Symmetric unbounded liquid bridges

Thomas Vogel

Vol. 103 (1982), No. 1, 205–241

DOI: 10.2140/pjm.1982.103.205

Abstract

A symmetric unbounded liquid bridge is that surface formed by capillary action when a disc is withdrawn from an infinite reservoir. As do all capillary surfaces, liquid bridges satisfy the condition that mean curvature is proportional to height. The profile curves of the bridge surfaces are parametric extensions of the curves obtained in the symmetric exterior capillary problem. The family of profile curves is shown to have an envelope, and stability and instability criteria are derived relating to this envelope.

Mathematical Subject Classification 2000

Primary: 53A10

Secondary: 49F10

Milestones

Received: 13 April 1981

Published: 1 November 1982