Film drainage and critical velocity of fluid particles in power-law fluids

This work studies the collision of fluid particles (bubbles or droplets) in non-Newtonian media whose viscosity obeys the power-law model, by analyzing the behavior of the drainage of the film between the particles. The model considers a time-dependent collision velocity governed by a force balance over each particle, which renders the estimation of both coalescence and rebound possible and as a result the critical velocity separating the two regimes. Results indicate that the shear-thinning behavior of the continuous medium favors coalescence, whereas shear-thickening films promote rebound. The critical velocity increases with decreasing power-law index and follows an exponential trend with the equivalent particle size for a given value of the power-law index. The exponent showing the dependency of the critical velocity on the equivalent particle size changes linearly with the power-law index within the investigated parameter range. Both the drainage behavior and the critical velocity are shown to be affected only negligibly by the selection of the drag force closure, i.e., whether they are proposed by considering Newtonian or non-Newtonian media.