Optimizing electroosmotic flow in an annulus from Debye Hückel approximation to Poisson–Boltzmann equation

Abstract

In this study, we consider steady and starting electroosmotic (EO) flow in an annulus channel with different zeta potentials (denoted by α, β, respectively) developed on the inner and outer channel walls. An analytical solution is first obtained under the linearized Debye–Hückel approximation (DHA), and then extended to the non-linear Poisson–Boltzmann equation (PBE) by the method of homotopy. The steady-state EO pumping rate for any given pair of (α, β) is optimized with respect to the ratio b of inner to the outer radii, and the corresponding temporal developments of the optimal EO flow are given detailed investigation of the effects of the electric double layer (EDL). The optimal EO pumping rates Q_M(α,β) are presented on the α–β plane for several electrokinetic widths (K) to illustrate their general trends versus the corresponding b (denoted by b_max), which serves as a useful guide for practical applications. Investigation is also given to the shifts of b_max and Q_M(α,β) with varying the parameter λ, which measures the nonlinearity of the PBE.