ELECTROCONVECTION IN A SUSPENDED FLUID FILM - A LINEAR-STABILITY ANALYSIS

A suspended fluid film with two free surfaces convects when a sufficie ntly large voltage is applied across it. We present a linear stability analysis for this system. The forces driving convection are due to th e interaction of the applied electric field with space charge that dev elops near the free surfaces. Our analysis is similar to that for the two-dimensional Benard problem, but with important differences due to coupling between the charge distribution and the field. We find the ne utral stability boundary of a dimensionless control parameter R as a f unction of the dimensionless wave number kappa. R, which is proportion al to the square of the applied voltage, is analogous to the Rayleigh number. The critical values R(c) and kappa(c), are found from the mini mum of the stability boundary, and its curvature at the minimum gives the correlation length xi(0). The characteristic time scale tau(0), wh ich depends on a second dimensionless parameter P, analogous to the Pr andtl number, is determined from the linear growth rate near onset. xi (0) and tau(0), are coefficients in the Ginzburg-Landau amplitude equa tion that describes the flow pattern near onset in this system. We com pare our results with recent experiments.