Surface tension effects on interaction between two fluids near a wall

Interaction between two fluids near a fixed solid surface is modelled, with surface tension acting as an important influence on the assumed planar motion. The two fluids are immiscible, incompressible and have small density and viscosity ratios; the heavier more viscous body of fluid is approaching the solid surface and the other fluid is lying as a thin layer in between. In the so-called supercritical range where, for both fluids, inviscid forces dominate over viscous ones, a pair of pressure–shape relations is found which leads to a nonlinear integro-differential equation for the unknown interface shape. Analysis, computation and comparisons are applied to the equation. Travelling-state solutions are found of periodic and non-periodic form, including interesting cases which exhibit parabolic growth of the layer thickness in the far field.