Micro&Nanofluidics

FluidicsReynoldsNumber(dimensionless)

Re = inertial termsviscous terms

=ρ vDη

Re<500:laminarflow(fluidflowsinparallellayers)Re>2000:turbulentflow

ρ:fluiddensityv:fluidspeedη  :fluidviscosityD:diameterofthepipe

Iner5a:resistanceofanobjecttoanychangeinitsmoGon(tokeepmovinginastraightlineatconstantvelocity,ortokeepsGll)

Viscosity:fluidresistanceflow(togradualdeformaGonbyshearstress)

ReynoldsnumberFornoncircularchannels,usethehydraulicdiametertocalculatetheReynoldsnumber:D=DH

DH = d pipe diameter

DH =2

1h+1w

channel height and width

DH =4AP

A:crosssecGonareaP:weNedperimeter

DefiniGon:

wh

Workonexercise1

FluidicsTurbulent

Laminar

Bloodinbloodcapillaries

Airinairwaycapillaries

Laminar

Turbulent

Turbulent

Turbulent

LowReynoldsnumberprevailnotonlyinthemicroworld…

B. H. Weigl, R. L. Bardell, and C. R. Cabrera, "Lab-on-a-chip for drug development", Advanced Drug Delivery Reviews 55 (3), 349 (2003).

D =100mv =10m / year = 0.3µms−1

η =1010kgm−1 s−1

ρ =103 kgm−3

Re = ρ vDη

= 3⋅10−12 <<1

Viscoustermsdominateandwehavelaminarflow

Inalaminarflow,theviscoustermsdominateImage=honeyflowinginachannel

Liquidandsampletransport-Pressuredrivenflow

SGck-boundarycondiGons(u=0atr=±a)giveaparabolicflowprofile:

€

u(r) = umax 1−r2

a2#

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aisthetuberadius

UniversityofTwente–groupofAlbertvandenBerg

r

ParGclesattheperipherytravelslowerthanparGclesinthecenter.AplugofsampleisthereforespreadoutasittravelsinthetubewhichmaylowerresoluGonofafluidicssystem.Itcanalsobeuseful:LargeparGclesareexcludedfromtheedgesandtravelonaveragefasterthansmallparGcles,thatcanbeclosertotheedges(hydrodynamicchromatography).

pubs.acs.org/doi/pdfplus/10.1021/ac034663l

2a

Microandnanofluidics-LabonachipMicroandnanofluidics:CanbeusedforfundamentalstudiesmadepossiblethankstotheproperGesofthesmallchannelsLabonachip:applicaGonofmicroandnanofluidics-analysisanddiagnosGcsorientedAdvantagesovertradiGonalmethods:-smallersampleandreagentamountneeded-fasterexperiments

FabricaGon–PhotolithographyandSoeLithography

PDMS

Master

PDMS

Master

PDMS

SiliconWaferorglassslide

Diffusion:becomesimportantinmicrofluidicsduetothesmallsizeofthechannels.

BrownianmoGon:randommovementofmolecules/objectsinafluidduetothefastmovingofatomsinthefluid.

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x 2 = 2Dt

DiffusioncoefficientD:Einstein’srelaGonship:

D = µkBT =kBT6πηa

kB:Boltzmannconstant=1.38064852×10-23m2kgs-2K-1T:temperatureη:viscosityofthefluidµ:mobilityoftheparGclea:parGculeradius

Inonedimension

MovementineachorthogonaldirecGonisindependent.

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r2 = x 2 + y 2 = 4DtTwodimensions

€

r2 = x 2 + y 2 + z2 = 6DtThreedimensions

€

x 2€

y 2

€

r2

heremeansaveragingovermanyaNemptseachoneofduraGont.

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Diffusion

Ingeneralinmicrofluidics,theflowislaminarandthereisnoconvecGvemixing.Duetoshortdistances,insteaddiffusionbecomesimportant.

Rhodamine

Anthocyanin

OUTLET

TWOIN

LETS

Diffusivemixer

ThemixingofRhodamineandanthocyanineisachievedbydiffusiononly(noturbulentflow)

Workonexercises2and3

Ingeneralinmicrofluidics,theflowislaminarandthereisnoconvecGvemixing.Duetoshortdistances,insteaddiffusionbecomesimportant.

FITC

TexasRed

X

ThewidthsofthestreamsattheoutletarefuncGonsoftherelaGveflowratesattheinletchannels.

OUTLET

THRE

EINLETS

Diffusivemixer

Anotherexampleofmicrofluidicdevice

Rcd

R < Rc R > Rc

1

2

3

4

5=N

Rc = distance between obstaclesperiod of array

Basicidea:streamlinesconsGtutepotenGaltrajectories.ParGclesshiestreamline,andthustrajectory,asaresponsetoaforce(heresteric:they“bump”intotheobstacles)

DeterminisGclateraldisplacement:Bumperarray

CriGcalRadius:

The parGcles with R<Rc followtheflowdirecGon.TheparGcleswith R>Rc travel through thedeviceatananglecomparedtothedirecGonoftheflow.

Rcd

R < Rc R > Rc

1

2

3

4

5=N

Rc = distance between obstaclesperiod of array

Basicidea:streamlinesconsGtutepotenGaltrajectories.ParGclesshiestreamline,andthustrajectory,asaresponsetoaforce(heresteric:they“bump”intotheobstacles)

DeterminisGclateraldisplacement:Bumperarray

CriGcalRadius:

Idealcase

The parGcles with R<Rc followtheflowdirecGon.TheparGcleswith R>Rc travel through thedeviceatananglecomparedtothedirecGonoftheflow.

ApplicaGon–Ultrasimplelabel-freesorGngoftrypanosomesTrypanosomabrucei->sleepingsickness.• Fatal(100%)disease.• Fatal(5%)treatment.à ImperaGvetominimizefalsenegaGvesaswellasfalseposiGves.

CurrentdiagnosisreliesonenrichmentbyionexchangechromatographyandcentrifugaGon.Simplerandcheapermethodsneededthatareadaptedtouseinremoteareas.Majorchallenge–NeedtodetectaslowconcentraGonsas100parasitespermL.

depth37µm

depth11µm

depth4µm

Holm,Beech,...LabChip2011

At99%RBCrejecGon

wehaveacaptureefficiency9%

wehaveacaptureefficiency99.5%

wehaveacaptureefficiency53%

ApplicaGon–Ultrasimplelabel-freesorGngoftrypanosomes