TY - JOUR
T1 - Energy dissipation due to viscosity during deformation of a capillary surface subject to contact angle hysteresis
AU - Athukorallage, Bhagya
AU - Iyer, Ram
PY - 2014/2/15
Y1 - 2014/2/15
N2 - 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.
AB - 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.
KW - Calculus of variations
KW - Capillary surfaces
KW - Contact angle hysteresis
KW - Navier-Stokes equation
KW - Two-point boundary value problem
KW - Viscous dissipation
UR - http://www.scopus.com/inward/record.url?scp=84893703311&partnerID=8YFLogxK
U2 - 10.1016/j.physb.2013.10.024
DO - 10.1016/j.physb.2013.10.024
M3 - Article
AN - SCOPUS:84893703311
VL - 435
SP - 28
EP - 30
JO - Physica B: Condensed Matter
JF - Physica B: Condensed Matter
SN - 0921-4526
ER -