Evolution of thin liquid film for Newtonian and power-law non-Newtonian fluids

Abstract

Analytical relations for slow-motion thin liquid films bounded by a fixed wall and free surface for Newtonian and non-Newtonian fluids are obtained in this work. Assuming long-wave approximation, the momentum and continuity equations for thin liquid films of power-law fluids are simplified and solved analytically to derive the evolution equation of thin liquid films. The evolution equation is derived for two- and three-dimensional cases. A relation for evolution of thin films is obtained for a simple case in which the liquid film is supported from below by a solid surface and subjected to gravity and constant surface tension forces. This evolution equation of thin film has been solved numerically in order to compare the behavior of Newtonian and non-Newtonian liquids for different Bond numbers. It is shown that the power-law model at low and high strain rates is invalid and it affects the results. The Rayleigh-Taylor instability is another subject that is studied in this work. This interesting phenomenon is investigated by numerically solving the evolution equation for different Bond numbers. The results show that the evolution of the free surface thin film for pseudo plastic fluids is different from that for Newtonian and dilatant fluids.