Unsteady electroosmosis in a microchannel with Poisson-Boltzmann charge distribution

The present study is concerned with unsteady electroosmotic flow (EOF) in a microchannel with the electric charge distribution described by the Poisson–Boltzmann (PB) equation. The nonlinear PB equation is solved by a systematic perturbation with respect to the parameter λ which measures the strength of the wall zeta potential relative to the thermal potential. In the small λ limits (λ≪1), we recover the linearized PB equation – the Debye–Hückel approximation. The solutions obtained by using only three terms in the perturbation series are shown to be accurate with errors