excited with interdigital transducers (IDTs), and those driven with bulk acoustic waves (BAWs) generated by piezoelectric transducers (PZTs).^21–30 Micropumps based on LWs or SAWs typically operate at high-frequencies (above MHz), resulting in the rapid dissipation of acoustic energy over a short distance. This energy is converted into the kinetic energy of the fluid, propeling the fluid in the direction of wave propagation. The substrates are typically lithium niobate LiNbO₃ or other piezoelectric crystals, which are incapable of withstanding high input power. Meanwhile, the pumping efficiency is compromised as a result of the limited Rayleigh angle at which the waves leak from the substrate into the liquid.^17–20

The use of BAW-based micropumps allows for the input of higher power, and often achieves satisfactory efficiencies through the resonance of microchannels²¹ or microstructures.^22–30 The resonance of in-channel bubbles^22–25 or sharp edges^26–30 significantly increases the spatial gradient of the acoustic pressure, a key factor in strengthening the acoustic streaming effect.^24,30–34 A pair of counter-rotating vortices are usually generated, e.g., in front a resonant sharp edge or in the neighborhood of a resonating bubble, resulting in a directional flow.

In bubble-driven micropumps, semi-bubbles are typically generated at cavities fabricated at the bottom or sidewalls of fluid-filled channels. The size of the bubbles may exhibit less uniformity,^26,27 especially when the channel is made of soft materials such as polydimethylsiloxane (PDMS), where the resonance frequency and vibration modes of the bubbles may fluctuate over time.^24,25 Meanwhile, the dimensions and morphology of the bubbles are dependent on the hydrophobic or hydrophilic properties of the solid surface, necessitating the implementation of pre-treatments.^22–25 Sharp-edge-based micropumps offer enhanced stability and simplicity. The geometric dimensions of lined-up sharp edges stemming from the sidewalls can be well determined during fabrication, enabling the devices to handle different carrier fluids with minimal necessity for pre-treatments.

In an early effort, the fabrication of sharp edges on the sidewalls of a PDMS channel was observed to facilitate the pumping of fluids within a closed channel.²⁶ Driven at a voltage of 50 V_p–p at 6.5 kHz frequency, the pump achieved a flow rate of 8 μL min⁻¹ and an equivalent pumping pressure of approximately 76 Pa. Subsequently, the impact of the channel width, sharp angle, and driving frequency on the magnitude and direction of the pumped flow was investigated.²⁸ It was also demonstrated that at a driving voltage of 28 V_p–p,³⁰ a single pair of resonant sharp edges made of silicon was capable of achieving a flow rate of 4.1 μL min⁻¹ and an equivalent pumping pressure of approximately 12 Pa. However, in conventional designs, the tops and bottoms of sharp edges that extend from the sidewalls are constrained, which limits their vibration efficiency. By employing a layer-by-layer manufacturing technique, Liu et al. isolated the top and bottom surfaces of PDMS sharp edges from the channel's ceiling and floor, thereby reducing damping and enhancing pumping efficiency. At a driving voltage of 200 V_p–p, a flow rate of 15 μL min⁻¹ was achieved.²⁷

The following factors should be considered when pursuing more practical micropumps based on sharp edges. Firstly, hard and easily mouldable materials should be selected to avoid excessive energy dissipation and device instabilities. Secondly, placing sharp edges solely on the sidewalls constrains the potential for further enhancement in pump performance – (a) the tilting angle of each sharp edge cannot be too small, much less parallel to the sidewalls; the propulsive force generated on the liquid is not parallel to the channel direction, resulting in a portion of the force being wasted;^26–28 (b) each sharp edge exerts a direct influence on the fluid within a limited area in its immediate vicinity. The vibration energies at the centre of the channel floor are not effectively exploited. Finally, previous prototypes are usually demonstrated by generating circulating flows within closed channels. Concerns are raised regarding the capacity of the micropumps to sustain the previously observed performances in the presence of flow resistance from downstream microfluidic components.

This work presents an acoustic-driven micropump based on the resonance of on-substrate sharp-edge micropillars made of SU-8 photoresists. Fabricating the arrayed micropillars in the bulk of the channel, instead of on the sidewalls as was done in previous works, enables the device to harness the acoustic energy provided by the substrate efficiently. The vibrating micropillars induce acoustic streaming around the sharp edges, propelling the liquid in a targeted direction into a cascaded microfluidic unit. The key innovation is that, as the micropillars stem from a quartz glass (QG) substrate and vibrate in the first-order lateral resonance mode, the device is endowed with high internal resistance and pumping efficiency. Two prototype devices are employed as feed units for a tilted-angle standing surface wave (TaSSAW) acoustofluidic device to separate particles, thereby demonstrating their potential to accurately and consistently pump fluids into downstream devices for microfluidic applications.

2 Methods

2.1 The working principle

The micropump consists of in-fluid SU-8 micropillars prepared on a QG substrate, each having a teardrop-shaped cross-section, as illustrated in Fig. 1(a). The sharp end points in the expected flow direction with a sharp angle of θ; at the blunt end is a circular arc of radius R tangent to both sides of the sharp angle; the height of the micropillar (H) is slightly shorter than the channel height, allowing the top of the pillar to vibrate freely. At the first-order resonance, the micropillar exhibits side-to-side oscillations, with an increase in vibration amplitude at higher planes. A forward streaming pattern with two counter-rotating vortices around the tip is generated in front of the sharp edge due to the volume force resulting from the velocity gradient.^32–36 In contrast, the blunt end generates a much smaller gradient and volume force, reducing the potential backflow.³² Distributions of the volume force (F_M) and streaming velocity (v₂) at different heights are shown in Fig. 1(b) and (c). Thus, as the vibration amplitude increases with height, a larger volume force and streaming velocity are generated, while the streaming patterns are similar at different heights. The theories for this calculation are given in the ESI.†

Fig. 1 The working mechanism. (a) The first-order resonance of a single on-substrate micropillar immersed in water; the color indicates the normalized magnitude of the vibration velocity (white: 0, red: 1), and the arrow indicates the vibration direction. (b) The in-water volume force at planes of different heights, (c) is the corresponding streaming patterns, with the yellow star indicating the vortex centers, and (d) is the streaming pattern induced by four micropillars patterned in a “diamond” grid. (e) Illustration of the directional pumping effect.

For the arrangement of multiple micropillars, a diamond array pattern is chosen. This is because, as shown in Fig. 1(d), in such arrays two pillars can be placed at the left and right front of a given one, with their blunt ends located at the vortex centres (indicated by yellow stars in Fig. 1(c)) to minimise possible backflow. Thus, a continuous forward flow can be generated by “relaying” the streamings induced by each individual. The size of each grid cell is characterised by Δx in the lateral direction and Δy along the channel, as shown in the figure. Within a closed domain, the streamlines of the fluid flow must form closed loops to ensure mass conservation. Therefore, a directional flow cannot be defined. However, in a microchannel with open boundaries acting as the inlet and outlet, as shown in Fig. 1(e), the directional flow can be defined as the streamlines that flow through the downstream open boundary.

2.2 Device design and fabrication

Fig. 2(a) shows a schematic of the acoustic micropump. A QG plate (JGS2, Feilihua Quartz Glass, Hubei, China), whose size is 50(L) × 30(W) × 0.5(T) mm³, serves as the substrate. On-substrate sharp-edge micropillars of SU-8 (3050, Kayaku Advanced Materials, Westborough, USA) are fabricated using standard soft lithography technology. Each pillar has a height of 180 μm, a sharp angle of 12°, and a blunt-end radius of 20 μm. With a round corner of 0.6 μm radius at the sharp end, the length of each pillar is approximately 206 μm.

Fig. 2 The device design. (a) Schematic diagram of the micropump. 1 – The polytetrafluoroethylene (PTFE) tubes (lower left: inlet; upper right: outlet), 2 – the PDMS channel, 3 – the SU-8 sharp-edge micropillars, 4 – the QG substrate, 5 – the PZT transducer. The arrows indicate the direction of flow. (b) A photograph of the fabricated micropump, together with a zoomed-in view. (c) The observation chip. 1 – The PTFE tubes, 2 – the PDMS channel, 3 – the microscope slide. (d) The TaSSAW-based particle separation chip. 1 – The sheath flow inlet, 2 – the sample fluid inlet, 3 – the large particle outlet, 4 – the small particle outlet, 5 – the IDTs, 6 – the LiNbO₃ substrate.

The fluid-filled PDMS channel is snake-shaped with an inlet and an outlet at the ends. It is composed of ten parallelly oriented segments, each having a size of 25(L) × 1(W) × 0.25(H) mm³, see Fig. 2(b). The channel is bonded to the substrate after the micropillars have been fabricated. The size of each diamond grid cell is Δx = 160 μm and Δy = 356 μm. A total of 6 columns and 60 rows of pillars are distributed in each straight segment. The top view of the device design is shown in Fig. S1.†

A rectangular PZT transducer, whose size is 35(L) × 18(W) × 1(T) mm³, is attached to the QG substrate near the PDMS channel using two clamps. As will be shown later, the transducer can be conveniently placed at different locations on the upper/lower surface of the substrate. The vibrations generated by the transducer are transmitted to the QG plate via a coupling layer of silicon oil.

Three downstream devices are prepared to examine the performance of the micropump. The first is an observation chip, which is simply a straight long PDMS channel (dimension: 12(L) × 0.6(W) × 0.2(H) mm³), with an inlet and an outlet at the ends, bonded to a standard microscope slide, see Fig. 2(c). The rest two are acoustofluidic chips employing tilted-angle standing surface acoustic waves (TaSSAWs) for particle separation, with one of them shown in Fig. 2(d). The operating principles and fabrication details for such devices can be found elsewhere in the literature.⁴ For each of the devices, two IDTs (Au/Cr, thickness: 150/5 nm) are fabricated on a 2 inch 128° Y–X LiNbO₃ substrate by photolithography, magnetron sputtering, and lift-off techniques. Each IDT has an aperture size of 10.8 mm and consists of 30 pairs of 50 μm wide metal fingers. A straight long PDMS channel with dimensions of 20(L) × 1(W) × 0.04(H) mm³ is bonded on the substrate, which is oriented at an angle of 9° to the IDT fingers. The channel has two inlets, one to introduce the sheath flow and the other to feed the sample, and two outlets to collect the separated particles. More details about the device fabrication procedures can be found in Fig. S2.†

2.3 The experimental setup

In the first experiment, particle imaging velocimetry (PIV) measurements are performed to characterise the streamings generated by a micropillar array, using a water suspension of 1 μm-diameter polystyrene (PS) particles (Baseline, Tianjin, China) at a concentration of 0.125% (w/v) as tracers. The micropump is positioned on the stage of an inverted microscope (IX73, Olympus, Tokyo, Japan), and the moving particles are captured with a high-speed camera (FASTCAM Mini UX100, Photron, Tokyo, Japan). The recorded images are analysed with an open-source software PIVLab³⁷ to extract the velocities of the tracers. The focal plane of the microscope is at the mid-height of the channel. To facilitate observation, the PZT transducer is placed next to the channel on the top surface of the QG substrate, as shown in Fig. S3(a).† The transducer is driven by a sinusoidal signal provided by a signal generator (33622A, Keysight, Colorado Springs, CA, USA) cascaded with a 50 dB power amplifier (325LA, E&I, New York, NY, USA), where the driving frequency is determined using a network analyser (VNA 2180, Array Solutions, Texas, USA). The inlet and outlet of the micropump are connected to the same fluid reservoir.

The micropump is then connected to the observation chip but remains inactive. As illustrated in Fig. S3(b),† a syringe pump (Nemesys S, CETONI GmbH, Korbussen, Germany) delivers a water suspension of 1 μm-diameter PS particles into the observation chip at a volume rate of 0.05 μL s⁻¹, inducing an average tracer velocity of 426 μm s⁻¹ within the observation plane. This result is used to calibrate the flow rate of the micropump, which should have achieved the same flow rate when inducing the same tracer velocity in the observation chip.

Next, the internal flow resistance of the micropump-observation chip system is measured. As illustrated in Fig. S3(c),† the inlet of the micropump and the outlet of the observation chip are connected to two sample-filled tubes positioned at different heights, creating a pressure difference between the inlet and outlet of the system. The average tracer velocity in the observed plane is measured; with the flow rate determined from this, the flow resistance is obtained as the pressure difference divided by the volume flow rate. After testing at five different pressure differences, each repeated three times, the flow resistance is determined as 4818 ± 115 Pa s mm⁻³ (mean ± SD). Detailed testing data are listed in Table S1.†

The pumping pressure can now be measured. As illustrated in Fig. S3(d),† the system configuration is the same as in the previous step, except that the inlet and outlet of the system are connected to the same reservoir filled with a suspension of 1 μm-diameter PS particles. By activating the transducer and driving it at given parameters (i.e., frequency and voltage), the flow rate determined by PIV is multiplied by the calibrated flow resistance to obtain the achieved pumping pressure in the microfluidic system.

Finally, two micropumps are used as the feed units for the TaSSAW devices to perform particle separation experiments; see Fig. S3(e).† The first pump (driven at V_p–p = 45 V) connects a water-filled tube and an inlet of the separationchannel to produce bilateral sheath flows, and the second (driven at V_p–p = 15 V) feeds a water suspension of mixed PS particles into the other inlet of the TaSSAW chip. Two experiments are carried out. The first separates 3.2 μm (red fluorescence, 0.04% w/v) and 5.5 μm (green fluorescence, 0.1% w/v) diameter PS particles, where the ratio of bilateral sheath flows is 2 : 1, the two outlets have a flow ratio of 1 : 1, and fluorescent images are captured. The second experiment separates 5.0 μm (0.2% w/v) and 10.0 μm (0.5% w/v) diameter particles, the corresponding sheath flow ratio is 9 : 1, the two outlets have a flow ratio of 2 : 1, and the separation process is recorded in a bright field. In the two experiments, the IDTs are driven by a SAW generator (BSG F20, BELEKTRONIG, Freital, German) at a frequency of 19.76 MHz, while the driving power is 1.2 W and 1.03 W, respectively.

2.4 Numerical simulations

Three-dimensional finite element (FE) simulations are performed using the commercial software COMSOL Multiphysics (v6.1, COMSOL, Stockholm, Sweden).

Two types of models are considered. One is single-pillar models where a micropillar is placed in a cuboidal water-filled channel having a dimension (L × W × H) of 600 × 200 × 250 μm³, with the pillar height H, the arc radius R, and the sharp angle θ varied to obtain the corresponding resonance frequency and directional flow rate. In each single-pillar simulation, the first-order resonance frequency of the micropillar is first determined by “eigenfrequency” analysis. Then, frequency-domain simulations are performed at the determined frequency to obtain the acoustic field in the fluid and the micropillar vibrations with the “thermoviscous acoustics” and the “solid mechanics” interfaces, the two fields being coupled via a “thermoviscous acoustic-structure boundary”. Finally, the streaming field within the fluid domain is analysed using a “laminar flow” interface with the Reynolds stress^34,36 assigned as the “volume force”. At the bottom of the micropillar, a lateral velocity boundary (v_x = 1 × 10⁻³ m s⁻¹) is applied to simulate the actuation from the substrate. It is worth mentioning that, since the micropillars exhibit side-to-side oscillations during first-order resonance, vibration amplitudes induced by actuation in the y- and z-direction are negligibly small, simulation results to demonstrate this point are presented in Fig. S4.† For the cuboidal water domain, all six outer surfaces are assigned “impedance” boundaries in the computation of the acoustic-structure fields: the upstream and downstream surfaces set to 1.5 × 10⁶ Pa s m⁻¹ (for water), the two side surfaces and the ceiling are set to 1.1 × 10⁶ Pa s m⁻¹ (mimicking PDMS), and the bottom surface set to 1.32 × 10⁷ Pa s m⁻¹ (for QG).^38,39 In resolving the streaming field, the upstream and downstream surfaces are set as open boundaries characterised by zero normal stress, and all other boundaries are considered to be no-slip conditions. The directional volume flow rate is calculated by integrating the fluid velocity across the downstream open boundary.

The other is multi-pillar models, where an array of pillars is arranged in a 5000 × 1000 × 250 μm³ (L × W × H) channel to estimate the flow resistance in the micropump. The geometries and arrangements of the pillars are the same as in the device design. The flow field is resolved by assigning the upstream open boundary a static pressure of 1000 Pa and the downstream open boundary zero normal stress. All other boundaries are assigned no-slip conditions. The flow resistance is determined by dividing the 1000 Pa pressure difference by the induced volume flow rate. Since the channel length of the micropump is 250 mm, the overall resistance should be 50 times that determined from simulations.

The material parameters of SU-8 include a density of 1153 kg m⁻³, a Young's modulus of 2 GPa, a Poisson's ratio of 0.35, and a loss factor of 0.023.³⁹ The water parameters are taken from the COMSOL material library. In all models, the rounded corner with radius R₀ = 0.6 μm at the sharp end of each pillar ensures simulation convergence.³⁴ The ESI† contains all the governing equations involved in the above procedures.

3 Results

3.1 The streaming pattern

A voltage of V_p–p = 45 V and a frequency of 80.5 kHz is applied to the PZT transducer, the resultant streamlines determined with the PIV-measured velocity field in a local area of the chip is presented in Fig. 3. In accordance with the predictions in Fig. 1(d), the two vortices situated in front of each pillar are either diminished or absent, resulting in a directional flow. In particular, the blunt ends of the pillars in the subsequent row are situated at the centres of the vortices that the preceding row would have produced. This results in the closed streamlines becoming directional, in accordance with the principles of mass conservation. It is noteworthy that the abrupt appearance or disappearance of streamlines in the vicinity of the micropillars may be attributed to the vertical movement of the tracers, whereby they move into or out of the focal plane. With the recorded particle motions in Video S1,† the PIV-determined tracer velocity map is presented in Fig. S5.†

Fig. 3 The PIV-measured streaming pattern around acoustic-driven micropillars arranged in a diamond array.

Nevertheless, the presence of some vortices is still discernible between the micropillar columns and at the channel boundaries. The residual vortices between adjacent columns are a consequence of the non-identical vibrations of the micropillars, which result in incomplete elimination of the vortices. For instance, the fluid velocity in the right half of the current view is higher than that in the left half, whereas the residual vortices are mainly observed on the left of the pillars. The underlying cause of this phenomenon is complex, potentially involving an uneven distribution of substrate vibrations and the inconsistencies of micropillar geometry due to the limitations of fabrication techniques. The presence of vortices at the boundaries is a predictable consequence, given that the pillars that would otherwise serve to minimise them are absent due to the limited channel width.

As Fig. 3 only presents a small part of the channel, similar phenomena are observed elsewhere in the device. Consequently, the forward streaming pattern is relayed from one row to the next, forming a remarkable, continuous directional flow. The diamond grid pattern adopted here has significantly mitigated the vortices induced by the resonance of sharp-edge structures, with the achieved pumping effect outperforming that in a square arrangement. This will be discussed in more detail later.

3.2 The calibration results

The resonance frequency of an individual micropillar, as determined by a single-pillar FE model, is found to be 75.96 kHz in accordance with the design parameters outlined in sec. 2.2. Thus, a PZT transducer with a nominal operating frequency of 76 kHz is employed. By sweeping the frequency range from 65 to 85 kHz at a step of 0.1 kHz, an optimal flow rate (37.3 nL s⁻¹ at a driving voltage of 18 V) is identified in the downstream observation chip at 80.5 kHz. Subsequently, transducers with varying nominal frequencies (75, 80.5, and 85 kHz) are employed to activate the micropump. In all instances, 80.5 kHz is identified as the optimal operating frequency. Consequently, an 80.5 kHz transducer is ultimately selected and operated at its nominal frequency. The discrepancy between the predicted and identified resonant frequencies will be elucidated in subsequent sections.

The micropump performance is calibrated per the protocol described in sec. 2.3. As the PZT is driven at different V_p–p, the achieved flow rates are presented in Fig. 4(a), with the corresponding pumping pressures indicated by the vertical axis on the right. A flow rate of 271 nL s⁻¹ (approximately 16.2 μL min⁻¹) is achieved at V_p–p = 54 V, corresponding to a pumping pressure of 1306 Pa. The PIV results tracked in the observation chip, where 1 μm PS particles are used as tracers, are shown in Fig. S6.† Therefore, the current device achieves a pumping pressure that is more than an order of magnitude higher than one of its predecessors (approximately 76 Pa driven at 50 V_p–p)²⁶ at a comparable driving voltage. In comparison to the device developed by Liu et al.,²⁷ the driving voltage required to generate a comparable flow rate is reduced by 63%. Of particular significance is that the pumping pressure calibration is conducted subsequent to the micropump's integration with a microfluidic device, thereby substantiating the pump's capacity to facilitate fluid transfer into downstream devices. In comparison, the majority of preceding acoustic micropump demonstrations have been conducted within the confines of closed channels.^26–30

Fig. 4 The calibration results for the micropump. (a) The flow rate (the left axis) and pumping pressure (the right axis) generated by the micropump at different driving voltages. (b) The pumping rate of the micropump over a 50 min period.

To demonstrate the stability of the pump, the flow rate is examined at 20 s intervals over a continuous period of 50 min, with the PZT driven at a voltage of V_p–p = 30 V. The results in Fig. 4(b) demonstrate that the time-dependent flow rate exhibits a stable profile, with an average value of 105.6 ± 3.5 nL s⁻¹ (mean ± SD). Therefore, the proposed device can be considered a reliable microfluidic pumping unit for long-period applications.

3.3 The time response

A rapid response time is essential for a pump when flexible manipulations of the fluid are required, particularly when a time-varying flow rate profile is expected or transient phenomena are to be observed in microfluidics. At a voltage of V_p–p = 30 V, the driving signal for the PZT transducer is switched on and off at a frequency of 10 Hz and a duty cycle of 50%, resulting in a normalised flow rate as displayed in Fig. 5(a). The findings demonstrate that the proposed micropump can attain a steady and resting state within a response period of less than 40 ms.

Fig. 5 The time response of the micropump. (a) The flow rate profile when the driving signal is switched on and off at 10 Hz. (b) Comparison between the flow rate profiles achieved in the observation channel by a syringe pump (the black solid line and the bottom horizontal axis) and the proposed micropump (the red dashed line and the upper axis). Programmable pumping using the micropump by modulating the driving signal with a (c) sawtooth and (d) sinusoidal profile (the red dashed lines); the achieved flow rates are presented as black solid lines.

Subsequently, the feed unit for the observation chip is switched from the micropump to the aforementioned syringe pump. The syringe pump is activated at a preset flow rate of 100 nL s⁻¹ (close to that measured before switching) and deactivated after the flow rate inside the observation chip has stabilised. The normalised PIV-measured flow rate profile during this process is presented with the black solid line (and the bottom horizontal axis) in Fig. 5(b). For comparison, an ON/OFF cycle in the flow rate profile of the micropump in Fig. 5(a) is also plotted here as the red dashed line (and the top horizontal axis). It can be seen that the required response time for the micropump is approximately two magnitudes shorter than that of the syringe pump, which responds to an ON/OFF switching in several seconds.

The rapid response of the current micropump allows it to be readily programmed to achieve complex flow rate profiles. To illustrate this, the amplitude of the 30 V_p–p driving signal is modulated with a sawtooth or sinusoidal pattern at a modulation frequency of 1 Hz. The measured flow rates in the observation chip (the black solid lines) shown in Fig. 5(c) and (d) demonstrate a high degree of correlation between the modulation patterns (the red dashed lines) and the achieved rates (Pearson correlation coefficients of 0.985 and 0.987, respectively). The recorded pumping processes for Fig. 5 are given in Videos S2–S4,† respectively.

3.4 The micropump-assisted particle separation

In the first TaSSAW-based particle separation experiment, a standing SAW field is generated with the nodal lines at an angle to the flow direction. As different types of particles travel through the fluid-filled channel, some can be “locked” by nearby nodal lines, resulting in significant lateral displacement. In contrast, others may “drift” across multiple nodal lines, with the two particle lines subsequently collected at different outlets.⁴⁰ For the separation experiment described in sec. 2.3, it is possible to have the larger 5.5 μm PS particles “locked” and the smaller 3.2 μm particles “drifting”.

In this configuration, one micropump feeds a suspension containing the two types of particles into the channel, while the other generates a bifurcated bilateral sheath flow to focus the particles into a narrow band, see the fluorescent image in Fig. 6(a). Prior to the commencement of the experiment, the flow rates are calibrated to be approximately 0.6 μL min⁻¹ and 6.2 μL min⁻¹ for the sample flow and the sheath flow, respectively. In the absence of the TaSSAW field, particles naturally flow toward the lower outlet. Upon activation of the field, the “locked” 5.5 μm particles move upward on their forward journey and are collected at the upper outlet. The observed phenomena are similar to those previously reported in experiments employing bulky pumps.^1,2,4

Fig. 6 Particle separation using a TaSSAW chip with the proposed micropump working as the feed unit. (a) The pre-separation view showing large (green fluorescent) and small (red fluorescent) particles mixed in a continuous flow. (b) The corresponding post-separation view where the TaSSAW field is activated.

The second experiment separates 10 and 5 μm PS particles. The recorded particle motions are presented in the Video S5,† which is also similar to previous observations.^2,4

4 Discussion

4.1 The performance of a single micropillar

The vibration behaviour of a single micropillar can be likened to that of a small rod fixed at one end, given that its dimensions are much smaller than the working wavelength. A formula for estimating the resonance frequency of the pillar is provided in the ESI,† which indicates that the first-order resonance frequency is proportional to the blunt end radius and inversely proportional to the pillar height squared, i.e., f₁ ∝ R·H⁻². However, it is less intuitive how f₁ varies with the sharp angle (θ). Based on this theory, the predicted resonance frequencies at different H⁻², R and θ are plotted as the dashed red lines in Fig. S7(a)–(c),† respectively; the actual resonance frequencies determined with FE modelling are presented in the same figures as black solid lines for comparison.

As illustrated in Fig. S7(a),† at R = 20 μm and θ = 12°, the simulated f₁ values align closely with the theoretical predictions when the micropillar is of a relatively high height (H⁻² is small). In both the theoretical calculations and the simulated results, the value of f₁ increases nonlinearly with respect to θ, as shown in Fig. S7(c).† However, as the height of the pillar decreases, the resonance frequency becomes lower than predicted. A similar phenomenon can be observed in Fig. S7(b),† where θ = 12° and H = 180 μm, that a big blunt end radius also induces the simulated f₁ to deviate from the theory.

The reason for such deviations is that, as the micropillar becomes shorter, the teardrop cross-section becomes blunter at one end, or the sharp angle becomes too small, the micropillar can no longer be treated as a rod (which requires H > L^41,42), and the theoretical formula becomes less effective. Indeed, in all of these cases (a small H, a big R, or a minimized θ), the first-order resonance of a micropillar no longer shows a side-to-side pattern observed in Fig. 1(a). Instead, the vibrational energy is predominantly concentrated in the upper part of the micropillar tip. To illustrate this, with a reduction in the sharp angle θ, which increases the length of the pillar L, until H becomes smaller than L, one easily finds a transition of the resonance pattern in Fig. S7(d).†

A reduction in the resonance frequency is accompanied by an increase in the thickness of the viscous boundary layer (VBL) surrounding the resonating micropillar. Consequently, a more pronounced velocity gradient,^32,36 a larger area over which the volume force exerts influence, a wider gap between the two generated vortices,³⁴ and in turn, a more potent directional flow³¹ can be expected in the channel. In order to examine the directional flow rate induced by a single micropillar having different geometrical parameters, FE simulations have been conducted, and the results are presented in Fig. S7(e)–(g).† As expected, the directional flow rate is found to be positively correlated with the pillar height H and negatively impacted by increased blunt end radius R and sharp angle θ. It is noteworthy that, in the studies conducted by Doinikov et al.³³ and Nama et al.,³⁵ a sharper end (smaller θ) also resulted in increased heterogeneity in the velocity field and stronger streaming patterns.

Therefore, the design goal of the acoustic-driven pump should be a higher height, a smaller blunt end radius, and a sharper angle. Although a small θ may result in the transition of the resonance mode, the streaming patterns remain similar. For example, in Fig. S8,† the streaming pattern generated by a micropillar with a small θ is stronger but similar to that with a larger θ. However, it is worth mentioning that the locations of the vortices (and in turn, the grid dimensions) may change when the sizes of the pillars vary. As shown in Fig. S8,† a smaller θ results in a longer distance between the vortex centers and the sharp edge. The fabrication technologies may present certain challenges and limitations. It is observed that when the design height of the micropillars exceeds 180 μm, the height inconsistency of different pillars may become apparent after photolithography-based fabrication, resulting in their inability to achieve synchronised resonance. Furthermore, a small R may result in a thinning of the pillar, thereby increasing the likelihood of tilting or collapsing; when θ is insufficiently large, the sharp end is susceptible to bending. In light of these factors, the dimensions of the micropillars selected for the design are H = 180 μm, R = 20 μm, and θ = 12°.

4.2 The streaming pattern induced by a square array

As previously noted, the design employs a diamond-shaped array configuration rather than a square array. This is due to the fact that micropillars arranged in a square array would significantly diminish the pumping efficacy. In a square array, micropillars placed in the subsequent row may impede the directional flow induced by the preceding row. Specifically, in lieu of being eliminated, the counter-rotating vortices generated by the pillars may disrupt forward-going streamlines or even cause backflows.

To illustrate this point, a pumping device employing square patterns is fabricated. The grid dimensions Δx and Δy are identical to those used in the diamond pattern, and all other experimental configurations are the same as those in producing Fig. 4. The PIV-measured streaming pattern is given in Fig. 7, where, without surprise, vortex pairs in front of micropillars are observed elsewhere in the channel, and the “relaying” effect observed in Fig. 4 is nearly absent in this case. In some areas, particularly in proximity to the channel boundaries, backward flows are observed. While the maximum streaming velocity is approximately equivalent to that observed in a diamond arrangement (approximately 6.4 mm s⁻¹), the directional flow rate in the current view is only approximately 30 nL s⁻¹ (while that in Fig. 4 is 228 nL s⁻¹). The recorded particle motions are presented in Video S6,† with the PIV-determined particle velocities in Fig. S9.†

Fig. 7 The PIV-measured streaming pattern in a pumping device where micropillars are arranged in a square array.

4.3 The streaming-reversion effect should be avoided

The inherent limitations of lithography technology preclude the possibility of achieving ideal sharp edges. Consequently, the sharp angle in the teardrop shape is modified to a rounded corner of radius R₀ = 0.6 μm in the design. It is therefore crucial to recognise that the radius R₀ should be smaller than δ/2, where is the thickness of the VBL;^32,34,36 here, ν is the kinematic viscosity of the fluid, ω = 2πf₁ is the angular frequency. Otherwise, a reversed streaming may appear in the fluid.

The streaming pattern (at z = 60 μm) induced by a micropillar with a different sharp end radius (R₀ = from 0.3 to 1.5 μm at steps of 0.3 μm) is examined through FE simulations, where the other dimensions are fixed as H = 120 μm, R = 20 μm and θ = 12°. The resonance frequency is determined to be 168 kHz, and the thickness of the VLB is δ = 1.3 μm. From the results presented in Fig. 8(a)–(e), the first two cases satisfy R₀ < δ/2, the corresponding streaming patterns resemble those in Fig. 1(c), demonstrating the potential for forward pumping. For the latter three cases, R₀ > δ/2 has induced reversed streaming patterns, and backward flows should be expected when using such micropillars.

Fig. 8 The streaming reversion effect. (a)–(e) The FE-simulated in-channel streaming pattern induced by a single micropillar having a sharp end radius R₀ = 0.3, 0.6, 0.9, 1.2 and 1.5 μm; the other dimensions of the pillars are fixed as H = 120 μm, R = 20 μm and θ = 12°. (f) An experimental demonstration of the streaming-reversion effect, the pillar dimensions are the same as in (e).

An experimental demonstration of the streaming reversion effect is shown in Fig. 8(f), which shows the PIV-measured streaming pattern (z = 60 μm) induced by a micropillar with the same dimensions as in Fig. 8(e). A high consistency in the streaming reversion effect is observed between the simulated and measured results. The reversion effect was previously reported by Mohanty et al., where the streaming pattern and the pumping effect induced by a sharp edge reversed at high frequencies²⁸ (corresponding to thin VLBs, i.e., small δ values).

4.4 The importance of high internal flow resistance

The current micropump has demonstrated its ability, largely due to the high flow resistance of the pump itself, to pump fluids into downstream devices with high reliability and rapid response. An analogy can be drawn with the concepts of electrical circuits. If a downstream device (resembling a load) with a flow resistance R_out is connected to the pump (resembling a voltage source) having an internal resistance R_in, the flow rate (resembling the current) is determined as Q = Q₀R_in/(R_in + R_out), where Q₀ is the “short circuit” flow rate (i.e., before the load is connected) which should be a constant.^31,33,35 Therefore, to achieve a high flow rate in the downstream device, R_in must be as large as possible. Since the pumping pressure is determined as the product of the total resistance (R_in + R_out) and the achieved flow rate (Q), the micropump can be considered as a constant-pressure unit.

In the micropump design, the snake-shaped channel of parallel straight narrow sections provides a high flow resistance compared to a wide channel design. As the FE simulation for a 5 mm-long channel indicates a flow resistance of 15.68 Pa s mm⁻³, the overall flow resistance of the micropump should be that times 50, which is 784 Pa s mm⁻³. According to theories available in the literature,⁴³ the flow resistance of the observation chip and the connecting tube (length: 0.8 m) is estimated as 36 Pa s mm⁻³ and 3903 Pa s mm⁻³, respectively. Therefore, the total flow resistance when the micropump is connected to the observation chip is approximately 4723 Pa s mm⁻³, which is close to the experimentally calibrated value in sec. 2.3 (4818 Pa s mm⁻³).

Then it is important to note that for the TaSSAW device used in the particle separation experiment, the flow resistance is estimated as 3731 Pa s mm⁻³. Therefore, if the micropump adopts a wide-channel design rather than the current snake-shaped narrow channel, one would see a small R_in and a big R_out, which should induce a significantly lower flow rate in the system. To demonstrate this, a wide-channel micropump, as shown in Fig. S10,† is fabricated to replace the snake-shaped one in the experiment, the PIV-measured streaming pattern near the outlet is presented in Fig. 9. It can be observed that although the micropillar array successfully generates a directional downward flow, the device fails to pump outward – the streaming pattern reverses and the fluid flows backward. A similar observation was reported by Mohanty et al.,²⁸ where a steady-state directional flow can be induced by sharp edges in a narrow channel, while the flow direction is reversed in a wide channel.

Fig. 9 The flow field distribution around the micropump outlet in a wide channel (the black areas are outside the channel).

5 Conclusion

This paper presents a constant-pressure acoustic micropump based on the transverse resonance of in-channel sharp-edge micropillars prepared on a substrate. The teardrop-shaped cross-section of each pillar enables it to drive the fluid in the direction of the sharp end, while the diamond array arrangement of multiple pillars diminishes possible vortices and facilitates the streaming relay effect, thereby creating a directional flow. At an operating frequency of 80.5 kHz and a driving voltage of 54 V_p–p, the pump achieves a flow rate of 16.2 μL min⁻¹ and generates a pumping pressure of approximately 1.3 kPa. Meanwhile, the micropump exhibits a response time of less than 40 ms to changes in the driving voltage, enabling its use in programmed pumping. The snake-shaped microchannel endows the pump with a high internal flow resistance, which is crucial for its function as a feed unit for a downstream microfluidic device. The separation of PS particles with diameters of 3.2 and 5.5 μm is achieved using two micropumps integrated with a TaSSAW device. The demonstrated acoustic micropump offers the advantages of simplicity, reliability, flexibility, and controllability, and can be integrated with various microfluidic devices to enable lab-on-a-chip applications.

Data availability

The data supporting this article have been included as part of the ESI.† For any additional requests or queries regarding the data, please contact Dr. Xiasheng Guo at E-mail: guoxs@nju.edu.cn.

Author contributions

Conceptualization: Y. Z. and X. G.; methodology: Y. Z. and Z. W.; investigation: Y. Z., Y. Z., Q. W., H. Z., and X. G.; software: Y. Z. and Q. W.; data curation: Y. Z., Z. W., and H. Z.; formal analysis: Y. Z., Q. W., and X. G.; visualization: Y. Z., Q. W., H. Z., and X. G.; writing – original draft: Y. Z. and X. G.; writing – review & editing: D. Z. and X. G.; resources: D. Z. and X. G.; supervision: D. Z. and X. G.; funding acquisition: D. Z. and X. G.; project administration: X. G.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 82427901, 11934009, and 12374437).

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Footnotes

† Electronic Supplementary Information (ESI) available: The governing equations for finite element simulations, the calibration data for the internal flow resistance of the micropump, a theory for a rough estimation of the resonance frequency of an individual micropump, the top view of the micropump, the fabrication procedure of the devices, the experimental setup, simulated vibrations of a micropillar actuated in different directions, the particle tracking results, the performance of a single micropillar, the schematic diagram of a micropump with a wide channel design, and videos showing the particle motions in the experiments. See DOI: https://doi.org/10.1039/d4lc00997e

‡ D. Zhang and X. Guo are Fellows at the Collaborative Innovation Center for Cardiovascular Disease Translational Medicine, Nanjing Medical University.

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