ON SMALL OSCILLATIONS OF A CATENOIDAL LIQUID-DROP BETWEEN 2 PARALLEL PLATES IN ZERO-GRAVITY

This paper deals with the mathematical study of the problem of the small oscillations of a liquid drop with a free surface held together by surface tension between two parallel plates with free contact line. the contact angle being constant, under zero gravity, in the case of a catenoidal liquid drop in the equilibrium position. Using a functional method, we find again, at first, a condition of stability and, then, we obtain a variational formulation of the problem by means of which we prove the existence of the eigenfrequencies of the small oscillations of the liquid.