Lifting and drainage of Sisko fluid film with surface tension: A theoretical study on stationary points and thickness of uniform film

Abstract

This paper accords with the theoretical study of lifting and drainage of Sisko fluid film on a vertically upward moving cylinder with surface tension. The flow on cylinder is induced by the upward motion of the cylinder, gravity and surface tension gradient. The resulting nonlinear ordinary differential equation is solved for a series form solution by making use of the Adomian decomposition method (ADM). Expressions for the flow variables like velocity, volume flow rate, shear stress and surface tension are derived. Positions of stationary points and thickness of uniform film are computed numerically in MATHEMATICA. The inverse capillary number C, Stokes number [Formula: see text], Sisko fluid parameter [Formula: see text] and fluid behavior index n emerged as flow control parameters. The study showed that the positions of stationary points relocate towards the surface of the cylinder by the increase of C and [Formula: see text] while their positions relocate towards the fluid–air interface with increasing [Formula: see text] and n. Thickness of uniform film decreases when the values of C and [Formula: see text] are increased whilst it increases with the increase of [Formula: see text] and n. Analogy between the Newtonian fluid and the Sisko fluid’s shear thinning and shear thickening behaviors for positions of stationary points, thickness of uniform film and surface tension is also made.