Evolution of Thin Liquid Film for Newtonian and Power-Law Non-Newtonian Fluids

Abstract

Abstract. Analytical relations for slow-motion thin liquid lms bounded by a xed wall and free surface for Newtonian and non-Newtonian uids are obtained in this work. Assuming long-wave approximation, the momentum and continuity equations for thin liquid lms of power-law uids are simpli ed and solved analytically to derive the evolution equation of thin liquid lms. The evolution equation is derived for two-and threedimensional cases. A relation for evolution of thin lms is obtained for a simple case in which the liquid lm is supported from below by a solid surface and subjected to gravity and constant surface tension forces. This evolution equation of thin lm has been solved numerically in order to compare the behavior of Newtonian and non-Newtonian liquids for di erent Bond numbers. It is shown that the power-law model at low and high strain rates is invalid and it a ects 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 di erent Bond numbers. The results show that the evolution of the free surface thin lm for pseudo plastic uids is di erent from that for Newtonian and dilatant uids.

Origin of filaments in finite-time in Newtonian and non-Newtonian thin-films

“…Ox points horizontally along the liquid-substrateair contact line and Oy points directly down the slope. A standard thin-film equation for a non-Newtonian liquid (18) exhibiting power-law behaviour with exponent n is 3η ∂ ĥ…”

Experimental and numerical investigation of the Rayleigh-Taylor instability of the Newtonian and dilatant fluid system

“…As for the Rayleigh-Taylor instability of dilatant (power-law 1 ) fluids, then it is considered in [12]. But it should be noted that this phenomenon is studied analytically and in thin layer located on a solid surface in the gravity field and presence of the surface tension forces.…”