Electroosmotic flow through a microtube with sinusoidal roughness

Abstract

In this paper, a perturbation method is introduced to study the electroosmotic flow (EOF) in a microtube with slightly corrugated wall. The corrugation of the wall is described as periodic sinusoidal wave with small amplitude. Based on linearized Poisson–Boltzmann equation and the Cauchy momentum equation, the perturbation solutions for velocity and volume flow rate are obtained. The influences of the amplitude δ, the wave number λ, the nondimensional electrokinetic width K and the nondimensional pressure gradient G on the velocity and flow rate are analyzed graphically and discussed in detail. The results show that the flow rate Q of the EOF through a corrugated channel tends to the flow rate Q0 of the EOF through a smooth channel when amplitude δ tends to zero, but the flow rate Q is always smaller than the flow rate Q0 in the smooth channel. The flow retardation of the roughness on the flow rate of the EOF always increases with the augment of the nondimensional electrokinetic width K.