On stability of a catenoidal liquid bridge

Abstract

We derive a stability criterion for a catenoidal liquid bridge making contact angles γ1 and γ2 with two parallel plates. We show that for the case of equal contact angles γ1 = γ2 = γ the stability and instability sets are connected on the interval of admissible γ. We also give an example showing that for unequal contact angles, the family of stable catenoidal drops with one contact angle fixed can be disconnected with respect to the other angle. At the end of the paper we give a complete description of the stability and instability sets for various contact angles.