Electrohydrodynamic stability of poorly conducting parallel fluid flow in the presence of transverse electric field

Abstract

In this paper we study electrohydrodynamic instability (EHDI) in a poorly conducting parallel inviscid fluid in the presence of an electric field and space variation of electrical conductivity. It is shown that EHDI causes inhomogeniety in the material science processing. This inhomogeniety can be controlled by understanding the nature of EHDI in the presence of an electric field and a shear due to horizontal basic velocity. The condition for EHDI is determined in terms of the electric number rather than the point of inflexion of the basic velocity profile using both moment and energy methods combined with Galerkin expansion technique. From this analysis, it is shown that a proper choice of electric number controls inhomogeniety by controlling instability of a parallel poorly conducting inviscid fluid. For unstable motion it is shown that the growth rate, C_i, is confined in a semi circle region C_r² + C_i²-2(u_b-Ω/Φ) C_r + u²_b-2u_b Ω/Φ=0, which has the center (u_b-Ω/φ,0) and radius |Ω/φ| where C_r is the phase velocity, u_b the basic horizontal velocity, φ=D²u_b, Ω=W₁x₀²α² the electric number and D=d/dy. From this an upper bound for the amplification factor is shown to be as C_i²≤ max|Ω/Φ|² under the condition that φ has the same sign between 0 and 1.