Poisson equation based modeling of DC and AC electroosmosis

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1 COMSOL Conference Prague 2006 Page 1 Poisson equation based modeling of DC and AC electroosmosis Michal Přibyl & Dalimil Šnita Institute of Chemical Technology, Prague, Czech Republic Department of Chemical Engineering Michal.Pribyl@vscht.cz

2 COMSOL Conference Prague 2006 Page 2 Content Introduction electroosmosis principle Governing equations of electrokinetic flow full model slip approximation Mathematical models model of a biosenzor driven by an external DC electric field limitations of the slip modeling model of electrokinetic flow driven by an AC electric field in a microchannel properties of the AC electrokinetic flow Conclusion

3 COMSOL Conference Prague 2006 Page 3 Electric double layer (EDL) = = 0 V Microchannel wall EDL 1 nm 1 m Cation distribution c k, z k = 1 c K = c A = c 0 Anion distribution c a, z a = -1 F z c q 0 z i c i 0 Non-zero electric charge i i i el i Local electroneutrality

4 COMSOL Conference Prague 2006 Page 4 Electroosmosis induced by DC field Positive ions accumulates at the charged surfaces Axially imposed electric field acts on cloud of electric charge and starts fluid movement nonslip slip Santiago J.G., Stanford microfluidic lab

5 COMSOL Conference Prague 2006 Page 5 Governing equations Mass balances of ionic components (at least 2 equations) ci t J i j r ij j Navier-Stokes and continuity equations (3 or 4 equations, v x, v y, (v z ), p) Poisson equation Dv 2 g P ele v Dt v 0 el 0 r

6 COMSOL Conference Prague 2006 Page 6 Slip model of flow Simplified Navier-Stokes equation Non-zero velocity on microcapillary walls (Helmholtz- Smoluchowski approximation) v wall Electroneutrality i E z i c i Dv 2 g P el E v Dt eo wall r 0 eo el

7 COMSOL Conference Prague 2006 Page 7 Non-slip model of flow Navier-Stokes equation with electric volume force Zero velocity Dv g P ele Dt 0 Local deviation from electroneutrality v wall v 2 i z i c i el 0 el 0 0 r

8 COMSOL Conference Prague 2006 Page 8 Model of a biosenzor driven by an external DC electric field r = R = 0 < 0 < 0 = 0 r = 0 z = 0 z = L z = 2L z = 3L z = 4L z = 5L R r z Ligand + Receptor = Complex solution solid ph. solid ph. Device consists of 5 compartments DC electric field is applied Electric charge attached to walls

COMSOL Conference Prague 2006 Page 9 Meshing - 2860 rectangular elements - non-equidistant -

9 COMSOL Conference Prague 2006 Page 9 Meshing rectangular elements - non-equidistant - anisotropic - the ratio of the larger and the smaller edge of rectangles in interval

Formation of the ligand-receptor complex on microchannel

10 COMSOL Conference Prague 2006 Page 10 Short-time elecrokinetic dosing of a ligand in aqueous solution Formation of the ligand-receptor complex on microchannel wall Ligand concentration field Level of saturation of the receptor binding sites

11 COMSOL Conference Prague 2006 Page 11 Example of limitation of the slip model electrolyte concentration Water nonslip slip Bioapplication V slip V err 100 V nonslip nonslip

COMSOL Conference Prague 2006 Page 12 Example of the slip model limitations ligand-wall (receptor) electrostatic interaction Effects of the surface electric

12 COMSOL Conference Prague 2006 Page 12 Example of the slip model limitations ligand-wall (receptor) electrostatic interaction Effects of the surface electric charge and ligand charge number z Ab on formation of ligand-receptor complex on the microchannel wall NC is the total number of molecules of the ligandreceptor complex

13 COMSOL Conference Prague 2006 Page 13 Principle of AC electroosmosis M. Mpholo, C.G. Smith, A.B.D. Brown, Sensors and Actuators B Chemical, 92, pp , _ + _ + _ Distribution of electric potential along the electrodes (red line) induces tangential movement of the electric charge and thus eddies formation.

14 COMSOL Conference Prague 2006 Page 14 Model of electrokinetic flow driven by an AC electric field in a microchannel Periodic array of electrodes deposited a microchannel wall y = h l 1 l 2 l 3 l 4 l 5 y y = 0 x = 0 ~ Asin 2ft x Geometry and dimensions of the microchannel (l 1 = l 5 = h = 10 m, l 2 = 5 m, l 3 = 2 m, l 4 = 3 m).

15 COMSOL Conference Prague 2006 Page 15 Meshing rectangular elements - non-equidistant - anisotropic - the ratio of the larger and the smaller edge of rectangles in interval

16 COMSOL Conference Prague 2006 Page 16 Steady periodic regime A = 1 V, f = 1 khz Electric potential distribution (blue = -1V, red = +1V) Velocity distribution

17 COMSOL Conference Prague 2006 Page 17 Time course of global velocity Global velocity = the tangential velocity v x averaged over depth of the microchannel y 0, h Most of the stable periodic regimes (except f = s -1 ) exhibits changes in flow direction during one period (1/f ) fluid motion in the microchannel has a zigzag character. However, a continuous flux of electrolyte can be experimentally observed because of high frequency of the zigzag motion (2f or 4f ). f A = s -1, f B = s -1, f C = s -1, f D = s -1, f E = s -1, f F = s -1.

18 COMSOL Conference Prague 2006 Page 18 Dependence of global velocity on AC frequency, A = 1 V The dependence of the global velocity averaged over one period (1/f ) on the applied frequency of AC electric field. This dependence is in a good qualitative agreement with the experimentally reported one. For the given set of parameters, there are several flow reversals observed in the studied frequency interval. The maximum global velocity is few tents of microns per secondd in the frequency interval 10 2,10 4 Hz.

19 COMSOL Conference Prague 2006 Page 19 Conclusions COMSOL Multiphysics software enables numerical analysis of electro-transport processes based on EDL in macroscopic objects Slip approximation is not necessary Limitations of the slip approximation in a DC system were identified Electroosmosis induced by AC electric field was analyzed in a microfluidic channel Dependence of global velocity on AC frequency was computed Experimentally observed phenomenon (flow turnover at some frequencies) was proved by numerical analysis This phenomenon probably does not rely on chemical and/or electrode reaction

Fast Biofluid Transport of High Conductive Liquids Using AC Electrothermal Phenomenon, A Study on Substrate Characteristics

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