Configurations of a drop stuck between two parallel laminae under zero gravity

Abstract In a zero-gravity environment and under static conditions, the interface between a drop and the surrounding fluid forms a surface of constant mean curvature. This concept is based on a general parametric representation proposed by Kenmotsu in 1980 with further developments discussed in 2003. In this article, we focus on studying the resulting axisymmetric surfaces in detail. Additionally, we rigorously characterize various configurations of a drop that is trapped between two parallel plates in the absence of gravity, while maintaining a fixed volume. These configurations depend on the contact angle with the plates (a phenomenological parameter) and the gap between them (a controllable parameter). Special attention is given to the case where the contact angle is equal to $$ \pi /2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>π</mml:mi> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> .