Drop trapping in axisymmetric constrictions with arbitrary contact angle

Abstract

The differential Young-Laplace equations are solved numerically with an iterative solution using the method of steepest descent to determine the shape of a drop trapped under gravity in an axisymmetric ring constriction. Prior work for non-wetting drops with a contact angle of π is extended to arbitrary values of the contact angle at the three-phase contact lines. The critical Bond number, representing a dimensionless ratio of gravitational and interfacial forces, and separating static trapping at lower Bond numbers from dynamic squeezing at higher Bond numbers, decreases with decreasing contact angle, indicating that drop squeezing occurs more easily at smaller contact angle. Indeed, a critical contact angle, which depends only on the drop-to-hole and ring-cross-section-to-hole size ratios, is found, below which all drops squeeze through the hole.