Structure and stress in the gas–liquid–solid contact region

Abstract

The physics of the region where a fluid–fluid interface meets a solid, a region where wetting phenomena are governed, is studied with the gradient theory of an inhomogeneous equilibrium fluid. The results illuminate the molecular origins of contact angle and relate this quantity to local fluid structure and stress.

Liquid and vapour in equilibrium between two flat, parallel walls is the system examined. The distance between the walls is varied to study the effect of confinement on the contact region. The fluid is a one-component, Peng–Robinson fluid. The solid–fluid potential model is based on the Lennard-Jones 6–12 molecular pair potential.

The contact region is divided into subdomains and the density field is expanded in finite-element basis functions. On each subdomain the Galerkin weighted residual of the gradient equation is put equal to zero and the resulting set of non-linear algebraic equations is solved by Newton's iteration process. The converged Jacobian from Newton's process provides information about parametric sensitivity and thermodynamic stability. Asymptotic approximations are used wherever possible to enhance the power of the basis set.

The primary results are density and stress profiles. Young's equation of capillarity is found to be valid when properly interpreted. There is, however, a contact region near the solid where Young's equation is not valid and where the fluid–fluid meniscus loses its meaning. Moreover, in the small systems for which theoretical or molecular dynamics calculations are presently affordable the angle of inclination of the meniscus is a function of distance from the wall and therefore cannot be identified with Young's contact angle.

Besides their value to surface and colloid science the results testify to the power of modern computer-aided analysis by finite-element subdomain methods.