Bhagya Athukorallage

Macroscopic theory for capillary-pressure hysteresis.

In this article, we present a theory of macroscopic contact angle hysteresis by considering the minimization of the Helmholtz free energy of a solid-liquid-gas system over a convex set, subject to a constant volume constraint. The liquid and solid surfaces in contact are assumed to adhere weakly to each other, causing the interfacial energy to be set-valued. A simple calculus of variations argument for the minimization of the Helmholtz energy leads to the Young-Laplace equation for the drop surface in contact with the gas and a variational inequality that yields contact angle hysteresis for advancing/receding flow. We also show that the Young-Laplace equation with a Dirichlet boundary condition together with the variational inequality yields a basic hysteresis operator that describes the relationship between capillary pressure and volume. We validate the theory using results from the experiment for a sessile macroscopic drop. Although the capillary effect is a complex phenomenon even for a droplet as various points along the contact line might be pinned, the capillary pressure and volume of the drop are scalar variables that encapsulate the global quasistatic energy information for the entire droplet. Studying the capillary pressure versus volume relationship greatly simplifies the understanding and modeling of the phenomenon just as scalar magnetic hysteresis graphs greatly aided the modeling of devices with magnetic materials.

Elastic Surface Model For Beta-Barrels: Geometric, Computational, And Statistical Analysis

Over the past 2 decades, many different geometric models were created for beta barrels, including, but not limited to: cylinders, 1‐sheeted hyperboloids, twisted hyperboloids, catenoids, and so forth. We are proponents of an elastic surface model for beta‐barrels, which includes the minimal surface model as a particular case, but is a lot more comprehensive. Beta barrel models are obtained as numerical solutions of a boundary value problem, using the COMSOL Multiphysics Modeling Software. We have compared them against the best fitting statistical models, with positive results. The geometry of each individual beta barrel, as a rotational elastic surface, is determined by the ratio between the exterior diameter and the height. Through our COMSOL computational modeling, we created a rather large variety of generalized Willmore surfaces that may represent models for beta barrels. The catenoid is just a particular solution among all these shapes.

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.

Model of a contact lens and tear layer at static equilibrium

In this paper, we study the static stability of a spherical cap lens and a tear layer. The contact angle of the tear meniscus with the cornea and contact lens may have a range of values due to capillary effect hysteresis. As the lens is in static equilibrium all the forces and moments sum to zero. Capillary effect hysteresis is found to be a beneficial effect aiding the stability of the lens. The forces acting on the lens are its weight, force due to hydrostatic and atmospheric pressures and surface tension on the periphery of the lens due to the tear meniscus. The fixed parameters in the model are weight of the lens, coefficient of surface tension, magnitude of gravitational acceleration, density of the tear liquid and physical parameters of the lens such as the diameter and base curve radius. The adjustable parameters in the model are contact angles of the tear meniscus with the cornea and contact lens respectively and the position of the lens on the cornea. Numerical experiments suggest that there exists a range of values for the adjustable parameters that lead to physically reasonable solutions, for lens position; extent of overlap of the lower lid on the lens; pressure due to the lid on the lens; and the thickness of tear layer between the lens and the cornea.