Charged layer with undulated surface: configuration of electrical double layer

A charged layer with undulated surface exists commonly in natural entities (for example the biological membrane layer and the surface of charged colloid) and in artificial fabrications (for example the peripheral surface of ion-exchange membrane pores). When the micro- or nano-scale charged layer systems are concerned, the effect of undulation of charged layer surface on the electrical phenomenon may become great significant. In this work, using the perturbation method, the significance of undulated surface on a charged layer in the electrical phenomenon is investigated. Under assumptions that the undulation amplitude is small and that the Debye-Huckel approximation is applicable, the electrical potential field in three regions is solved simultaneously. Based on the analytical results it is found that, if compared with that in condition of flat surface, the undulation of charged layer surface decreases/increases the magnitude of electrical potential field near the wave crest/trough, due to the curvature of undulated surface. In addition, the surface potential on the undulated surface shows a wavelike distribution. The analytical results also show that, the significance of undulated surface is determined by the physical parameters, including the geometry of undulated surface, the amplitude and the period of undulation, and the fixed charge density in charged layer.