TY - JOUR

T1 - On a Two-point Boundary Value Problem for the 2-D Navier-Stokes Equations arising from Capillary Effect

AU - Iyer, Ram

AU - Athukorallage, Bhagya

PY - 2020/3/12

Y1 - 2020/3/12

N2 - In this article, we consider the motion of a liquid surface betweentwo parallel surfaces. Both surfaces are non-ideal, and hence, subject to contact angle hysteresis effect. Due to this effect, the angle of contact between a capillary surface and a solid surface takes values in a closed interval. Furthermore, the evolution of the contact angle as a function of the contact area exhibits hysteresis. We study the two point boundary value problem in time whereby a liquid surface with one contactangle at t=0 is deformed to another with a different contact angle at t = infinity while the volume remains constant, with the goal of determining the energy loss due to viscosity. The fluid flow is modeled by the Navier-Stokes equations, while the Young-Laplace equation models the initial and final capillary surfaces. It is well-known even for ordinary differential equations that two-point boundary value problems may not have solutions.We show existence of classical solut

AB - In this article, we consider the motion of a liquid surface betweentwo parallel surfaces. Both surfaces are non-ideal, and hence, subject to contact angle hysteresis effect. Due to this effect, the angle of contact between a capillary surface and a solid surface takes values in a closed interval. Furthermore, the evolution of the contact angle as a function of the contact area exhibits hysteresis. We study the two point boundary value problem in time whereby a liquid surface with one contactangle at t=0 is deformed to another with a different contact angle at t = infinity while the volume remains constant, with the goal of determining the energy loss due to viscosity. The fluid flow is modeled by the Navier-Stokes equations, while the Young-Laplace equation models the initial and final capillary surfaces. It is well-known even for ordinary differential equations that two-point boundary value problems may not have solutions.We show existence of classical solut

M3 - Article

SP - 31

JO - Mathematical Modelling of Natural Phenomena

JF - Mathematical Modelling of Natural Phenomena

SN - 0973-5348

ER -