# A Computational Model for Simulation of Electroosmotic Flow in Microsystem

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Electroosmotic flow is created by applying an external electrical field on the electrical double layer (EDL) formed due to the interaction of an electrolyte solution with dielectric surfaces. This kind of flow plays an important role in various microsystems (MEMS and BioMEMS) for fluid handing and analysis. Its governing equations with the assumption of an equilibrium Boltzmann distribution of ion concentration for single-charged ions are: Eq. 1, Eq. 2, Eq. 3, Eq. 4 where V is the velocity vector, _ the density, P the pressure, _ the viscosity, _E the charge density, E (= ¡rÁ) the electrical field intensity, F is the Faradays constant, R the gas constant, T the temperature, C0 the ionic concentration in the bulk solution, _ the permittivity, Ã the potential due to EDL, and Á the applied potential. The above equations in their two-dimensional and steady forms have been solved numerically in [1-4] while three-dimensional and steady numerical solution was carried out in [5] with the Debye-Huckel approximation applied on the right side of Eqn.(4). In the present paper, a numerical model was developed to solve Eqns.(1)-(4) in their three-dimensional and transient form along with the following volume-of-fluid (VOF) equation for volume of fluid function (F) Eq. 5. to simulate the replacing of one fluid by another fluid in microchannels due to electroosmotic flow. Due to the adoption of the Boltzmann distribution, the solutions for the fluid and potential fields are independent. The solution algorithm and computer code for Eqns.(1), (2) and (5) have been developed and validated (Hirt et al., 1980). However,the solution of Eqn.(4) poses some challenges due to the exponential nonlinearity associated with the hyperbolic-sine function as pointed out in [2]. In the present paper, instead of using the Debye-Huckel approximation as done in [5],which is only valid for small potentials created by an EDL, a matrix free GMRES method is invoked to solve Eqn.(4). The developed code was validated against the analytical solution given in[2]. To illustrate the simulation of transient and three-dimensional cases, electroosmotic flows in rectangular channels with di®erent zeta potentials in its walls are simulated for one fluid and two-fluid cases respectively. Practical applications of the presented model are discussed. As a representation of the presented results, Figure 1 shows the potential created by an EDL and velocity profile in a two-dimensional microchannel obtained by the presented numerical method and analytical solution. The numerical predictions fit with the analytical solution very well.

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Journal: TechConnect Briefs
Volume: 1, Technical Proceedings of the 2003 Nanotechnology Conference and Trade Show, Volume 1
Published: February 23, 2003
Pages: 218 - 221
Industry sectors: Medical & Biotech | Sensors, MEMS, Electronics
Topic: Micro & Bio Fluidics, Lab-on-Chip
ISBN: 0-9728422-0-9