Investigation and optimization of geometry and zeta-potential effects on electroosmotic mixing efficiency in converging-diverging microchannels by response surface methodology

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.