Energy dissipation due to viscosity during deformation of a capillary surface subject to contact angle hysteresis

• Published in: Physica. B, Condensed matter Vol. 435; pp. 28 - 30
• Main Authors: Athukorallage, Bhagya, Iyer, Ram
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15.02.2014
• Subjects: Calculus of variations; Capillarity; Capillary surfaces; Computational fluid dynamics; Contact; Contact angle; Contact angle hysteresis; Fluid flow; Fluids; Hysteresis; Navier-Stokes equations; Navier–Stokes equation; Two-point boundary value problem; Viscous dissipation; Two-point boundary value problem; Contact angle hysteresis; Navier–Stokes equation; Viscous dissipation; Calculus of variations; Capillary surfaces
• ISSN: 0921-4526; 1873-2135
• DOI: 10.1016/j.physb.2013.10.024

A capillary surface is the boundary between two immiscible fluids. When the two fluids are in contact with a solid surface, there is a contact line. The physical phenomena that cause dissipation of energy during a motion of the contact line are hysteresis in the contact angle dynamics, and viscosity of the fluids involved. In this paper, we consider a simplified problem where a liquid and a gas are bounded between two parallel plane surfaces with a capillary surface between the liquid–gas interface. The liquid–plane interface is considered to be non-ideal, which implies that the contact angle of the capillary surface at the interface is set-valued, and change in the contact angle exhibits hysteresis. We analyze a two-point boundary value problem for the fluid flow described by the Navier–Stokes and continuity equations, wherein a capillary surface with one contact angle is deformed to another with a different contact angle. The main contribution of this paper is that we show the existence of non-unique classical solutions to this problem, and numerically compute the dissipation.