Three-dimensional simulation of droplet dynamics in a fractionally-wet constricted channel

Abstract

This study presents droplet dynamics due to capillarity-wettability interaction through a constricted capillary channel. Previous research has investigated the droplet motion in a constricted capillary channel with a two-dimensional geometry and uniform wettability to determine the critical pressure necessary for the droplet to pass through the constriction, but did not consider the change of pressure as the droplet crosses through a constricted geometry. To explore the dynamic behavior of droplet motion across a constriction, a direct numerical simulation of a droplet in a three-dimensional fractionally-wet constricted channel is performed where we have two different contact angles on opposing faces of the constriction. The results show that the fractional wettability condition significantly affects the evolution of fluid-fluid and fluid-solid interfaces, pressure drop, and displacement patterns. We show that droplet dynamics in a fractionally-wet channel do not necessarily follow the same behavior as in a uniform capillary channel and cannot be predicted using uniform wettability surfaces depicted by an average contact angle. In particular, the pressure difference needed to push the droplet through the restriction with fractional wettability is lower than that for a uniform channel with a constant contact angle representing the less favorable wettability state. The fluid-fluid meniscus often forms saddle-shaped interfaces with curvature of opposite sign in orthogonal directions. Moreover, the effects of droplet size, capillary number, viscosity ratio, and constriction shape are elucidated. The pressure difference increases with droplet size and capillary number. Triangular cross-sections can be accessed at a lower pressure because of wetting layer flow.