Stability of time-modulated electroosmotic flow

Abstract

We present a linear stability analysis of parallel electroosmotic flow in a slot geometry. A spatially uniform time harmonic electric field is applied to a dilute electrolyte solution contained between two infinite parallel plates. The base state ion concentrations and electric potential are determined using the Poisson–Boltzmann equation in the Debye–Hückel approximation. The base velocity field is found to be time harmonic and parallel. It is shown that the original system can be replaced by an equivalent one consisting of an electrically neutral fluid enclosed between oscillating parallel plates, whose speed and frequency of oscillation depend on the modulated electric field. Further, the system of linearized disturbance equations can be decoupled into two stability problems: The first, called the electrokinetic problem, describes the evolution of disturbance ion concentrations and electric potential and is independent of the disturbance velocity components. The second, called the Stokes layer problem describes an oscillatory Stokes layer forced by an electrical body force. The stability of each system is determined by Floquet analysis of a dynamical system obtained from a truncated Galerkin expansion of the perturbation quantities. Our calculations show the system to be linearly stable over a wide range of parameters, with damping rates that become quite small for certain combinations of Stokes and Reynolds numbers. © 2004 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69805/2/PHFLE6-16-7-2349-1.pd