Analysis of an electroosmotic flow in wavy wall microchannels using the lubrication approximation

We present the analysis of an electroosmotic flow (EOF) of a Newtonian fluid in a wavy-wall microchannel. In order to describe the flow and electrical fields, the lubrication and Debye-Huckel approximations are used. The simplified governing equations of continuity, momentum and Poisson-Boltzmann, together with the boundary conditions are presented in dimensionless form. For solving the mathematical problem, numerical and asymptotic techniques were applied. The asymptotic solution is obtained in the limit of very thin electric double layers (EDLs). We show that the lubrication theory is a powerful technique for solving the hydrodynamic field in electroosmotic flows in microchannels where the amplitude of the waviness changes on the order of the  mean semi-channel height. Approximate analytical expressions for the velocity components and pressure distribution are derived, and a closed formula for the volumetric flow rate is obtained.  The results show that the principal parameters that govern this EOF are the geometrical parameter, e, which characterizes the waviness of the microchannel and the ratio of the mean semi-channel height to the thickness of the EDL, κ.