The generation of electric currents by the laminar flow of dielectric liquids

Abstract

The electric current generated by the laminar flow of an insulating liquid through a cylindrical pipe has been calculated using a model that incorporates nonequilibrium boundary conditions at the wall. Analytical solutions to the model equations are derived in the limits of high and low electrical conductivity and numerical solutions are given at intermediate conductivities. The solutions depend on four parameters that are dimensionless representations of the electrical conductivity, the rate of adsorption of positive ions, the rate of adsorption of negative ions and the ratio of the diffusivities of positive and negative ions. The results are presented as graphs of current versus the electrical conductivity parameter for various values of the other three parameters. Physical reasons for the shapes of the current/conductivity curves are discussed. According to the model, the currents are generated by differences in the ionic diffusivities and/or by differences in the ionic adsorption rates at the wall.