The equilibrium shape of rolled out meniscus

Abstract

The paper considers the issue of the equilibrium shape of the rolled out capillary meniscus in a homogeneous gravitational field. The approach used in this work differs from the earlier ones, as it takes into account the size dependence of the surface tension. With the help of such models, it will be possible to understand better the behaviour of small capillary bodies and to reveal the effects caused by the size dependence of physical parameters. For the purpose of the study, we propose to use an analogue of the well-known Tolman formula expressing the size dependence of the surface tension for the case of an interface with an arbitrary geometry. Taking into account the size dependence of the surface tension gives us equations which are predictably more complicated than the classical ones. Because of their complex nonlinearity, they cannot be solved by elementary functions, hence numerical methods are applied. The mathematical model of the meniscus is presented in a form that is better suited for numerical modelling of the profiles. We carried out computational experiments to determine the degree and nature of the effect of the parameter responsible for the size dependence of the surface tension on the equilibrium shape of the meniscus. We analysed the special cases when the exact solution of the Laplace equation and the exact relations between the meniscus profile coordinates can be obtained.

Keywords

• capillary meniscus
• surface tension
• size dependence
• capillary surface
• laplace equation
• capillary phenomena
• interfaces