Chebyshev Spectral Collocation Simulation of Nonlinear Boundary Value Problems in Electrohydrodynamics

Abstract

The Chebyshev Spectral Collocation Method (CSCM) is applied to two nonlinear boundary value problems in electrohydrodynamic (EHD) ion drag pump flows. We consider two fundamental one-dimensional flows: EHD flow in a conduit and EHD ion drag pumping in a pipe. In the first case, a single dimensionless momentum equation for axial flow velocity is considered. In the second case, three coupled equations for electrical field, potential and charge density are considered. Both models comprise ordinary differential equations. The present study finds applications in micro-fabrication and biomicrofluidic systems. The excellent accuracy and potential of CSCM in nonlinear electro-hydrodynamics is demonstrated.