Oscillating Streaming Potential and Electro-osmosis of Multilayer Membranes

Abstract

Artificial membranes consist of multilayers that have different physical or chemical properties. They are often considered as an equivalent single-layer membrane without taking into account the detail inside. Based on the Debye−Hückel approximation, we have provided analytical solutions of oscillating electrokinetic flow in multilayer membranes. Both pressure-driven flow (streaming potential) and electric-field-driven flow (electro-osmosis) were studied. The pressure and electric-field distributions in each layer can be obtained from our analytical solutions. This allows a better understanding of electrokinetic flow in multilayer membranes and benefits the design and selection of artificial membranes. The derived analytical solutions are useful for more-general time-dependent problems through a superposition of time-harmonic solutions weighted by appropriate Fourier coefficients. The properties of each membrane layer are reflected as complex quantities; therefore, a method is proposed to determine the electrokinetic properties (such as the zeta potential) of each layer by applying a high-frequency alternating electric field or pressure.