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Flow analysis in the microchannels has recently accelerated dramatically. In this paper, numerical investigation of Joule heating effects on the electroosmotic flow through a microchannel with the trapezoidal cross-section and constant wall temperature have been presented. The energy equation for the temperature distribution, Navier–Stokes equation for the velocity distribution and a Poisson equation for the electric potential distribution have been solved by using the finite-volume method in a system curvilinear coordinates. Thermophysical properties such as the dynamic viscosity and electric conductivity vary with temperature. Results show that by increasing the Joule number, the temperature, velocity and mass flow rate increase with constant EDL number. Without considering the Joule heating effects, the increments of EDL number causes in the mass flow rate to increase, but with considering the joule heating effects, the increasing of mass flow rate continues until EDL number 15 and after that the flow rate decreases. On the other hand, when the cross-section is reduced by the increasing aspect ratio, the joule number remains constant while the mean temperature decreases.

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In the present work a new lattice Boltzmann (LB) framework has been developed to study the electroosmotic flows in a 2-D flat microchannel. The governing equations are presented in the continuum model, while a set of equivalent equations in LB model is introduced and solved numerically. In particular, the Poisson and the Nernst–Planck (NP) equations are solved by two new lattice evolution methods. In the analysis of electroosmotic flows, when the convective effects are not negligible or the Electric Double Layers (EDLs) have overlap, the NP equations must be employed to determine the ionic distribution throughout the microchannel. The results of these new models have been validated by available analytical and numerical results. The new framework has also been used to examine the electroosmotic flows in single and parallel heterogeneous microchannels.

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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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Uncertainty at experimental results usually adds to experimental data in the form of error bound. Since uncertainties at input parameters play an important part at the discrepancy between numerical and experimental results, considering uncertain parameters in comparison of numerical and experimental results would be logical. Electroosmotic flow is one of the cases which uncertainty quantification on its numerical simulation is necessary because of the presence of uncertain parameters. In this study, uncertainty quantification of electroosmotic flow in the micro T-channel has been presented. Numerical method was first validated by comparison between numerical simulation results of electroosmotic flow with certain inputs and experimental data. At the first step of uncertainty quantification, sample generation of the uncertain parameters has been performed by Latin hypercube method. At the next step, governing equation of electroosmotic flow has been solved by finite element method for every sample. Mass flow rate and velocity field have been selected as objective functions and adjoint method was employed for calculating the derivatives of them. At the final stage uncertainty quantification has been performed by enhanced Monte Carlo method. Results of the adjoint method show geometry parameters and fluid viscosity as the most effective factors on the results. While temperature and density of fluid demonstrate the least effect on the objective functions. Results of the Monte Carlo method illustrate 22.4% uncertainty for the results of mass flow rate and 12.6% on average for the results of velocities.

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In situations involving large zeta potential, the classical Poisson-Boltzmann theory of electrolytes breaks down and a modified Poisson-Boltzmann equation which takes into account the finite size of the ions must be utilized. In addition, most biofluids cannot be treated as Newtonian, therefore, simultaneous effects of finite size of the ions and non-Newtonian behavior of the fluid in combined electroosmotic and pressure driven flows have been examined in the present study. The Governing equations are solved by a finite-difference-based numerical procedure in a rectangular microchannel. The ion size is introduced into the modified Poisson-Boltzmann equation by the steric factor, which allows considering the ions as point charges or finite sizes. Considering the ionic finite size, generally enhances the velocity of the shear-thickening fluid, while reduces the velocity of shear-thinning fluid. The Cross sectional aspect ratio is also considered and it was found that the adverse pressure gradient greatly affects the velocity profile, when aspect ratio increases, while velocity profile is less sensitive to aspect ratio variations in favorable pressure gradients. Furthermore, friction coefficient of both shear thinning and thickening fluids increases with the increase in zeta potential for point charge model, which for finite size charges decreases. Cross sectional averaged velocity reduces under steric effects for shear thinning fluids at large zeta potentials, while it is slightly influenced by shear thickening fluids.

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In this paper, switching process of electro osmotic flow is numerically and analytically investigated in a two dimensional Y-shape three-way channel. In this research, it is shown that changing the flow direction through a three-way channel can be simply conducted by varying applied electrical voltage at channel’s ends. In theoretical approach, three equations are introduced to approximate switching voltage ratio and dimensionless flow rate before and after switching process, respectively. These equations are derived base on some simplifying assumptions when distance between output branches and dimensionless double layer thickness parameter are assumed to be flow variables. Numerical simulations are also conducted by using the lattice Boltzmann method to solve all governing equations including the Navier - Stokes, the Poisson - Boltzmann, and the Laplace equations in a 2D three-way channel geometry. Comparison between analytical and numerical results indicates that introduced approximated equations can successfully predict switching voltage ratio and dimensionless flow rate (before and after switching process) by employing considerably lower computational efforts in comparison with numerical approach. In this regard, the introduced semi-analytical equations can be useful for better understanding and to more effectively designing of micro electro mechanics systems.

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