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Modeling the spreading and sliding of power-law droplets

Abstract

This work is a numerical investigation of the rheology effect on the spreading and/or sliding of droplets on surfaces. This paper first presents a mathematical model based on the long-wave approximation which encapsulates the non-Newtonian rheology using a power-law model. The resulting highly non-linear coupled set of equations are discretized using finite difference and the resulting algebraic system solved via an efficient Multigrid algorithm. Results for the spreading of fully wetting droplets on a horizontal substrate show that, for all other quantities being equal, an increase of the flow index leads to a more rapid wetting. The study also shows that, even for non-Newtonian fluids, the droplets velocity asymptotes to a constant value when sliding down an inclined plane. This terminal velocity is strongly dependent on the rheological parameters and as it is reached, the droplets travel with a visibly constant profile. Finally, the numerical simulations revealed the formation of a tail at the rear of the droplet as it slides down the incline plane in the case of shear-thickening fluids.

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