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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

A novel design for a strip-type microthrottle pump with a rectangular actuator geometry is proposed, with more efficient chip surface consumption compared to existing micropumps with circular actuators. Due to the complex structure and operation of the proposed device, determination of detailed structural parameters is essential. Therefore, we developed an advanced, fully coupled 3D electro-fluid-solid mechanics simulation model in COMSOL that includes fluid inertial effects and a hyperelastic model for PDMS and no-slip boundary condition in fluid-wall interface. Numerical simulation resulted in accurate virtual prototyping of the proposed device only after inclusion of all mentioned effects. Here, we provide analysis of device operation at various frequencies which describes the basic pumping effects, role of excitation amplitude and backpressure and provides optimization of critical design parameters such as optimal position and height of the microthrottles. Micropump prototypes were then fabricated and characterized. Measured characteristics proved expected micropump operation, achieving maximal flow-rate 0.43 mL·min^{−1} and maximal backpressure 12.4 kPa at 300 V excitation. Good agreement between simulation and measurements on fabricated devices confirmed the correctness of the developed simulation model.

One of the main challenges in the development of micropumps appropriate for integration in complex lab-on-chip devices (LOC), total analysis systems (μTAS) and other MEMS [

Here, we propose a modified design of MT pump that differs from reported ones in the shape of the actuator (piezoelectric) and the membrane. We find that the rectangular shape of the actuator and the membrane used in our “strip-type MT pumps” is superior to circular actuators and square membranes [

Numerical device simulation using finite elements discretization has been used for modeling operation of the pump and optimization of crucial design parameters. We developed a fully coupled three dimensional time dependent electro-structural mechanic-fluidic numerical simulation model in which three differential equations are coupled and solved for seven unknowns: electric potential, three structural mechanics displacement components and three components of fluid flow velocities. No reports were found in the literature on 3D numerical models of micropumps with check valves (including throttle type) with PZT actuation. The few investigations of this type mainly cover diffuser type micropumps. Two dimensional (2D) numerical simulation models were presented by Cui

Numerical simulation enabled detail analysis of device operation at a frequency of 1 Hz. Differences between the low (1 Hz) and high frequency (>10 Hz) operation are identified and related to the membrane deflection and the fluid inertia. We used numerical simulation to optimize two crucial design parameters of a proposed strip-type MT pump: height and position of the throttles. These data were used in design and fabrication of a prototype MT device. Measurements were performed on a developed device and the results are compared to the numerical simulation results.

The glass-PDMS-glass-PZT structure is in short described as follows: PDMS part of the micropump (cavity, fluid channel and throttles) was fabricated using soft lithography. A PDMS Sylagard^{®} 184 (Dow Corning Corporation) two-part kit consisting of a pre-polymer (base) and a cross-linker (curing agent) mixed at a ratio 10:1 was applied. A soft replica was fabricated from a silicon mold by using a two-step photolithography and Deep Reactive Ion Etching (DRIE) of silicon. Oxygen plasma activation was used to seal (bond) the PDMS layer between a thicker supporting bottom glass and a thin rectangular shaped glass membrane. Fluid ports were also made from PDMS and bonded onto the supporting bottom glass by oxygen plasma activation. Micropump is driven by a PZT actuator (PIC 255, PI Ceramic^{TM}) that was glued on the top of the glass membrane.

Numerical simulation software Comsol Multiphysics (Ver. 4.2a) has a special module for simulation of MEMS structures that includes piezoelectric materials [

Fluid flow is described by the Navier-Stokes equation:
_{u}_{E}_{E}_{E}^{T}_{0}_{rS}_{rS}^{T}

Electric field is given by a Gauss law:
_{e}

_{E}_{rs}^{TM}). A two-component epoxy adhesive layer between the glass membrane and the PZT is considered to be very thin. As we were not able to measure its thickness its influence was not taken into account in the simulation model.

For PDMS material the density ^{−3} [_{01} = 0.05 MPa, _{10} = 0.25 MPa [

While the no-slip condition is physically more correct, the simulations using the slip condition are usually numerically easier to solve [

The complete mesh was constructed of 116,487 (tetrahedral, prism, pyramid, triangular) elements. Fluidic mesh was densified in the throttles region. Size of the elements in this region was decreased down to 3 μm, while maximum allowed elements size in the remaining channel was set to 200 μm. Usage of coarser mesh (52,430 elements) resulted in less accurate solution (up to 30% deviation as compared to the proposed mesh) for the outlet fluid flow and was therefore inappropriate for simulation purposes.

The solver can be set as a segregated or a fully coupled. In the first case the electro-mechanical solution is obtained first for structural deformations of the channel wall boundaries including the membrane, channel bottom and the throttles. Then the simulation model is solved for the fluid velocity and the pressure. The boundary pressure is fed back to the electro-mechanical solver as a boundary load _{A}^{5}.

The piezoelectric was biased with a sinusoidal voltage signal of amplitude 300 V and a frequency of 1 Hz starting at time 0 s.

^{−1}. For positive applied excitation signal the middle part of the membrane (together with a PZT) moves upwards while the part of the membrane not covered by the PZT moves downwards. This enables widening (opening) of the channel cross-section at the left throttle and narrowing (closing) of the channel cross-section at the right throttle. This can be regarded as a suction phase. During the suction phase the volume between the throttles is increased, however, the flow through the outlet is negative (time frame 0.14 s, Φ_{out} < 0) meaning that the fluid flows into the pump also from the outlet. At maximal excitation signal the membrane is maximally deflected. In this particular moment there is no volume change and due to a low frequency of the applied signal there is also no fluid inertia. Consequently, the volume flow-rate is zero at this moment. During the second quarter of the period (time frame 0.28 s and 0.42 s) the membrane deflection is reducing, the left throttle closes and the right throttle opens. During this-pumping-phase, the volume between the throttles decreases, resulting in a fluid flow in both directions towards the inlet and the outlet. In fact, more fluid flow is observed towards the inlet than the outlet.

The pumping phase continues also through the third quarter of the period when the membrane deflects in the negative

Average flow-rate at the outlet can be computed from simulation results by time integration of the outlet flow-rate divided by the integration time. These results are presented together with the applied excitation signal and the flow-rate in ^{−1}).

The pump operation at higher frequencies (10 Hz–70 Hz) of the applied excitation signal differs substantially from the low frequency operation (1 Hz) due to differences in the speed and shape of the membrane deflection, which result in different maximal volumes between the throttles and opening heights at the throttles.

The main goal of optimization was to determine the positions of throttles that would result in maximal average flow-rate. As already discussed in Subsection 4.1, optimal throttle positions and heights depend on several parameters in particular on the frequency and amplitude of the excitation signal. Measurements as well as simulation (see _{THin} and d_{THout}, respectively).

The optimal position of the right throttle was determined from the position of maximal negative membrane deflection which occurred at d_{THout} = 3 mm. The optimal position of the left throttle has been obtained from a study of average flow-rates at varying positions of the left throttle. As shown in _{Thin} = 8 mm, which was thus chosen as a position of the left throttle in the design of a prototype device.

Influence of throttle height on average flow-rate was analyzed at optimized positions of the throttles determined in the previous paragraph for two different boundary conditions for the fluid velocity (

Strip-type MT pump prototype was designed according to the processing steps in Section 2 and device dimensions described in Section 3 and the positions and heights of the throttles determined through numerical simulation (Section 4). Flow rates were measured on a prototype device using a volumetric method while the back pressure was determined by measuring the height of the fluid column. DI water was used as a pumping fluid in all measurements.

The average flow-rate is increased with increasing frequency of the excitation signal, as presented in ^{−1}·Hz^{−1}) saturating to a value of about 0.43 mL·min^{−1} at a frequency of 60 Hz. Numerical simulation results are shown for two different boundary conditions for the fluid flow at the channel walls. For the slip boundary condition a linear increase with frequency at a rate of 0.007 mL·min^{−1}·Hz^{−1} was obtained and no saturation effect is observed. More realistic results were obtained for no-slip boundary condition resulting in a similar shape of average flow-rate increase but on average about 0.03 mL·min^{−1} smaller than experimentally determined. Average flow-rate saturated at a frequency of 70 Hz. The differences between the measurements and the simulation can be a consequence of several elements starting from non-ideal fabrication process to non-suitably chosen material parameters. In particular, the material parameters of the PDMS can vary substantially depending on the processing steps in particular on the curing temperature and the proportion of the curing agent [

The throttles never completely close the channel during operation. For this reason they are additionally susceptible to the increased back pressure. ^{−1}·kPa^{−1} reaching zero at a back pressure of 12.4 kPa. The point of zero average flow was determined by the maximal height of the fluid column (DI water). Numerically obtained rate of decrease was 0.04 mL·min^{−1}·kPa^{−1} reaching zero at a back pressure of 9.5 kPa.

Increased amplitude of the excitation signal increases also the magnitude of the membrane deflection. Here, it should be noted that membrane deflection depends also on the frequency of the applied signal as presented in

In the present work a novel, rectangular strip-type micro-throttle pump is proposed and investigated by numerical device simulation as well as experimental work. The pump structure is based on rectangular actuator geometry, resulting in more efficient chip surface consumption compared to existing micropumps with circular actuators. Proper determination of design parameters was made possible by development and usage of a fully coupled electro-fluid-structural mechanics 3D numerical simulation model in COMSOL Multiphysics. Only after taking into account the inertial fluid flow, no-slip boundary conditions and hyperelastic material model for the PDMS, did simulations yield good agreement with measured results. In order to assure convergence and accuracy of the simulation results the mesh has been locally refined, in particular in the regions near the throttles. Convergence has been improved after the variables, in particular the pressure, were appropriately scaled. Significant differences in simulation results were obtained for boundary conditions taking into account zero-fluid velocity at the channel walls (no-slip condition) and non-zero boundary fluid velocity (slip condition). More accurate results were obtained with the no-slip condition.

Numerical simulations were used for optimization of important design parameters such as optimization of the position and height of the throttles. For optimal pump operation with sinusoidal actuation signal of amplitude 300 V and frequency 70 Hz, the throttles position were 8 mm and 3 mm from the PZT edge, for the right and left throttle, respectively. Optimal height of the throttles for a 100 μm channel height was determined at 80 μm.

The analyzed strip-type micropump structure was designed and fabricated in accordance to the optimal positions and height of the throttles found by numerical simulation. Measurements on fabricated prototypes revealed saturation of average flow-rate to a value of 0.43 mL·min^{−1} at a frequency of 60 Hz. In simulations, the average flow-rate saturated to a value of 0.39 mL·min^{−1} at a frequency of 70 Hz. The agreement between simulated and measured results was particularly good at low (10 Hz) and higher (above 50 Hz) frequencies. Average measured flow-rate linearly decreases with back-pressure at a rate of 0.034 mL·min^{−1}·Pa^{−1}, reaching zero at a back-pressure of 12.4 kPa. Numerically obtained rate of decrease was 0.04 ml·min^{−1}·Pa^{−1} reaching zero at a back pressure of 9.5 kPa. Good agreement between measurements and simulations was found for average flow rate increase with increasing amplitude of the excitation signal in particular up to 300 V. Approximately quadratic increase was obtained in both cases.

The agreement between simulation and measurements on fabricated devices confirmed the correctness of the developed simulation model. Measured pump characteristics proved expected micropump operation, achieving maximal flow-rate 0.43 mL·min^{−1} and maximal backpressure 12.4 kPa at 300 V excitation. Thus, the microthrottle simulation model proposed here might be useful in aiding further optimizations of the device as well as facilitate the design of improved micropumps based on piezoelectric actuation.

Authors would like to thank the Slovenian Research Agency/ARRS and Ministry of Education, Science, Culture and Sport for their support of this work.

COMSOL Inc. Available online:

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Fabricated strip-type MT pump.

Geometry and dimensions of the analyzed structure (dimensions are not to scale).

Deflection of the membrane together with a PZT actuator at maximal value of the excitation signal (300 V). Scaling factor in

Structural deformations, pressure distribution and fluid velocity (vectors) for selected time frames (1 Hz, 300 V).

Numerical simulation of time dependent fluid flow at the channel outlet as a consequence of 1 Hz 300 V sinusoidal excitation signal.

Numerical simulation of membrane deflection at maximal excitation signal (300 V) in a middle cross-section along the channel for three frequencies: 1 Hz, 50 Hz and 70 Hz. An insert provides data on of the channel opening height.

Numerical simulation of time dependent fluid flow at the channel outlet as a consequence of 70 Hz 300 V sinusoidal excitation signal.

Design details of the MT pump and positioning of the throttles.

Numerical simulation of average flow-rate depending on the position of the left throttle after five time periods (70 Hz, 300 V). Right throttle is fixed at 3 mm.

Numerical simulation of average outlet flow-rate for varying throttle heights after five time periods (70Hz, 300V).

Average flow-rate depending on the frequency of the applied excitation signal (at amplitude of 300 V).

Average flow-rate depending on the back pressure (70 Hz, 300 V).

Average flow-rate depending on the amplitude of the excitation signal (at frequency of 70 Hz).

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