Electrohydrodynamic Bulk instability of a Slightly Conducting Fluid between Two Coaxial Cylinders with a Small Temperature Gradient

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This study deals theoretically with the bulk instability of a viscous, incompressible, slightly conducting, dielectric fluid contained between two coaxial cylinders with a radial temperature gradient and under a radial electric field. A gradient in electrical conductivity resulting from the temperature gradient causes free charges to accumulate in the fluid when the electric field is applied. In the case considered, the gradient in dielectric constant can be neglected with the significant electric force being that due to the free charges. It is found that the stability criteria depend on the magnitude of the imposed potential, temperature gradient, fluid properties and geometrical configuration. In solving the stability problem by the linear perturbation theory it is assumed that the motion due to instability is two-dimensional and stationary. The limiting cases when the electrical conductivity goes to infinity or zero are discussed.