Conductivity Models of Electrothermal Convection in a Plane Layer of Dielectric Liquid

Experiments have demonstrated that a d-c voltage applied across a thermally stabilized plane layer of dielectric liquid can induce both stationary and oscillatory instabilities and thereby significantly augment heat transfer. While a unipolar charge injection model can explain both types of instability, the predictions of a conductivity model depend crucially upon the way the electrical conductivity varies with temperature. Here a conductivity model is derived from a dissociation and recombination model in an Ohmic limit, and its linear instabilities for linear, quadratic, and Arrhenius-type conductivity variations are investigated numerically. Oscillatory instability is usually predicted and an energy argument rules out stationary instability for the type of conductivity variation observed experimentally. This casts doubts on the experimental relevance of earlier quadratic conductivity models predicting stationary instability. The relative merits of conductivity and charge injection models are discussed in the light of empirical evidence.