Stability of a poorly conductive liquid subjected to unipolar autonomous charge injection in an electric field

Abstract

We study a model of autonomous unipolar charge injection from the cathode in a poorly conductive liquid in a steady electric field of a flat horizontal capacitor. According to this model, the charge density injected into the liquid has a constant term and a term directly proportional to the electric field strength in the capacitor. An electrohydrodynamic approximation is used. The case of weightlessness in an isothermal liquid is considered. The equilibrium distributions of the electric potential and charge density in the limiting case were found in analytical and numerical form. The linear stability of the poorly conductive liquid was studied. The boundary value problem was solved numerically by the targeting method using the Runge–Kutta–Fehlberg integration procedure. Neutral curves were obtained. Critical parameters were determined. The dependences of the convection thresholds on two injection parameters were found. With an increase in the modulus of either of the two injection parameters, the threshold for the occurrence of electroconvection decreases, it occurs with a smaller electric field.