ELECTRO-OSMOTIC FLOW IN A MICROCHANNEL CONTAINING A POROUS MEDIUM WITH COMPLEX WAVYWALLS

In the present paper, we simulate the electro-kinetic transport of aqueous solution through a microchannel containing porous media. The microchannel walls are simulated as a complex wavy surface and are modeled by superimposing the three wave functions of different amplitudes but the same wavelength. The microchannel contains an isotropic, homogeneous porous medium, which is analyzed with a generalized Darcy law. The nonlinear-coupled governing equations for mass, momentum, and electrical potential conservation are simplified using low Reynolds number and long wavelength approximations, and Debye electrokinetic linearization. Following nondimensional transformation of the linearized boundary value problem, closed-form analytical solutions are presented for the velocity components, pressure gradient, local wall shear stress, average flow rate, and stream function subject to physically appropriate boundary conditions. Validation with a finite difference method is also conducted. The effects of permeability parameter, Debye length (i.e., characteristic thickness of electrical double layer), and electro-osmotic velocity on flow characteristics are illustrated graphically and interpreted at length. The study finds applications in chromatography, hybrid electroosmotic micropumps, transport phenomena in chemical engineering, and energy systems exploiting electrokinetics.