The Spreading of an Insoluble Surfactant on a Thin Non-Newtonian Fluid

In this paper, we explore fluid flow caused by the presence of an insoluble surfactant on a thin, incompressible power-law fluid over a horizontal substrate. The gradient in surface tension caused by the surfactant results in fluid flow away from the region where the surfactant was deposited. Work has been conducted with Newtonian fluids and surfactants; however, the extensive effect surfactants have on non-Newtonian fluids has not been studied as thoroughly. Using the lubrication approximation, we derive a system of coupled nonlinear partial differential equations (PDE) governing the evolution of the height of the fluid and the spreading of the surfactant. We also numerically simulate our system with a finite difference method and vary the power-law index to explore differences in profiles of shear-thickening and shear-thinning fluids. Next, we find significant agreement between our results and previous studies involving Newtonian fluids with power-law relations. Finally, we determine similarity scalings and solutions around the leading edge of the surfactant, which describe the behavior of the fluid and surfactant towards the region of the fluid where the surfactant ends.