Stability of a bounded liquid layer on a rotating horizontal plane

Abstract

The paper is devoted to the study of the stability of the relative equilibrium of a bounded liquid layer on a flat solid rotating base. A uniform gravity field is oriented perpendicular to the solid surface and presses the droplet against it. The equilibrium shape and its perturbations are axisymmetric. The free surface is simply-connected. The analysis is performed both for the case of the free contact line and for the case of the fixed one. The results obtained by these two models are compared, and the effect of the input parameters on the stability is investigated. It is established that the second model is in better accordance with empirical data. Unlike the first one, it allows the possibility of a zero height of the layer at the center at certain values of the contact angle and determines the negative effect of a low wettability of the solid substrate on the stability of the droplet. The minimum potential energy principle is used as a stability criterion. In this process all physically admissible small variations of a free surface shape are considered. An equilibrium state is supposed to be stable if and only if it corresponds to a minimum potential energy on the set of allowable virtual displacements, which is more restricted when the contact line is fixed.