Convective instability of dielectric liquid subjected to unipolarinjection of charge trough free surface

摘要

A problem for the Marangoni instability in a liquid layersubjected to an injection of ions is studied. The eigenvalue problemobtained after the linearization of the governing equations is solved byusing the Runge-Kutta-Merson's method of fourth order. When an uppersurface is deformable, we found that both stationary and oscillatoryinstabilities may occur. Two kinds of stationary instabilities have beendetected. The corresponding critical wave number k, the Marangoni numberMa and electrical analog of the Rayleigh number Ra have been obtainednumerically. Besides, we have revealed two types of wave instability:the gravity-capillar wave and thermocapillary wave with non-zerofrequency ω at k=0