Modelling thin films of truncated power-law fluids between bubbles and surfaces

When a bubble in a liquid approaches a surface, a thin film forms in the gap. Drainage of this thin film controls its stability. For Newtonian fluids, the Stokes–Reynolds–Young–Laplace (SRYL) model, which combines the lubrication equations and a surface force balance, predicts how the film evolves. We build on the SRYL model to predict how the film evolves for a truncated power-law fluid by modifying the lubrication equations. When a bubble approaches a surface at constant velocity, once the bubble is close enough to the surface, a dimple forms. For a shear-thinning fluid, this dimple forms earlier at a thinner film height compared to a Newtonian fluid with the same zero-shear viscosity. If the bubble stops, after long times the centre and minimum film thicknesses are similar for shear-thinning and Newtonian fluids in the absence of disjoining forces. Repulsive disjoining pressures result in an equilibrium flat film regardless of rheology, whereas attractive disjoining pressures cause the film to collapse. Films of shear-thinning fluids collapse earlier compared to Newtonian fluids. For shear-thickening fluids, the opposite effects are observed.