Marangoni effect and spreading of an insoluble surfactant over a deep layer of a power-law fluid

In this work, a numerical study is conducted to analyze the spreading dynamics of an insoluble and non-diffusive surfactant through the Marangoni convection mechanism on the surface of a deep layer of a shear thickening fluid, whose behavior follows the power-law fluid rheological model. The momentum and convective–diffusion equations are non-dimensionalized and solved numerically by an implicit finite-difference scheme. The dynamic of the physical problem depends on dimensionless parameters that control the decay of the temporal variations in the surfactant concentration: the Reynolds number $Re$, the power index $n$, and $\varepsilon$ is the ratio between the wave amplitude and the mean surfactant concentration. The main findings show that opposite to shear-thinning fluids, shear-thickening fluids require less time to reach the uniform condition in the surfactant distribution due to a lower response to the inertia of the fluid; this time is even less than that needed for Newtonian fluids. Besides, both types, pseudoplastic and dilatant fluids, showed a similar response when varying the Reynolds number; as this parameter increases, the temporal decay of the surfactant concentration on the fluid surface increases while the distance over which the fluid motion is diffused towards the bottom of the fluid layer decreases.