Investigation of energy dissipation due to contact angle hysteresis in capillary effect

Capillary action or Capillarity is the ability of a liquid to flow in narrow spaces without the assistance of, and in opposition to, external forces like gravity. Three effects contribute to capillary action, namely, adhesion of the liquid to the walls of the confining solid; meniscus formation; and low Reynolds number fluid flow. We investigate the dissipation of energy during one cycle of capillary action, when the liquid volume inside a capillary tube first increases and subsequently decreases while assuming quasi-static motion. The quasi-static assumption allows us to focus on the wetting phenomenon of the solid wall by the liquid and the formation of the meniscus. It is well known that the motion of a liquid on an non-ideal surface involves the expenditure of energy due to contact angle hysteresis. In this paper, we derive the equations for the menisci and the flow rules for the change of the contact angles for a liquid column in a capillary tube at a constant temperature and volume by minimizing the Helmholtz free energy using calculus of variations. We describe the numerical solution of these equations and present results from computations for the case of a capillary tube with 1 mm diameter.