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Numerical modeling of electro-osmotic flow in heterogeneous micro-channels using two different models is presented in this article. For the through modeling of such flows, the coupled equations of Navier-Stokes, Nernst-Planck and the Poisson-Boltzmann are solved for the flow field, electric charges transport and electric field, respectively. Numerical solution of these equations for the heterogeneous micro-channels is complicated and difficult. Therefore, simple and approximate models such as Helmholtz-Smoluchowski have been proposed in which the solution of Poisson-Boltzmann, Nernst-Planck are neglected and the effect of the electric field on the flow field is applied through a prescribed slip boundary condition at the walls of micro-channel. The electro-osmotic flow fields within the heterogeneous micro-channels are usually complex and contain the vortex region that is ideal for mixing purpose. Hence, in this paper, the micro-channels designed so that they are capable to serve as micro-mixers in the mixing applications. For the micro-channels proposed here, the flow fields are obtained both with approximate modeling and the full simulation of electro-osmotic flows so that a comparison can be made to discuss the accuracy of the approximate model. The results of this study can be used to model the electro-osmotic flow field within heterogeneous micro-channels.

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Mixing within electrokinetic micromixers is studied numerically in this article. Micromixer studied here is simply a heterogeneous parallel plate microchannel which is imposed to the electroosmotic flow field. For the through modeling of such flows, the coupled equations of Navier-Stokes, Nernst-Planck, Poisson-Boltzmann and concentration equations are solved for the flow motion, electric charges transport, electric field and species concentrations, respectively. Numerical solution of these set of equations for the heterogeneous microchannels is complicated and difficult. Therefore, simple and approximate model such as Helmholtz-Smoluchowski has been proposed which is basically appropriate for the case of microchannels with the homogenous properties on the walls. Validation of Helmholtz-Smoluchowski model is well-examined for the prediction of two dimensional flow fields, yet its applications is rarely validated for the prediction of concentration field and mixing performance. In this article mixing due to electroosmotic flow field is investigated using Nernst-Planck equations as well as Helmholtz-Smoluchowski models and the accuracy of the Helmholtz-Smoluchowski model is evaluated. Comparison of the results indicates that for the proper conditions, approximate model can predict the mixing performance accurately along the micromixer length.

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In this article numerical simulation of electroosmotic flow in heterogeneous microchannel is performed using approximate model of Helmholtz-Smoluchowski in which the effect of electric field on the fluid flow is applied through a slip boundary condition. Solving the concentration equation, the mixing performance of microchannels with heterogeneous zeta-potential is studied both qualitatively and quantitatively. This study shows that combining the electroosmotic and pressure-driven flows in a single microchannel with proper arrangement of the heterogeneities can easily lead to design of electroosmotic micromixers with adjustable mixing performance. The mixing behavior of such micromixers is dominated by the arrangement of zeta-potential distribution as well as the applied external pressure drop. In this article we introduced relative mixing performance and mixing capacity rather than well-discussed factor of mixing performance in order to perform a thorough analysis of mixing. Using these factors, it is found that presence of heterogeneities has a small augmentation on mixing performance when the pressure drop is extremely small or large. Therefore, performance of micromixers with combined flow of electroosmotic and pressure-driven has an optimum point. Furthermore, it is seen that asymmetric level of the charge pattern is more effective on the mixing performance compared to absolute values of wall charges. This promises proper mixing even when surfaces with moderate zeta-potential are used in micromixer.