A microscale pulsatile flow device for dynamic cross-slot rheometry.

A microscale pulsatile flow device for dynamic cross-slot

rheometry.

Citation for published version (APA):

Burgt, van der, R. C. H., Anderson, P. D., Toonder, den, J. M. J., & Vosse, van de, F. N. (2014). A microscale

pulsatile flow device for dynamic cross-slot rheometry. Sensors and Actuators, A: Physical, 220, 221-229.

https://doi.org/10.1016/j.sna.2014.09.019

DOI:

10.1016/j.sna.2014.09.019

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Published: 01/01/2014

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ContentslistsavailableatScienceDirect

Sensors

and

Actuators

A:

Physical

jo u r n al hom e p a g e :w w w . e l s e v i e r . c o m / l o c a t e / s n a

A

microscale

pulsatile

flow

device

for

dynamic

cross-slot

rheometry

René

C.H.

van

der

Burgt

_,

_Patrick

_D.

_Anderson

_,

_Jaap

_M.J.

_den

_Toonder

_,

Frans

N.

van

de

Vosse

a_{CardiovascularBiomechanics,DepartmentofBiomedicalEngineering,EindhovenUniversityofTechnology,TheNetherlands}

b_{StructureandRheologyofComplexFluids,DepartmentofMechanicalEngineering,EindhovenUniversityofTechnology,TheNetherlands} c_{Microsystems,DepartmentofMechanicalEngineering,EindhovenUniversityofTechnology,TheNetherlands}

a

r

t

i

c

l

e

i

n

f

o

Articlehistory:

Received30January2014

Receivedinrevisedform21August2014 Accepted2September2014

Availableonline31October2014

Keywords: Microfluidics Diaphragmpump Micro-PIV Pulsatileflow

Instantaneousflowmeasurements Dynamicrheometry

a

b

s

t

r

a

c

t

Thedesignofmicropumpsreceivedfullattentionsincemicromanufacturingandmicrofluidicstechniques havebecomepartoftheengineeringtoolbox.Thefocusofmoststudieshasbeenontheefficiencyofthese pumps:maximalnet(mean)flowatminimalinputpower.

Weintroduceapulsatilemicropumpsystem,thatisdesignedtodynamicallyperfuseacross-slot micro-rheometer.Tocharacterizecomplexmaterialsdynamically,unsteady(oscillatingandpulsating)flows withafrequencyrangeof0.1–20Hzatamplitudesof10–100nl/sarerequired.Hence,inourstudythe priorityconcerningmicropumpsshiftsfromefficiencytotheabilitytoproducewell-definedflowpulses. Forthispurpose,anoscillatorymicropump,basedonadeflectingdiaphragm,isdesignedandtested. Byperiodicallydeflectingasteelplateintoarigidfluidicchamberusingavoicecoil,anoscillatoryflow isproduced.Platedeflectionisgovernedbybending,suchthatthestrokevolumeisproportionaltothe currentthroughthevoicecoil.Theoscillatoryflowissuperimposedtothesteadyflowofasyringepump. Thepumpsystemobtainedischaracterizedbymicroparticleimagevelocimetry(␮-PIV)measurements usingfluorescencemicroscopy.

Theresultsshowthatthesuperpositionofthemeanflowofthesyringepumpandanoscillatoryflow ofthediaphragmpump,isvalid.Alinearscalingofflowamplitudewithfrequencyanddrivingvoltageis foundforfrequenciesupto4Hz,afterwhichexcessivedampingtakesplace.Thecausesforthisbehavior areidentifiedandexplaintheresultswell.Withthisinformation,amplitudescalingforsinusoidalflow wavesofdifferentfrequenciescanbeperformed.Inconclusion,withthepresentsystem,pulsatileflow withawell-definedwaveformandadynamicrangeupto16Hz,canbecreatedinanopen-loopdriven fashion.

©2014ElsevierB.V.Allrightsreserved.

1. Introduction

The last 30 years, various micromachining techniques were

introduced,which openedthefield of MEMSandmicrofluidics.

Theneedtodisplacefluidsatsmallscalefollowed,whichresulted

inthedesignandevaluationofdozensofmicroscalepumps(for

extensivereviews,see[1–7]).Indisplacementmicropumps,a

mov-ingboundaryorliquiddisplacementexertsapressureforce,while

dynamicmicropumpsrelyonadirectenergytransfertothefluid

tobepumped.Theformerusuallygeneratepulsatileflow,the

lat-terdrivethefluidinacontinuous,constantmanner[3].Thefocus

hereisondiaphragm displacementmicropumps,where a solid

diaphragmisdeflectedintoavalvechambertopushfluidforward.

∗ Correspondingauthor.Tel.:+31402474218.

Thesepumpscanbeequippedwithpassivecheckvalveswith

mov-ingparts(flaps[8]orballs[9,10]),ornon-movingvalves(e.g.Tesla

microvalve[11]),orbevalveless(nozzle-diffuserdesign[12,13],

vortexareas[14]).

Actuationis performedinseveralways,amongwhich

piezo-electric [15–18] and electromagnetic or voice coil actuators

[9,12,15,19]aremostpopular.Often,thepumpisintegratedwith

afluidicsystem,rangingfromlab-on-a-chip[20]or

micro-total-analysissystems(␮-FACS,-ELISAor-mass-spectrometer[21])to

miniaturizedfossilfuelcellbatteries[22].

During characterization of these pumps, thefocus has been

ontheefficiencyandabsolutenetflow:howcanamaximalnet

flowbeproducedwithaminimalamountofpowerinput.

How-ever,forsomeapplications,suchastheculturingof endothelial

cellsinamicrofluidicchannel,theperiodicpulsatilityisofinterest,

whereasefficiencyisofsecondaryimportance.Anotherapplication

http://dx.doi.org/10.1016/j.sna.2014.09.019

222 R.C.H.vanderBurgtetal./SensorsandActuatorsA220(2014)221–229

symbol description,unit

A transferfunctiongain,–

a diaphragmradius,m

at connectingtuberadius,m

C compliance,m4_s2_kg−1

Csat compl.saturatedfluid,m4s2kg−1

D plateconstant,m DH hydraulicdiameter,m E Young’smodulus,Pa FL Lorentzforce,N f flowfrequency,Hz f0 naturalfrequency,Hz fc cutofffrequency,Hz

fres resonancefrequency,Hz

H channelheight,m

Hc heightpumpchamber,m

h diaphragmthickness,m

I inertance,kgm−4

Ic inertance,kgm−4

k diaphr.springconstant,Nm−1

L tubelength,m

Lt tubelength,m

M equivalentmass,kg

p1,2 transferfunctionpoles,–

¯

Q meanflow,m3_s−1

Q1,2 outflowofcross-slot,m3s−1

Qout systemicoutflow,m3s−1

Qpulse pulsatileflow,m3s−1

Qsyringe syringepumpflow,m3s−1

R(1,2) hydraulicresistance,kgm−4s−1

Remax (max.)Reynoldsnumber,–

r radialcoordinatediaphr.,m

r0 pistonradius,m

s Laplaceparameter,–

Vmax maximumvelocity,ms−1

W channelwidth,m

y(r) diaphragmdeflection,m

˛ Womersleynumber,–

Vstroke strokevolume,m3

 dampingconstant,–

 kinematicviscosity,m2_s−1

p Poisonratio,–

 fluiddensity,kgm3

ω angularvelocity,rads−1

ωn naturalfrequency,rads−1

isexperimentalcharacterizationofdispersion-inducedboundary

layermixing,demanding two well-controlledpulsatile flows in

counter-phase[23].

Inthecurrentwork,adeviceisdevelopedthatcanserveasa

pul-satileflowpumpforamicrofluidicrheometer,inwhichcomplex

micromaterialbehavior(microgels,cells,elasticcapsules,droplets)

canbemechanicallyprobed.Themicro-rheometerisbasedona

cross-slotsetup(see[24,25]foranapplicationwithvisco-elastic

dropsanddilutedpolymersolutions,respectively),whichconsists

ofa microfluidicchipwithcrossingchannels,ametering valve,

andafeedbacksystem.Withthecross-slotsetup,inwhich

elon-gationalflowexists,suchasinthefourrollmill[26],aparticle

canbecaptured(Fig.1,similartothehydrodynamictrapof[27]).

Whencaptured,hydrodynamicforcesareusedtoapplystressto

theparticle.Fromtheobservationoftheresultingdeformationof

theparticle,itsrheologicalpropertiescanbedetermined.

Inthiswork,thedeviceisdesignedtobeappliedtothe

dynami-calprobingofredbloodcellmechanics.Toextendthecross-slot

principle towards a micro-rheometry setup, the inflow of the

deviceshouldbemadepulsatile(non-zeromeanflow)with

well-controlledperiodandamplitude,suchthatfrequency-dependent

behavior oftheredblood cellunder investigationcanbe

char-acterized. Concerning the redblood cellmembrane, which has

(relaxation)timeconstantsof0.15–0.5s,apumpthatdrives

pul-satileflowswithafrequencyofabout20Hz,andamplitudesdown

to10nl/s,isrequired.Itisalsoessentialthatthewaveformofthe

flow ispurely sinusoidal,suchthat thecellcanbeprobedat a

singlefrequency.Althoughliteratureconcerningmicropumpsis

abundant,toourknowledgenodataofinstantaneousflows(i.e.

waveforms)atthesescaleshavebeenpublished.

State-of-theartsyringepumpscouldnotdeliversinusoidal

pul-satileflows viathe programmingfunction (Harvard PHD 2000,

HarvardApparatus)orthecommandlineoption(Nexus3000,

Che-myx).Hence,apulsatilemicropumpsystemisneeded,withwhich

theflow waveformiswell-controlledandeasilytunable.Toour

knowledge,suchadeviceisneithercommerciallyavailable,nor

reportedaboutinliterature.

Altogether,ourgoalistodesignapumpsystem,whichproduces

pulsatileflowsthatarewell-controlledintermsofamplitude,

fre-quency,andpulseshape.Intherestofthispaper,amotivationfor

thespecificdesignisgiven,inwhichtheflowisproducedinan

open-loopdrivenway.Duringthedesignphase,aspects

concern-inggeometry,systemdynamics,andfluidactuation,aretakeninto

account.

Next,to assessthe qualityof thewaveformsthe microscale

flowsaremeasuredwithhightemporalresolution, usingmicro

particleimagevelocimetry (␮-PIV). Third,theresultsof steady,

oscillatory,andpulsatileflowarepresented,aswellaspassiveand

activenoiseresponses.Thisshoulddemonstratethebehaviorof

thepumpsystem,aswellasitscapabilities.Thedynamic

behav-iorofthesystemcanbeexplainedbydiscussingdifferentphysical

phenomena.Theseinsightscanbeusedtogainfullcontroloverthe

flowwaveform.

2. Materialsandmethods

2.1. Pumpsystemdesign

Theexactcomputationofimpedanceinoscillatorymicroflow

isnotstraightforward[28].However,weassumedthatoursystem

islinearandtimeinvariant(LTIsystem),suchthatapulsatileflow

canbegeneratedusingasyringepumpandareciprocaldiaphragm

pumpinseries:accordingtothesuperpositionprinciplethe

con-stantandoscillatingflowaresummed[29].Thishassuccessfully

beenappliedinlargerlinearhydraulicsystems[30].

The produced pulsatile flow of the pump system equals

the stroke volume per unit of time: Qpulse=Qsyringe+

lim

t→0Vstroke/t. The required flows impose restrictions to

thegeometryanddimensionsofthepump(Fig.2a).Themaximum

flowamplitudeisdependentonthepulsefrequency.Whenthe

meanflow ¯Q =100nl/s,andtheminimuminthepulseliesatzero,

thenecessarystrokevolumeVstroke= ¯Q·1/2f.Thisimpliesthat

afrequencyof0.1Hzdemandsavolumedisplacementof159nl.

On the other hand, at higher frequencies and low amplitudes,

the necessarystroke volume is reduced and noise suppression

becomesmoreimportant.

Tobeintherightrangeoffrequenciesandflows,an

axisym-metricvalvechamber(radiusa=6.5mm,heightHc=2mm)holds

acircularplatewithathicknessofh=200_␮m.AnO-ringbetween

thediaphragmandthelidofthepump,whichisfullycompressed

Fig.1.Schematicrepresentationofthecross-slotrheometer.Thevelocityfield,visualizedwithfluorescentbeadsontheright,ishyperbolic(elongationalflow).Theflow canexertstressforlongertimeonaparticlesituatedinthecenteratthestagnationpointoftheflow.Afeedbacksystemisrepositioningtheparticlebydisplacementof thestagnationpoint.ThisisachievedbychangingtheoutflowratioQ1/Q2withamicrovalve.Theparticleunderconsiderationisguidedtothecenterofthegeometryand

stabilized.Oncethere,theparticlewillbeprobedbydifferentwell-controlledoscillatoryandpulsatileflows,suchthatfrequency-dependentmaterialcharacteristicscanbe extracted.Thepumpsystemtoproducetheseflowsisdescribedinthispaper.

Moreover,byusinga bendingelasticplateincombination with

theO-ringseal,hysteresis,stick-slip,andcompliancearelargely

avoided,whereasaccurateplatepositioncontrolisstraightforward

(seeSection2.1.2).

2.1.1. Dynamics

Concerning pulsatile flow, frequency-dependent behavior is

crucialforcreatingwell-definedflow pulses.Anycompliancein

thesystemincombinationwiththelargehydraulicresistancesof

thenarrowchannelsdownstreamofthepump,willactasa

low-passfiltersuchthathigherfrequenciesaredampedmore.Toavoid

compliance,setupcomponentsaremaderigidbyfabricatingthem

outofstainlesssteel:acircularstainlesssteelplateisperiodically

deflectedintoarigidfluidicchamber,whereplatedeformationis

fullyelastic.

Theimpedance ofthediaphragm pump,includingtubing, is

schematicallygiveninFig.2c.Theinertiaforcesonthefluidplaya

significantroleathigherfrequenciesinthesemicrofluidiccircuits

[31].AstheReynoldsnumber,Re,thatistheratiobetweensteady

inertiaandviscousforces,issmall(Remax=at·Vmax/=0.05,with

Vmaxthemaximummeanvelocity,atthetuberadius,andthe

kine-maticviscosity),steadyinertiaforcescanbeneglected.However,

theWomersleynumber˛,thatrelatestheunsteadyinertiaforces

totheviscousforces,islargerthan1:˛=at·



 =3.5,whereω

istheradialvelocity.Consequently,unsteadyinertiaissignificant.

TheinertanceI,whichcanbeseenasthepressuredifferencethatis

requiredtochangetheflowintime[32],ishighestintheconnector

tubing,andisgivenby

I= Lt

a2

t =

7_.9×108kgm−4 _. (1)

HereisthefluiddensityandLtthetubelength.

Themaincontributortothehydraulicresistance,R,isthe

resis-tanceoftherectangularglassductofwidthWandheightH,where

thevelocitymeasurementsareperformed,seeSection2.2.1.The

valueofRisgivenby[33] R= 12L WH3











whereisthedynamicviscosityandListhechannellength.

2.1.2. Liquidactuation

Achoiceforclosed-loopflowcontrolcanbemade,suchthata

differencebetweenthereferenceflow(desiredflow)andtheactual

flowiscorrectedforbyasensor-actuatorsystem.However,flow

controlonamicroscalelevelisnottrivial,assensorsandactuators

needtobemore sensitivethanin macroscopicsystems.On the

scaleof nl/s,itisnot straightforwardtomeasure theflow with

sufficientsensitivitywithoutinfluencingtheflowitself.Moreover,

Fig.2. (a)Schematicoverviewofthepulsatilepumpsetup,whereasyringepumpisputinserieswithadiaphragmpump.Avoicecoildeflectsastainlesssteelmembrane (withradiusa=6.5mm,andthicknessh=200␮m)intoachamberofheightHp.DeflectionyovertheradiusrisgivenbyEq.(3).BymakingR1R2,theflowpulsewill

mainlytraveldownstream.(b)Schematicrepresentationoftheplatedeflection:thestainlesssteelplatewiththicknesshisclampedoveritscircumferenceatradiusa,asit isdeflectedbytheactuatorwithaforceFL,whichactsonasmalldiskwithradiusr0.In(c)aschemeoftheimpedanceofthediaphragmpumpsystemisshown,whichis

governedbyahydraulicresistance(R)thatcoversthefluidviscousdissipation,aninductor(I)thatstandsfortheunsteadyinertanceofthefluid,andacompliance(C)that coverstheelasticityofthediaphragmandcompressibilityofairinthefluid.Vinputistheinputsignalofthecurrentdriver,whereasQoutistheoutput,whichismeasured.

224 R.C.H.vanderBurgtetal./SensorsandActuatorsA220(2014)221–229

correctionsdemandforafastandaccurateactuator(msand<nl/s,

respectively).

Asimplerapproachistakenhere,whereanopen-loopsystem

isdesigned,built,andcalibrated.Platedeflectionisalways

gov-ernedbypurebendingmechanicswhenthefollowingcriteriaare

met[34]:theplateisflatinthenon-deflectedstate,deflectionis

lessthanhalftheplatethicknessh,andthethicknessislessthana

quarterofradiusa.Furthermore,allforcesontheplatemustwork

onitinnormaldirection,resultingindeformationsthatarewithin

thelinearelasticlimit.Thedesignofthepresentdiaphragmpump

fulfillsthesedemandsasthemaximaldeflectionymax=0.62␮mat

0.9N(currentof1.3A).Hence,thedeflectionandstrokevolumeare

proportionaltotheforceexertedontheplate.Consideringthatthe

plateisfullyclampedatitscircumferenceandtheforceisexerted

onasmallconcentricdiskwithradiusr0(Fig.2b),thedeflectiony

overtheradiusrisgivenby[34]

y(r)=FL a 2 16D









inwhichFL thetotalforcetotheplateandDtheplateconstant

givenby D= Eh 3 12(1−2 p) (4)

whereEistheYoung’smodulusandp thePoisson’sratio.The

strokevolumecansimplybefoundbycomputingtheintegralof

revolutionofEq.(3).

Alinearvoicecoilactuatorisused(LVCM013-013-02,Moticont),

exertingaforceproportionaltothecurrentthroughthecoil.When

usingacurrentsource,pumpactuationisruninopen-loop:coil

self-inductioniscanceled.Moreover,thecounter-electromotiveforce

isnegligible,asthedisplacementsareintheorderofamicron.In

thatway,alinearscalingbetweendrivingsignal(voltage)andfluid

displacementisachieved.

2.2. Measurementsetup

Amodel,builtwiththereal-timeworkshopofMatlabSimulink,

runsat10kHzonaquadcoredesktopcomputertodrivethe

actu-atorandlogelectronicdata.Thepulsatingsignalforthepumpis

sentoverEthernettoanEthercatD/Aconverter(BeckhoffEL3102).

Thissignalpassesa 1storderlow-passfilter(cut-offfrequency,

fc=36Hz)tofilteroutelectronicbackgroundnoise,beforeitgoes

tothecurrentdriver(TU/eDACS,inhousemanufactured).The

fil-teredsignal,aswellasthecameratriggersignal,which isused

tosynchronizeflowanddrivingsignal,arelogged(A/Dconverter,

BeckhoffEL4132).

2.2.1. Flowvisualization

A steady flow is produced by a syringe pump (Harvard

PHD2000,USA),usinga250␮lgastightglasssyringe(Hamilton).

Thediaphragmpumpis connectedwithPEtubing(1.6mmOD,

0.7mmID),whereastainlesssteelnarrowingisplacednearthe

entrancetocreateextraimpedance.Fromtheexitofthediaphragm

pump, the fluid flows towards a rectangularglass tube (inner

dimensions:2mm×0.1mm),in which the flow measurements

takeplace.Thefluidisseededwith1.0␮mdiameterfluorescent

polystyrenebeads (FluoSpheres505/515, Invitrogen). Bead

pat-ternsareassessedusingafluorescencemicroscope(ZeissM200,

63×NA0.75LDobjective),equippedwithahighspeedvideo

cam-era(PhantomV9,vision-research).Thiscombinationensuresahigh

enoughspatialandtemporalresolution(settingof512Hzisused

here),and sufficient lightsensitivity (exposuretime of 300_␮s).

Themaximaldepthforimagingusingfluorescencemicroscopyis

limited,suchthatthecamerafocusissetjustabovetheplaneof

symmetryoftheglasstube,at33␮mdepth.Fromthebeadpatterns

velocity fieldsaredetermined usingparticleimage velocimetry

(PIV),asdescribedbelow.

2.2.2. Micro-PIVanalysis

BeforethePIVanalysiscanbeperformed,therecorded

out-of-planefluorescencesignal,thatlowerstheimagecontrast,mustbe

removed.Out-of-focusparticlesappearasblurred,largerdisks,that

moveslowerorfaster,causedbythevelocitygradientinthe

chan-nel.High-passfilteringin thefrequencydomain(FFT-algorithm

inImageJ,cutoffof 10pixels) partlyremovesout-of-focusbead

images, which are furthersuppressedby thresholding. Filtered

imagesaredividedintosmallerinterrogationareasof128×128

pixels(75%overlap),whicharecross-correlatedoverconsecutive

timestepswithGPIVtools([35];forPIVfundamentals,see[36,37]).

Asnumerousoutliersarepresentinthevelocityfields,especially

becauseofthepoorlightingconditions,aspatialdatavalidation

procedurehastobeperformed.First,extremeoutliersareremoved

by thresholding withthe maximum measurablevelocity. Next,

peakslyingoutsideonestandarddeviationfromthemeanvelocity

ofthevectorfieldareremoved.Last,thevelocityfieldsare

sub-jectedtothenormalizedlocalmediantest[38],witharadiusof3

pixelsandathresholdof0.2.Eventually,assuminguniformityof

themeasuredvelocityfield,thevectorspertimestepareaveraged

andscaledtoaflowusingthesyringepumpflowsettings.

2.3. Pumpcharacterization

Steadyand oscillatoryvelocitymeasurementsareperformed

tocalibrate theopen-loopresponse. The steady flows,that are

knownàprioriastheyaresetbythesyringepump,canbeusedto

converttheuniformvelocityfieldstoaflow.Subsequently,these

resultsareusedtocreatepulsatileflows,inwhichtheminimum

is nearzero. During both oscillatory and pulsatile flow

experi-ments,measurementsatdifferentamplitudes(Vinput=0.25–1.00V)

and frequencies(1–16Hz)have beenperformed.The qualityof

themeasuredflowisdeterminedbyasignal-to-noiseratio(SNR),

whichisdefinedasthesignalmagnitude(amplitudeofthemain

frequency component)dividedby thesumof theother

signifi-cantfrequencypeaksinthespectrum.Byregisteringthetrigger

andfilteredelectronicsignal,magnitudeandphaseshift

informa-tionhasbeenobtained,whichcanbevisualizedinBodediagrams.

Passiveandactivenoisemeasurementsareperformedtoevaluate

backgroundnoiseandtheopen-loopfrequencyresponsefunction.

Furthermore,extrainsightsintothesystemsbehaviorareobtained

byperformingfrequency-dependentdeflectionmeasurementson

thebareplatewithalasertriangulationdistancemeter(LK-H1W,

Keyence).Last,resultsofsomespecialcases,beingnon-sinusoidal

flows,aregiventodemonstratetheversatilityofthispumpsystem.

3. Results

3.1. Steadyflow

Table1displaysthefluidvelocities,measuredwithPIV,of3

dif-ferentsteadyflows,whichmakeupatotalof22measurements.

257imagesareshotduring1s,fromwhich256velocityfieldsare

determined, which are proportional to the flow set on the

Table1

Overviewofthe3steadyflowsmeasuredwithPIVinthecurrentsetup.

Syringepumpflow Meanvelocity Standarddeviation

33.3nl/s(n=10) 47.7␮m/s 4.7␮m/s

50.0nl/s(n=4) 70.4␮m/s 10.7␮m/s

Fig.3.(a)Spatiallyaveragedvelocityintimeforanoscillatoryflowexperiment:drivingamplitudeis0.75V,frequencyis2Hz.(b)Thefrequencyspectrum,wherethesignal peakat4rad/sisclearlyvisible.Furthermore,the1stharmonicisfound(8rad/s),whichisusedtodeterminetheSNRofthismeasurement:SNR=22.1.(c)and(d)similar data,butnowforadrivingamplitudeof0.50Vand16Hz.Asexpected,thesignalpeakislocatedat32rad/s.The1stharmonicispresentagain,butthe2ndisunexpectedly higherinmagnitude.BoththesepeakvaluesaresummedindeterminingtheSNR,whichis19.3inthiscase.In(e)and(f)thevelocitypeakvaluesofalloscillatoryflow experimentsarevisualized.(e)Thescalingbetweenflowandactuationvoltageforthe5differentfrequencies,and(f)showshowthepeakvelocityscaleswithfrequencyfor fourdifferentactuationamplitudes.

syringepump.Theconversionfactorcomesdownto1_␮m/s0.70 (±0.01)nl/s.

3.2. Oscillatoryflow

InFig.3aandc,two oscillatoryflowmeasurementsof2and

16Hz,respectively,areshown.TheirfrequencyspectrainFig.3b

anddshow,nexttothegroundfrequencypeak,concentrationsof

energyaroundspecificfrequencies:higherharmonicsareclearly

presentin mostcases.Thevelocityamplitudein theoscillatory

flow experimentsshows a linearscaling withtheapplied

volt-age,asshownin Fig.3e.On thecontrary,therelationbetween

amplitudeandfrequencyislinearonlyupto4Hz,afterwhich

level-ingoccurs(Fig.3f).Theerrorbarsrepresentthespreadwherethe

numberofmeasurementsn=3.Themeanamplitudeandthemean

SNRaregiveninTable2.Theflowsofthemeasurementsatthe

lowestvoltageamplitudeandlowestfrequencyhavethelowest

flowamplitudeandthelowestSNR(≈12).Ontheotherhand,the

higherflowamplitudemeasurementsarelesstroubledbynoise

(SNR≈20).

3.3. Pulsatileflow

Thefluidvelocity,andcorrespondingfrequencyspectrumoftwo

pulsatileflowexperimentsareshowninFig.4aandb,respectively.

Here,alsothesyringepumpisswitchedon,whichcontributestoa

morenoisyflowthanincaseoftheoscillatoryexperiments.Higher

harmonicsareagaindistinguishablefromthenoisyspectrum.

3.4. Noisemeasurements

The result of a velocity background noise measurement, in

whichthefluidshouldbeatrest,isshownin Fig.5.Lookingat

thefrequencymagnitudespectrum,somesignificant

concentra-tionsofnoisearefoundatcertainfrequencies(112,81,186,10Hz,

fromhighesttolowestmagnitude).However,magnitudesarelow

enoughtohaveinsignificantinfluenceontheflowsunder

consid-eration,whichtypicallyhaveavelocitymagnitudeof50–200␮m/s.

Thefluidvelocityresponseontheappliedband-limitedwhite

noise(0–5kHz)isrepresentedbythegray graphsin Fig.6.The

black dotsinFig.6bare theresultsfromalloscillatory

226 R.C.H.vanderBurgtetal./SensorsandActuatorsA220(2014)221–229

Table2

SummaryofthemeanamplitudesandSNRsoftheoscillatoryflowexperiments,averagedover3measurements(n=3).

Voltage→ 0.25V 0.50V 0.75V 1.00V

Frequency↓ Meanampl. SNR Meanampl. SNR Meanampl. SNR Meanampl. SNR

1Hz 15.0␮m/s 11.4 30.7␮m/s 20.2 45.3␮m/s 14.0 59.1␮m/s 11.5

2Hz 25.6␮m/s 13.2 57.1␮m/s 20.3 87.3␮m/s 15.3 116.6␮m/s 16.4

4Hz 44.8␮m/s 27.6 100.9␮m/s 16.7 156.1␮m/s 23.9 199.2␮m/s 11.1

8Hz 53.4␮m/s 28.5 123.8␮m/s 23.7 186.7␮m/s 26.3 – –

16Hz 51.6␮m/s 13.2 112.1␮m/s 22.6 178.3␮m/s 22.0 – –

Fig.4.In(a),thetimedomainresultsoftwopulsatileflowexperimentswithapulsefrequencyof4Hz,andameanflowof33(blackcurve)and67nl/s(graydashedcurve) areshown.Theminimumvelocityinthepulsesisalmostzerowhenactuationvoltagesof0.25and0.50Vareusedforthe33and67nl/smeanflow,respectively.In(b),the frequencyspectraofbothmeasurementsareshown.

butarehardlyvisiblebecauseoftheirsmallvalue.Allvoltagesper frequencytestedarenormalizedandsubsequentlyaveraged, per-mittedbythelinearscalingoffluidvelocitieswithdrivingvoltage, observedinFig.3e.Thefrequency-dependentrelationshipbetween

themeasuredfluidvelocityandtheappliedactuatorinputvoltage

isgivenbythefollowingtransferfunction,clarifiedinSection4:

v

whereAistheamplitudescalingand−p1isthelocationofthe

stablepoleoftheelectronicfilter.

Thefirstordersubsystemwithpole_−p2comesfroma

hydro-dynamiceffect(seeSection4).ωnandarethenaturalfrequency

anddampingconstantofthesystem,respectively,whichare

typi-callypresentinalinear2ndordersystemasinFig.2c.Thetransfer

Fig.5.Passivenoisemeasurementwiththediaphragmunderalightprestress (0.2V).Flowisoscillatingaroundzero,withmostimportantfrequencycomponent at112Hz.Additionally,asignificantamountofenergyisfocusedbetween81and 186Hz,andsomearound10Hz.Thesecomponentsarealsopresentwhenthe actu-atorisoffline,fromwhichcanbeconcludedthatthesearemechanicalvibrations alwayspresentinthesystem.

functionisrepresentedbytheblackcurveinFig.6bandfitsthe

experimentaldatauptoafrequencyofabout500rad/s(80Hz).

3.5. Morecomplexflowcases

Theresultsofflowexperimentsthathaveamorecomplex

fre-quencyspectrum,areshowninFig.7b–d.Tocompare,asinusoidal

oscillatoryflowisshowninFig.7a.Incaseofthesquarewaveflow

(Fig.7b),arelativelylongrisetimeandanoverdampedresponseis

observed.Alsoshownarethetimederivativesofthedrivingsignals,

synchronizedwiththemeasurements,whichstandforthevelocity

ofthepumpdiaphragm(proportionaltothestrokevolume).The

phaseshiftsbetweenfluidvelocityanddrivingvoltageareclearly

visible.

4. Discussion

Weintroducedapumpsystemdesignfordynamiccross-slot

rheometry,basedonadiaphragmreciprocalpump,whichis

capa-ble of producing microscale pulsatile flows with well-defined

flowwaves.Pulseswithnonzeromeanflowwithfrequenciesof

0.1–20Hzandamplitudesof10–100nl/scanbeobtained,where

thepulseshapeiscontrollable.Linearityand time-invariancyof

thepumpsystemisconcludedfromtheafitoftheoscillatoryflow

andfrequencysweepmeasurementswithalineartransfer

func-tion.Thisimpliesthatthesuperpositionprincipleisvalidhereand,

hence,pulsatileflowscanbeproducedbyaddingtheoscillatory

flowsofthediaphragmpumptosteadyflowsofthesyringepump.

Thepulsatileflowmeasurementsconfirmthis.

Furthermore,particleimagevelocimetryappearstobeasuitable

methodformicrofluidicflowassessment.Bymakinguseofahigh

speedvideocameraandacontinuouslightsourceincombination

withfluorescentbeads,sufficienttemporalresolutionisobtained

tocharacterizethepresentmicrofluidicpulsatilepumpsystem.

Themeasuredvelocitiesinstationaryflowexperimentsare

pro-portionaltotheappliedflow,asexpected.Concerningthecasesof

oscillatoryflow,alinearscalingoftheamplitudewithfrequency

wasexpectedovertheentirefrequencyrange,whichwasrather

Fig.6.(a)Thefrequencyspectrumoftheactivenoisemeasurement.In(b),aBodediagramofthesamedataisdisplayedingray.Theblackdotsarethedatapointstaken fromtheoscillatoryflowexperiments,whichareperfrequencyaveragedoverallvoltages.TheblackcurveisthefittedtransferfunctionofEq.(5).

(Fig.3f)dampingisobserved.Thisbehaviorisconsistentwiththe

activenoiseresponseplotofFig.6a,whichisfoundtoresemble

flowgraphsinliterature,e.g.Fig.10in[10].Physicalphenomena

concerningthisdampinginthesekindofmicrofluidicdeviceshave

beenidentified.First,thedominanteffectisthesystemimpedance

ofthehydraulics(pumpchamber,tubing,andotherchannels),that

canbedescribedasthelumpedparametermodelofFig.2c.Second,

hydrodynamiceffectsinvolvedinoscillatoryflow,likeWomersley

velocityprofiles,influencelocalvelocitymeasurements,whenthe

unsteadyinertiaforcesbecomecomparabletotheviscousforces,

whichisthecaseat8Hzandhigher.

Below,thesephenomenaareconsideredonebyone:the

con-tributionofeacheffectonthefrequencyresponsefunction(see

Eq.(5))isdeterminedbymodelingthephenomenonunder

con-siderationandquantifyingthemodelparameters.Hence,àpriori

knownphysicsconcerningthisproblemleadtotheeventualfitof

themodeltotheoscillatoryflowdataandtheactivewhitenoise

responseinFig.6b.Thetransferfunctionzero(firsttermofEq.(5))

iscausedbythefactthattheflowscaleswiththevelocityofthe

diaphragm,implyingQ=dVstroke/dt=A·dVinput/dt.Thisderivative

givesatransferfunctionzeroats=0,multipliedbygainA.

Whentheinfluenceof thefluidis neglected,thediaphragm

dynamicsaredescribedbyamass-springsystem: ¨y =k/My,where

yisthecentraldeflectionoftheplate.Thespringconstant,k,of

theplateis high(k=Eh3_/0.217a2_=1.66×105_{N/m [16]), and the}

equivalentmass,M,wouldbethemassofthemembraneand

actu-atorbody(7.8gintotal).Theexpectednaturalfrequencywould

bef0=



k/M/(2)=734Hz.Inaccordance,the‘dry’deflection

measurementinairusingalasertriangulationmetergivesa

res-onancefrequencyfres=714Hz.However,fromliteratureitiswell

knownthattheunsteadyinertiaforcesgreatlyreducethenatural

frequencyofthepump[16,31].

Theimpedanceofthepumpsystem,whichtoalargeextent

determine its frequency response, can be modeled by the

resistance–inertance–capacitance(RIC)circuitfromFig.2c[11].

TheRICcircuittranslatesintoasecondordertransferfunction

intheLaplacedomainwithtwocomplexpoles[39],whichforms

thesecondterminEq.(5).Thenaturalfrequencyωn is √1

IC,and

thedampingconstantis R₂



chan-nels,thatplayasignificantrole,areknown,thevaluesforIandR

arecalculatedusingEqs.(1)and(2),respectively.Thecompliance

componenthastwocontributors,namelythemembraneandthe

airpresentinthepumpchamber’sfluid[11].Asthepump

cham-berandthemembranearethickcomponentsofstainlesssteel,the

pumpscomplianceisnegligible.However,theairpresentinthe

Fig.7.Plotsoffourdifferentfluidvelocitywaves:(a)oscillatorysinusoidalflow,(b)squarewaveflow,(c)triangularflow,(d)flowasaresultofaphysiologicalbloodpressure curveasinput.Thetimederivativeoftheinputsignalsareshowningray.

228 R.C.H.vanderBurgtetal./SensorsandActuatorsA220(2014)221–229

Fig.8.Themidlinevelocityofthevelocityprofile,normalizedtotheviscositydominatedcase(Poiseuilleflow),fortwodifferentimagingdepths(50␮m,whichistheplane ofsymmetryofthechannel,and33␮mwherethemeasurementsareperformed).TheWomersleynumberisdefinedas˛=aH



ω/,inwhichisthekinematicviscosity andaHrepresentsthechannelhydraulicdiameter,definedbyaH=W+H2WH.TheincreaseinamplitudedampingaswellasthephaselagisobservedforhigherWomersley

numberswhen(a)and(b)arecompared,wheretheWomersleynumberis1(16Hz)and2(64Hz),respectively.

fluidturnedouttobedeterminantinthesystemiccompliance.The

exactvalueforCisunknown,andtherefore,Cisoneofthefitting

parametersinEq.(5),togetherwiththemagnitudegain,A.The

fit-tedcomplianceis7.1×10−14kg−1m4_s2_{,whichisofthesameorder}

ofmagnitudeastheestimatedcomplianceofapumpchamber

vol-umeofwaterfullysaturatedwithair:Csat=4.3×10−13kg−1m4s2

(seeEq.8in[11]).

Thepoleofthe3rdtermofEq.(5)isdeterminedbythe

pas-sivelow-passfilterintheelectronics.TheLaplacerepresentation

ofthisfirstordersubsystemcontainsastablepole,whichliesat

−p1=−72 (fc=36Hz),whereas thefilter DC gain, obtainedby

measurements,is0.68andispartofthetotalmagnitudegain,A,

fromabove.

Aphenomenonthatpartly explainsthedynamic behaviorat

higherfrequencies,isthepresenceofinertiainducedalterationsof

theassumedPoiseuilleprofile(Womersleyprofiles).Inthesehigh

aspectratiochannels(W/H=20),aparabolicvelocityprofileonly

existsintheheightdirection,whiletheprofileisplug-likeonthe

longsideoftheslit(fortheequationsoftheslitvelocityprofilesin

3D,see[40]).Bytakingthehydraulicdiameter,whichisdefinedas

WH/(W+H),afirstorderapproximationforthevelocitygradients

nearthewallsat−1/2Wand1/2Wisobtained.Dependentonthe

Womersleynumber,thevelocityprofilechanges[41]:thecoreof

theflowwillbemoredominatedbyunsteadyinertiaforces,

caus-ingalowermaximalvelocityandaphaselaginthemeasurement

volume.Inthecaseofaflowoscillatingat16Hz,theWomersley

numberinthemeasurementchannel,˛,isabout1,suchthatthe

velocityprofilehasundergoneasignificantchange,displayedby

thecenterlinevelocityshown inFig.8. Thisbehaviorcanquite

wellberepresented byafirst orderdampedsysteminthe

fre-quencyrangeinvestigatedhereresultinginastablepolelocated

at−p2=−134inEq.(5).

ThetransferfunctionEq.(5)fitstheexperimentaloscillatory

measurements,includingthephase shiftbetweendrivingsignal

andthemeasuredflows,andexplainsthesuddendampingofthe

measurementsat8and16Hz(Fig.6b).Italsofollowstheactive

noiseresponsequitewelltoabout500rad/s(80Hz).Nowthatthis

relationbetweenvelocitymagnitudeandfrequencyisknown,one

cancompensateforthenon-proportionalitiesintheinput–output

scaling,providedthatthesystemislinear.Pulsatileflow

experi-ments,wheretheoscillatoryflowisaddedtoasteadyflow,show

validityof thesuperpositionprinciple,which indicatesthatthe

systemisindeedlinear.Underthiscondition,amplitude

correc-tionsatdifferentfrequenciesofsinusoidalflowscanbeperformed.

Toextendthelinearrelationofthesinusoidalflowamplitudeand

frequencytohigherfrequenciesthantestedhere,moreattention

shouldbegiventothedesignofthecompletesystem.Asdiscussed,

thesystemimpedanceisdetermined byinertia,resistance, and

compliance,whichareallnon-negligibleinthisrangeof

oscilla-toryflows[11].Therefore,forbetterperformance,diffuser/nozzle

configurations,pumpchamber,andconnectionchannelsshouldbe

redesigned,usingcorrectmodelingoftheimpedance[28].

Con-cerningthecompliance,allhydraulicpartsshouldbeasstiffas

possible,butmoreimportantly,thoroughdegassingofthe

work-ingfluidshouldbeperformedinavacuumoven.Takentogether,

thisshouldresultinahighernaturalfrequencyandlowerdamping

constant,implyingalargerbandwidthinwhichthepumpsystem

canoperate.

5. Conclusion

A pump system, connecting a syringe pump and reciprocal

diaphragmpumpinseries,isdesignedtoproducewell-controlled

pulsedflows,intermsofamplitude,frequency,andpulseshape.

Thisisachievedbyconstructinganopen-loopdrivendiaphragm

pump,actuatedbyavoicecoil.Diaphragmdeflectionisgoverned

purelybybendingmechanics,suchthatthedisplacedfluidvolume

isproportionaltothecurrentthroughthevoicecoil.With␮-PIV

analysesofbeadimagepatterns,capturedinafluorescence

micro-scope,thegeneratedfluidvelocityfieldsintimearedetermined.By

scalingthevelocityvalueswiththevelocitymagnitude,obtained

duringsteadyflowexperiments,inwhichtheflowisknown,the

instantaneous flow is determined. Pulsatile flows, obtained by

addinganoscillatoryflowtoasteadyflowofasyringepump,show

thevalidityofthesuperpositionprincipleforthissystem.

Oscilla-toryflowmeasurements,togetherwiththefrequencyresponseon

awhitenoiseinputmeasurement,showsubstantialdamping.To

alargeextentthisdampingcanbedescribedbyincluding

physi-calphenomenaoccurringinthesystem,themainonesbeingthe

correct impedancewithinertanceand compliance,a firstorder

low-passbehaviorfortheelectronicfilter,andtheoccurrenceof

Womersleyvelocityprofilesinthemeasurementvolume.

Assum-ingthesystemis linearandtime invariant,this enablesscaling

oftheinputsignal,suchthatsinusoidalflowpulseswitha

well-controlledamplitudecanbeachievedaccuratelyinanopen-loop

sense.Thedynamicrangecanbeincreasedbytakingthetotal

sys-temicimpedanceintoaccountinthedesignphasewhenthepump

isintegratedintomicrofluidicdevices.Thedevicetestedhereis

suitabletoperfusethecross-slotmicrorheometerwithpulsatile

flows.

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Biographies

RenévanderBurgt,bornon22April1984,received theBiomedicalEngineeringBachelordegreein2006,and MasterdegreeinFebruary2009,bothattheEindhoven UniversityofTechnology.AsapartofhisMasterresearch RenévanderBurgtspentfivemonthsattheCalifornia InstituteofTechnology

attheAeronauticsdepartment.Heexperimentallyinvestigatedtheinfluenceof dif-ferentgasflowsonthebreakupofasupersonicliquidjet.DuringhisMasterThesis, Renéconductedexperimentalandnumericalwork,servingrisk-of-rupture assess-mentofintracranialaneurysms,usingparticleimagevelocimetryinphantomsand videodensitometryonangiograms.

In2009hestartedhisPh.D.inthegroupofCardiovascularBiomechanicsunder Prof.FransvandeVosse.Hehasworkedonaminiaturizedcross-slotrheometer, aimingatthecharacterizationofthedynamicsoftheredbloodcell.Thepump presentedhereisbuilttoperfusethismicrofluidicrheometer.

Currently,RenévanderBurgtisworkingasatechnicalprojectleaderatSoLayTec BV,adeveloperandproducerofultrafastspatialatomiclayerdepositionmachinery forthephotovoltaicwaferindustry.There,hisinterestsinmicrofluidics, (thermo-)fluidmechanics,dynamics,controlsystems,andmechatronicsaremetbynew challenges.

PatrickAndersonisprofessorinstructureandrheology ofcomplexfluids.HestudiedAppliedMathematicsatthe EindhovenUniversityofTechnologywithProf.Dr.Arnold A.Reuskenashisadvisor.In1999hereceivedhisPh.D. degreefromtheDepartmentofMechanicalEngineering atthesameuniversitywithProf.dr.ir.HanE.H.Meijeras hisadvisor.FollowingayearbreakatOcéTechnologieshe joinedthePolymerTechnologygroup.

Hispresentinterestsincludestructuredevelopment duringflow,interfacialphenomena,microfluidics,and polymerprocessing.

In 2008 he received the International Polymer ProcessingsocietyMorandLamblaaward.

JaapdenToonder receivedhis Master’sdegree (cum laude)inappliedmathematicsfromDelftUniversityof Technologyin1991andhisPh.D.degree(cumlaude)in mechanicalengineeringfromthesameuniversityin1996. In 1995, he joined Philips Research Laboratories inEindhoven,TheNetherlands.Heworkedonawide variety of applications such as optical storage sys-tems, RF MEMS,biomedical devices, polymer MEMS, immersionlithography andmicrofluidics. In2008, he becameChiefTechnologist,leadingtheR&Dprogramson (micro-)fluidicsandmaterialsscienceandengineering. NexttohismainjobatPhilips,hewasapart-time profes-sorofMicrofluidicsTechnologyatEindhovenUniversity ofTechnologybetween2004and2013.In2013,JaapdenToonderwasappointed full-timeprofessorandchairofMicrosystemsintheDepartmentofMechanical Engi-neeringatEindhovenUniversityofTechnology(TU/e).

Hiscurrentmainresearchinterestsaremicrofluidics,out-of-cleanroom micro-fabricationtechnologies, mechanical propertiesof biologicalcells and tissues, nature-inspiredmicro-actuators,andorgansonchips.

FransvandeVosseisprofessorofCardiovascular Biome-chanics.From1976to1982hestudiedAppliedPhysics atEindhovenUniversityofTechnology(TU/e).Heearned hisPh.D.degreefromthesameuniversityin1987.His Ph.D.researchwasfocussedonthenumericalanalysis ofcarotidarteryflow.From1987to2001hewas lec-turerinfluidmechanicswiththeMaterialsTechnology groupinthedepartmentofMechanicalEngineering(W, TU/e).In2001hewasappointedatthedepartmentof Biomedicalengineering(BMT,TU/e).Hiscurrentresearch interestsarerelatedtothecomputationaland experimen-talbiomechanicalanalysisofthecardiovascularsystem anditsapplicationtoclinicaldiagnosisandintervention, cardiovascularprostheses,extracorporealsystemsandmedicaldevices