Marangoni-Stokes flow in plane geometries

An analytical examination of Marangoni-Stokes flow for a plane fluid bridge between two walls maintained at different temperatures is presented. Gravity, viscous, and thermal coupling effects are considered negligible, and the discussion is confined to steady conditions. It is shown that inner and outer flow fields exist when unequal temperatures are encountered at the interface, and that solutions are separate for each fluid motion. It is noted that once the inner solution is determined then the outer solution follows. A detailed listing of characteristic numbers appearing in dimensionless equations is presented. A simplified problem is defined, with the temperature gradient along the interface being the only driving force. Varying aspect ratios of the geometry are considered, and calculated streamlines, velocity profiles, isobaric lines, and interface shapes are provided.