Combination Rules for Multichamber Valveless Micropumps

JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 22, NO. 5, OCTOBER 2013 1133

Combination Rules for MultichamberValveless Micropumps

Alireza Azarbadegan, Ian Eames, Adam Wojcik, Cesar A. Cortes-Quiroz, and William Suen

Abstract—The general design rules indicate that when identicalmacroscale pumps (each with a maximum flowrate Qm, andmaximum pressure drop �Pmax) are combined in series, themaximum flowrate is Qm, but the maximum pressure dropbecomes 2�Pmax, while combined in parallel the maximumflowrate becomes 2Qm, and the maximum pressure is �Pmax. Inthis paper, we test whether these design rules apply to microscalevalveless micropumps using highly resolved CFD calculations.The variation of flow with pump pressure drop is studiedby varying the resistance of an external circuit. The analysisconfirmed that the macroscale design rules for macroscale pumpsare applicable to microscale pumps. The study also enabled theinfluence of different forcing strategies on the pump performanceto be analyzed. [2012-0208]

Index Terms—CFD, microfluidics, micropump, microsystemdesign, multichamber, numerical analysis, valveless

I. Introduction

P LANAR valveless micropumps have many favorablecharacteristics, such as ease of manufacture, miniaturiza-

tion, and the absence of moving parts. Many configurationshave been previously examined, including single-chamber [1]and double-chamber in parallel [2], and double-chamber inseries configurations [3], but the effect of having more thantwo pump chambers and the requisite driving sequence hasnot yet been studied. Due to the complicated nature of theflow in these pumps, especially when there are more thantwo chambers, it is important to be able to apply simplerules for estimating pump performance and characteristics.In this paper, the performance of multichamber valvelessmicropumps in a closed circuit is examined, using CFD, tobetter understand their behavior.

In the context of macroscale pumps, established designrules exist for how the performance envelope is changed whenidentical pumps are combined, either in series or in parallel [4].For instance, when macroscale pumps with maximum flowrate,Qm, and maximum pressure-drop, �Pmax, are combined inseries, they generate a maximum flowrate of Qm and the

Manuscript received July 18, 2012; revised February 16, 2013, acceptedFebruary 19, 2013. Date of publication April 23, 2013; date of current versionSeptember 27, 2013. This work was supported in part by a kick-start fundfrom the U.K. SIRAC Network at the initial stage of the project. SubjectEditor Y. Zohar.

A. Azarbadegan, I. Eames, A. Wojcik, and W. Suen are with University Col-lege London, London, WC1E 7JE, U.K. (e-mail: [email protected]).

C. A. Cortes-Quiroz is with the University of Hertfordshire, Hatfield, AL109AB, U.K.

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JMEMS.2013.2253717

Fig. 1. Schematic of (a) 2CP , (b) 4CPP , and (c) 4CPS configurations. Vmp

and Asys are the total volume and surface area of each pump, respectively.Lch is the length of the connecting channel which is indicated as a filled line.

maximum pressure-drop of 2�Pmax, while in parallel, themaximum flowrate is 2Qm and the maximum pressure-dropis �Pmax. Therefore, a critical question in developing designrules for microscale pumps is whether these design tools workfor small scale systems. With a particular pump chambersarrangement, there are multiple forcing strategies, which canbe applied, so another question is whether, for a multichamberpump, can such strategies help bolster the performance of thesystem.

As a starting point, a double-chamber pump [Figs. 1(a) and2(a)] was considered. In this configuration, chambers A and Bare forced out of phase. This configuration was chosen becauseit represented the smallest number of chambers required toensure that the total volume of a closed system remained fixed.

Schematics of the micropumps studied in this paper areshown in Figs. 1 and 2, in which the four-chamber pumpsresulted from combining the pumps in Figs. 1(a) and 2(a) inparallel and series. Thereby, the design rules were examined by

1057–7157 c© 2013 IEEE

1134 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 22, NO. 5, OCTOBER 2013

Fig. 2. Schematic of (a) 2CS, (b) 4CSP , and (c) 4CSS. Vmp and Asys arethe total volume and surface area of each pump, respectively. Lch is the lengthof the connecting channel which is indicated as a filled line.

combining the basic building blocks (single chamber pump)into parallel and series configurations. In total, six differentconfigurations were considered including a double-chamberpump in parallel (2CP), two parallel double-chamber pumpsin parallel (4CPP), two parallel double-chamber pumps inseries (4CPS), a double-chamber pump in series (2CS), twoseries double-chamber pumps in parallel (4CSP), and twoseries double-chamber pumps in series (4CSS). These pumpsare considered in a closed-circuit arrangement with an incom-pressible fluid, hence the chambers are normally forced outof phase. The simulations to determine the design rules areidentified as T1 and correspond to when the chambers A and B

are forced out of phase by π rad (see discussion in [5], [6], and[7]). In this case, the chambers C and D are forced in the samemanner as A and B, respectively, so that the configurationsrepresent in parallel and in series pumps. To test the influenceof forcing strategy, chambers A and B are forced in phase,and the corresponding configurations identified as T2; theseconfigurations require both chambers C and D to be drivenout of phase (by π radians) compared to chambers A and B.

Pump characteristics are usually defined in terms of thevariations of flowrate with circuit pressure-drop. The max-imum volume flux, Qm, and maximum pressure that thepump can withstand, �Pmax, characterize the performanceenvelope of the device. In this paper, the pump performanceenvelopes were calculated using CFD by varying the resistanceof an external circuit which was connected to the two sidesof the micropump. The CFD simulations also permitted anexamination of the effect of geometry, number of chambers,and forcing arrangement, upon pertinent aspects of the flowthat define the pumping efficiency.

It is important to note that the characteristics of a pumpare generally reported in the form of a performance curve,i.e., flow rate versus pressure difference, where the pressuredifference refers to a constant external pressure against whichthe pump works. In particular, most experimental studies forassessing microscale pumps involve setting a resistance tothe pump in the form of a hydrostatic head in an open loop

Fig. 3. (a) Schematic of a double-chamber valveless micropump (2CP).(b) Plot of the actuator deflection based on (1).

system. Nevertheless, in practical applications, the resistanceto the pump is caused by a circuit resistance, for instance,in the case of micro-heat exchangers. In this paper, as it hasbeen indicated, the resistance applied to the pump is causedby an external closed loop circuit. For valveless micropumps,which are characterised by a weak rectified mean, this is asensible way to examine pump performance for incompressiblefluids [8]. Otherwise, the boundary conditions for open loopconfigurations applied at the inlet or outlet (such as oscillatoryvelocity or pressure) require a semi-empirical closure. Themultichamber configurations studied in this paper (with eitherforcing strategy, T1 or T2) significantly reduce the largeroscillating component of the flow observed in single-chambervalveless micropumps [5]. Also, their boundary conditionsare physically consistent, since that inlet and outlet bound-aries need not to be considered. The fluctuating flow in themultichamber valveless micropump configurations is analyzed,and the resulting data are used to develop the curves ofvariation of the average flow rate through the connectingcircuit with the mean pressure drop (circuit resistance). Themaximum flow rate and pressure-drop, which determine thepump performance, are obtained by extrapolating the leastsquare linear fit through the data in these curves.

This paper is organized as follows. The pump ge-ometry is described in Section II-A, the computationalmodel in Section II-B, and flow diagnostics and model inSection II-C. This is followed by the computational resultsand discussion in Section III, including velocity analysis inthe channel in Section III-A, pressure-drop along the channelin Section III-B, and maximum flowrate in Section III-C. Theimplications of this paper for the design of multichambervalveless micropumps are then discussed in Section IV.

II. Computational Model and Parameters

In this section, the computational methodology and modelto analyze a series of closed-circuit valveless micropumps isdescribed. Fig. 3(a) shows a detailed schematic of a paralleldouble-chamber micropump (2CP), which contains the pumpchambers, the diffuser/nozzle elements and a central channelthat gives the flow resistance. Fig. 3(b) depicts the pumpchamber deflection. To increase the computational efficiency,

AZARBADEGAN et al.: COMBINATION RULES FOR MULTICHAMBER VALVELESS MICROPUMPS 1135

TABLE I

Variation of Vch,p and �PCFD with Mesh Quality

the channel width Wch (connecting the ends of the pump),which sets the resistance of the connected circuit, was madeshort to reduce the burden of a large computation domain. Fora fixed forcing frequency, the maximum deflection of center ofactuator, Xd (Fig. 3(b)), generates the pump volume flowrate,Q. The CFD analysis, varying Wch, over the range 0.5−2mm,changes the resistance of the fluid circuit and enables exploringthe relationship between volume flowrate and pressure-drop.Experimental studies of pump characteristics, typically, havevaried the external pressure-drop across the pump, using ahead of liquid, rather than an external resistance [2], becauseit is easier to implement and assess pump characteristics usingthis method.

A. Pump Geometry

For the model, the pump forcing angular frequency, ω, andchamber radius, R, were fixed at 540Hz and 6.5mm, respec-tively. These parameters were chosen because they are typicalof a valveless micropump, as for instance in [2]. The pumpdepth, h, diffuser/nozzle throat width, Wt , diffuser/nozzleelement length, Lv, and diffuser/nozzle larger width, W0, wereset to be 0.3mm, 0.3mm, 4.1mm, and 1mm, respectively. Toinvestigate changes in the flow characteristics, such as pressurefield, Reynolds number and vorticity field, one can varyeither Wch or Xd (Fig. 3). In this paper, the chamber volumedisplacement, Xd , was fixed as 5.6μm and the channel width,Wch, varied (0.5, 1, and 2mm) to change the circuit resistance.To understand the performance of these micropumps in detail,30 simulations were carried out, considering the three differentcircuit resistances given by the width of the connecting channelfor each configuration (Table II.

The deflection of a clamped circular membrane under auniformly distributed force can be approximated [9] as

W(r) = Xd

(1 − r2

R2

)2

, (1)

and is plotted in Fig. 3(b). This relationship satisfies theboundary conditions W(R) = W ′(R) = 0 and W ′(0) = 0 whichare consistent with a clamped circular actuator. This modelis valid, provided the chamber pressure is much smaller thanthe pressure that blocks the actuator deflection. The membranedeflection generates a chamber fluctuating volume of

Vc = Vmsin ωt, (2)

where Vm = 2∫ R

0 2πW(r)dr = 23πR2Xd (here each chamber

has two actuators on both sides).

Fig. 4. Variations of average velocities, Vch, versus time for 20 cycles for(a) parallel configurations (2CP , 4CPP , and 4CPS). (b) Series configurations(2CS, 4CSP , and 4CSS), for Wch = 1mm and Xd = 5.6μm.

B. Implementation of Computational Model

The computational fluid domains were meshed using AN-SYS 11. The mesh resolution varied from 1.9 million elements(for 2CS with Wch = 0.5mm) to 4.7 million elements (for4CPP with Wch = 2mm) for the defined geometries. The flowin this closed-circuit configuration is driven by the movementof the pump chamber walls and does not require inlet nor exitboundaries to be considered. The influence of mesh quality onthe results of the numerical simulations was investigated withfive different grid sizes (higher and lower resolutions) and bycomparing mean channel velocity and pressure drop results.Table I summarises the mesh sensitivity analysis. In the finalanalysis, case four was chosen as the optimum grid size forthis paper.

To compute the velocity and pressure fields, the laminarincompressible model of ANSYS CFX 11 was employed withwater, as the working fluid, at room temperature. The transientsimulations were performed over a time period t = 0 tot = 20Tp, where Tp = 2π/ω was the forcing period of onecycle. Similar to the study described in [8], the initial transientbehavior settled down after six cycles.

C. Flow diagnostics and model

The average channel velocity, Vch,p, and the average pres-sure drop, �PCFD, were defined over one forcing cycle afterthe system passes its transient response mode (t > 10Tp)

Vch,p =1

Tp

∫ t+Tp

t

V ch(t)dt t > 10Tp, (3)


Fig. 5. Pressure-drop across the circuit resistor, �PCFD, is plotted as afunction of time for 18 < t/Tp < 20 for (a) parallel configurations (2CP ,4CPP , and 4CPS), and (b) series configurations (2CS, 4CSP , and 4CSS),for Wch = 1mm and Xd = 5.6μm.

�PCFD =1

Tp

∫ t+Tp

t

�PCFD(t)dt t > 10Tp, (4)

where Vch, the average velocity on a transverse plane in themiddle of the connecting channel of cross-sectional area Ach

is defined by

Vch(t) =1

Ach

∫Vch(t)dA, (5)

and �PCFD is the pressure drop across the connecting channel.By mass conservation, the volume flux through any section ofthe connecting channel is the same, for convenience we choosethe channel mid point. Hence, the average flowrate through theconnecting circuit can be estimated by

Q = Vch,ρAch. (6)

The maximum Q and �P determine the pump performance.To understand the performance, it is necessary to focus uponthe diagnostics in more detail and to understand the rectifiedflow through the diffuser/nozzle. The average velocity, V t(t),and the maximum average velocity in the diffuser/nozzlethroat, V t,max, are defined as

V t(t) =1

At

∫Vt(t)dA, V t,max = max

τ<t≤τ+Tp

V t(t), (7)

TABLE II

Summary Table Of All Simulations. Predicted Circuit

Pressure-Drop, Channel Reynolds Number, Rch , And

Corresponding Area-Averaged Channel Velocity Are Listed

For Each Configuration

where At is the throat cross-sectional area of the dif-fuser/nozzle element. The time average is taken over the period10 < τ/Tp < 19 after the initial transients have decayed. Therectification efficiencies of valveless pumps are typically low,so that the maximum velocity V t,max � Vmω/2At , as it formsthe largest component to the flow compared to the rectifiedcomponent.

III. Results and discussion

A. Average Velocity in the Middle of Channel

Fig. 4 shows the modeled time variation of the area-averaged velocity measured in the middle of the channel,Vch(t), for different configurations with a fixed channel widthof Wch = 1mm. After around six cycles the initial transientcaused by the flow starting from rest has decayed. The effect offorcing arrangement has a significant effect on the amplitudeof velocity fluctuations in cases 4CPS, 4CSS, and 4CSP . Anobservation from Fig. 4 is that the velocity response of 2CP

and 4CPP T2 are very similar. The same occurs for 2CS and4CSS T1. The difference is so small that the curves lie onone another, and are difficult to distinguish. Fig. 4(a), showsthat for the case 4CPS T2, there is a large scale oscillationin the external circuit as fluid is shifted mainly betweenthe individual pump chambers. Large scale oscillations occurin all the series pump configurations except in 4CPS T2[Fig. 4(b)].


Fig. 6. Mean flow-pressure characteristics are plotted for (a) parallel con-figurations (2CP , 4CPP , and 4CPS); (b) series configurations (2CS, 4CSP ,and 4CSS), for different circuit resistances, but for a fixed forcing frequencyof 540Hz.

B. Pressure-Drop Along the Channel

Fig. 5 shows the modeled pressure-drop across the connect-ing channel for the last two cycles (18 < t/Tp < 20) and afixed channel width of Wch = 1mm. The values of �PCFD

and Vch,p for each pump configuration and different channelwidths are summarized in Table II. Also, in the connectingchannel of each configuration, the nondimensional Reynolds(Rech) and Womersley (Woch) numbers are calculated byRech = ρVch,pDhch/μ and Woch = Dhch

√ρω/μ, where Dhch

is the channel hydraulic diameter. It is evident that changingthe forcing arrangement leads to the change in the amplitudeof �PCFD and �PCFD. The higher chamber pressure, Pch,max,can be a limiting factor for the pump performance, because ithinders the effective displacement of the actuator, which in-fluences the performance of the whole system. From Table II,it can be concluded that 4CPP T2 and 4CSS T2 cases arenot desirable as Pch,max values for these cases are much higherthan other cases, which could make them more susceptible tocavitation and actuator problems.

The parallel configurations, 2CP , 4CPP ∗, 4CPS T1, donot generate a large scale oscillating movement of fluid in thepump circuit that is evident for 2CS, 4CSP T1 and 4CSS ∗.The ∗ here denotes either T1 or T2. This explains why thepressure amplitudes in Fig. 5(a) are much smaller than that

Fig. 7. Normalized mean pressure-normalized mean flow characteristicsare plotted for (a) Type 1 forcing arrangement, and (b) Type 2 forcingarrangements. The full line corresponds to the response curve of a singlepump while the red/black dashed lines correspond to pumps operating inseries/parallel.

in Fig. 5(b) (except, for 4CPS T2). The maximum pressureoccurs at twice the frequency in Fig. 5(a) than in Fig. 5(b).This is because the pressure-drop in Fig. 5(a) is largely due tothe variation of the fluid kinetic energy, 〈u|u|〉 (where u is theflow speed), which has a frequency of 2ω, whereas, in Fig. 5(b)the pressure is dominated by the fluid acceleration du/dt,which has a frequency of ω. The intercepts t/Tp = 18, 19, and20 are noted on the abscissa, and highlight that the pressure hasa phase lag from the channel velocity. This is approximately0.05π and 0.45π in Figs. 5(a) and (b), respectively, as com-pared to the anticipated values of 0 and π/2. This differenceis due to the unsteady nature of the flow and viscous effects.

We see that for the T1 examples, �P typically decreasesby a factor of four as Wch increases from 0.5 to 2.0 mm whichis consistent with the pressure drop estimates of �P ∼ LchμQ

Wchh3

valid for viscous flow in pipes. However, this behavior is notobserved in the T2 examples. In these cases, the oscillatorycomponent of the flow may be significantly larger than themean component. A major part of the total resistance to thepump is provided by the pipes connected to the circuit resistorand �P varies over a much greater range than for T2 examplesthan for T1 ones.

C. Maximum Flowrate

The variation of the maximum flowrate with the meanpressure-drop (Table II) is shown in Fig. 6. These Q − �P


TABLE III

The Maximum Flowrate, Qm , (Extrapolated from Fig. 6) and

Pumping Efficiency of Different Pump Configurations

curves typically take on a reasonably linear shape for valvelessmicropumps as confirmed by many theoretical and experimen-tal studies, [5], [6], [7]. The maximum flowrate and pressurethat each pump produces are obtained by extrapolating theleast square linear fit through the data, listed in Table III. Thelines are plotted in Fig. 6. The forcing strategy correspondsto parallel and series configurations of 2CP and 2CS. TheQ−�P curves for 4CP and 4CS were normalized by the 2CP

and 2CS values, respectively, for flowrate and pressure-drop,and are plotted in Fig. 7. In Fig. 7, the dashed curves representthe operation under general design rules of large scale pumpsplaced in series and parallel. The design rules give a reasonableprediction of pump properties, except for the case of 4CPP

and low circuit resistances. This is likely to be due to thelength of the connecting pipes being typically longer than theother examples, and narrower than the circuit resistor.

A measure of pump efficiency is calculated by dividing Qm

by the maximum theoretical flowrate that can be generatedif all the occupied fluid volume inside a pump, Vmp, isdisplaced in one cycle. This is a measure of micropumpflowrate compared to its size, so it can be described as thesize efficiency. Based on Table III, 2CP and 4CSP T2 arethe most size-efficient configurations in this paper. It is alsointeresting to see that the 4CSP T2 configuration has thehighest Qm, whereas 2CS has the lowest Qm amongst thecases under study. This highlights the importance of chamberarrangement and forcing sequence to optimize the systemdesign. It is clear that by changing the forcing arrangement andconfiguration from 4CSS T1 to 4CSP T2, the maximumflowrate can be increased about 2.5 times.

The explanation is that the resistance in the pump circuit isa combination of that in the connecting channel and that ofthe pump. The flowrate does not change as the resistance inthe connecting channel varies, because it is dominated, in thiscase, by the resistances in the pipes connected to the circuitresistor.

IV. Conclusion

The main purpose of this paper was to examine whetherthe design rules for combining macroscale pumps apply to

microscale valveless pumps. A series of numerical modelswere developed using a basic (parallel or series) pump, whichwere studied in parallel and series. This configuration waschosen because the individual pumps conserved mass. Thepump characteristics were studied in the same manner as amacroscale pump by varying the resistance across the pumpand analyzing how the volume flux varied. The resistance wasvaried by altering the width of the connecting pipe whichforms the external circuit.

The general rules are that when identical pumps (eachwith a maximum flowrate Qm, and maximum pressure drop�Pmax) are combined in series, the maximum flowrate is Qm,but the maximum pressure becomes 2�Pmax; combined inparallel the maximum flowrate is 2Qm, but the maximumpressure is �Pmax. This new study largely confirms that thesedesign rules also apply to microscale valveless micropumps.It is likely that many microscale fluid networks will requiremultiple pumps connected as part of a circuit, and these simpledesign rules enable the effects of combining many pumps tobe better understood. This paper also provided an opportunityto examine how the forcing strategy for valveless micropumpscould potentially improve the pumping efficiency.

References

[1] E. Stemme and G. Stemme, “A valveless diffuser/nozzle-based fluidpump,” Sens. Actuators A, Phys., vol. 39, no. 2, pp. 159–167,1993.

[2] A. Olsson, G. Stemme, and E. Stemme, “A valve-less planar fluid pumpwith two pump chambers,” Sens. Actuators A, Phys., vol. 47, no. 1–3,pp. 549–556, 1995.

[3] A. Ullmann, “The piezoelectric valve-less pump-performance enhance-ment analysis,” Sens. Actuators A, Phys., vol. 69, no. 1, pp. 97–105,1998.

[4] I. Karassik, J. Messina, P. Cooper, and C. Heald, Pump Handbook, Int.Student ed. New York, NY, USA: McGraw-Hill Professional, Nov. 2007.

[5] I. Eames, A. Azarbadegan, and M. Zangeneh, “Analytical model ofvalveless micropumps,” J. Microelectromech. Syst., vol. 18, no. 4, pp.878–883, 2009.

[6] A. Azarbadegan, C. Cortes-Quiroz, I. Eames, and M. Zangeneh, “Anal-ysis of double-chamber parallel valveless micropumps,” Microfluid.Nanofluid., vol. 9, no. 2-3, pp. 171–180, 2010.

[7] A. Azarbadegan, E. Moeendarbary, C. Cortes-Quiroz, and I. Eames, “In-vestigation of double-chamber series valveless micropump: An analyticalapproach,” in Proc. ICQNM, 2010, pp. 107–112.

[8] A. Azarbadegan, I. Eames, S. Sharma, and A. Cass, “Computational studyof parallel valveless micropumps,” Sens. Actuators B, Chem., vol. 158,no. 1, pp. 432–440, 2011.

[9] N.-T. Nguyen and S. T. Wereley, Fundamentals and Applicationsof Microfluidics, 2nd ed. Norwood, MA, USA: Artech House, May2006.

Alireza Azarbadegan is a Visiting Researcher andLecturer at the Department of Mechanical Engineer-ing, University College, London, U.K. His currentresearch interests include fluid mechanics from acomputational, mathematical and experimental pointof view, microfluidics, and modeling and simulationof multiphysic systems.


Ian Eames is currently a Professor of fluid mechan-ics at the University College, London, U.K. He wasa Leverhulme Senior Research Fellow from 2010 to2011, Advanced EPSRC Research Fellow from 1999to 2004, and a Junior Research Fellow from 1994 to1997 at St. Catharine’s College, Cambridge, London,U.K. His current research interests include fluidmechanics from a computational, mathematical, andexperimental point of view.

Prof. Eames was a recipient of the Royal Academyof Engineering Global Research Award in 2007.

Adam Wojcik received the Ph.D. degree in thin filmdeposition and growth techniques from the ImperialCollege, London, U.K, in 1989. In addition to thescience qualifications, he also received the B.A andM.A degrees in archaeology and classics.

He has been with the scientific instrument industryfor six years, and as a Visiting Lecturer with ImperialCollege before becoming a Lecturer at the UniversityCollege, London, U.K, in 1995. His experience liesin the deposition of thin films of materials, suchas oxides and semiconductors, using novel metal-

lorganic chemical vapor techniques, but he is also involved in the design anduse of equipment for detecting and monitoring the growth of cracks in metalsusing the ac and dc potential drop method. He works with electron beaminduced current techniques for the detection of defects in materials and hasresearch interests in the field of solid oxide fuel cells. His recent work includesthe development of a novel form of thermal cycling apparatus for ceramicspecimens, enhancing bond strengths of dental adhesives, and the use ofammonia gas as a fuel source in fuel cells. He also works in cross disciplinaryareas where material science meets archaeology and paleontology. His currentresearch interests include the study of materials and the development oftechniques for materials testing.

Dr. Wojcik is a member of the Department’s Materials and StructuralIntegrity Research Group.

Cesar A. Cortes-Quiroz received the B.Sc. de-gree in mechanical engineering from the PontificalCatholic University of Peru in 1995, the M.Sc. de-gree in mechanical engineering from the Universityof London, London, U.K., in 2004, and the Ph.D.degree in microfluidics from the Department of Me-chanical Engineering, University College London,London, U.K., in 2010.

He is currently a Post-Doctoral Research Associatein microfluidics and microengineering with the Sci-ence and Technology Research Institute, University

of Hertfordshire, Hatfield, U.K. He became an accomplished Project Engineerwith extensive experience acquired across several engineering, procurement,construction and management projects in energy, mining and metals, and oiland gas. Being a qualified Mechanical Engineer since 2000, his genuineinterest includes applied sciences and engineering that led him back toacademia. His current research interests include design and optimizationof microfluidic devices, integration of components of lab-on-a-chip andMEMS, characterization and control of multiphase flows, and application ofmultiphysics solutions in microsystems.

Dr William Suen is currently a Senior Lecturer withthe University College, London, U.K. He specializesin refrigeration and air-conditioning research, witha particular interest in evaluation and applicationof non-CFC replacement refrigerants. His other re-search interests include micro-refrigeration, controlsof ac systems, hybrid refrigeration systems, anddevelopment of FDD for binary ice systems.

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Combination Rules for Multichamber Valveless Micropumps