On stability of a catenoidal liquid bridge

Abstract

We derive a stability criterion for a catenoidal liquid bridge making contact angles 1 and 2 with two parallel plates. We show that for the case of equal contact angles 1 = 2 = the stability and instability sets are connected on the interval of admissible . We also give an example showing that for unequal contact angles, the family of stable catenoidal drops with one contact angle xed 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. A liquid bridge joining two parallel homogeneous plates in the absence of gravity will always take the form of a catenoid, nodoid or unduloid. We restrict attention here to catenoidal bridges, and ask under what condition the bridge will be stable in the sense of providing a local energy minimum. Given the contact angles 1, 2 of the plates and the separation distance h between them, it turns out that the volume of the liquid drop plays a crucial role in the stability of the bridge. Since we are only concerned with catenoidal liquid bridges in this paper, the volume is entirely determined by 1, 2 and h. We assume that h = 1 by scaling properly. Therefore it entirely depends upon the contact angles of the plates whether or not a stable catenoidal liquid bridge will be formed. In the rst part of this paper, we will derive a stability criterion for a catenoidal liquid drop making contact angels 1, 2. We show that such a bridge is stable if F (1; 2 ) 0, where