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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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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.

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In this article, mixing in the combined electroosmotic/pressure driven flows of non-Newtonian fluid in a microchannel with rectangular obstacles and non-homogeneous ζ-potential has been studied numerically. The non-Newtonian behavior of the fluid is considered for the flow field using power law rule. Also, the nonlinear Poisson-Boltzmann equation is used to model the distribution of ions across the channel and the electric potential. Numerical solutions of coupled equations of momentum, electric field and concentration field are performed by means of finite element method. In this study, the effects of various parameters such as pressure gradient, rheological behavior of the fluid and the geometrical and physical parameters of obstacles on the mixing quality are investigated. The results indicate that applying adverse pressure gradient to the flow, the dilatant behavior of the fluid, as well as the height of barriers, are highly effective in the enhancement of the mixing quality within the microchannel. It is found that for microchannels with heterogeneous ζ-potential, increasing the length of obstacles significantly increases the mixing efficiency while for the microchannels with homogeneous ζ-potential, barrier length has a slight effect on mixing efficiency.

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In this study, effects of zeta potential distribution and geometrical specifications are numerically investigated on mixing efficiency in electroosmotic flows. Considered geometries include straight, converging, diverging, and converging-diverging microchannels. Electroosmotic flow simulations are conducted based on the N-S and Nernst-Planck equations for momentum and ionic charges distributions, respectively, by lattice Boltzmann method. Numerical simulations are validated against available analytic electroosmotic flow solutions in homogeneous straight channels, and then flow patterns and mixing performances in the presence of non-uniform zeta potential distributions are investigated in search for enhanced mixing performances. Numerical results indicate that converging channel leads to a sizable increase in mixing efficiencies, while the flow rate decreases at the same time. In contrast, diverging channels increase the flow rate, while decrease the mixing efficiency. Therefore, it is expected to achieve a balance between the mixing efficiency and mass flow rate using converging-diverging geometries. Numerical results indicate that mixing efficiency of about 90% can be reached with a converging-diverging microchannel with a reasonable decrease in mass flow rate as compared to its geometrical diverging-converging counterpart channel.

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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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In this study, effects of zeta potential distribution and geometrical specifications are investigated on mixing efficiency in electroosmotic flows. Flow geometry in this research is a series of converging-diverging microchannels with different diverging ratios. Governing equations including the Navier Stokes equation for fluid flow and the Poisson-Boltzmann equation for internal electrical field are solved numerically in a two-dimensional domain by using the lattice Boltzmann method. Numerical simulations are validated against available analytic solutions for electroosmotic flow in homogeneous straight channels. The response surface methodology (RSM) is then employed to investigate relationship between flow variables and consequently to optimize mixing efficiency and flow rate of the channel. Results indicate that increasing the zeta potential ratio and diverging ratio, leads to increased value of flow rate, while meanwhile it decreases the mixing efficiency. Zeta potential pattern does not affect flow rate considerably, but its effects on mixing efficiency is noticeable. Furthermore, it is found that mixing efficiency and flow rate are more sensitive to zeta potential ratio than diverging ratio. At last, optimum parameters are determined by RSM which are 0.5 for zeta potential ratio, 0.6 for diverging height, and pp-nn pattern for zeta potential distribution, all associated to simultaneously maximized flow rate and mixing efficiency.

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The emergence of microfluidic devices for various applications has created a demand for enhancing the efficiency of the mixing. In this article, an electroosmotic micromixer based on G-shaped electrodes that are excited by AC waveform was designed. The proposed micromixer was simulated using COMSOL Multiphysics and the effects of various parameters including voltage, frequency, distance between electrodes, and the number of electrodes on the mixing efficiency have been characterized. By compiling the obtained results, the performance of the optimized model with four electrodes each having a 6.5 µm distance between their opposite polarities, excited with voltage of 1 V and frequency of 16 Hz was evaluated. The results demonstrated that the proposed micromixer was able to achieve a mixing efficiency of over 99.7% with a response time of 220 ms. Furthermore, the proposed device was designed regarding practical consideration, enabling the micromixer to be fabricated without the need of sophisticated instruments.