On the Solutions of Electrohydrodynamic Flow in a Circular Cylindrical Conduit

Abstract

This article considers the nonlinear boundary value problem (BVP) for the electrohydrodynamic flow of a fluid in an ion drag configuration in a circular cylindrical conduit. We present rigorous results concerning the existence and uniqueness of a solution to this BVP for all relevant values of the parameters. We also show that the solution is monotonically decreasing and derive bounds on it in terms of the parameters. In [1] McKee et al. develop perturbation solutions in terms of the parameter governing the nonlinearity of the problem, α. This is done for both large and small values of α. For large α the solutions calculated here are qualitatively different from those calculated in [1]. This stems from the fact that for α large the solutions are O(1/α), not O(1) as proposed in the perturbation expansion used in [1].