On the analysis of time-dependent drainage of Sisko fluid film slowly down a vertical belt

Abstract

Theoretical analysis of time-dependent drainage of Sisko fluid film slowly down a stationary vertical belt is presented in this paper. Employing [C. Gutfinger and J. A. Tallmadge, AIChE J. 10, 774 (1964)] approach the subsequent nonlinear partial differential equation is simplified. The Adomian decomposition method is then used to solve the simplified nonlinear partial differential equation to obtain the analytic expression for velocity. The analytic expressions for volume flow rate, shear stress, average film velocity, surface profile and film mean thickness are also derived. It is delineated that the velocity decreases by an increment in the Sisko fluid parameter and time while it increases by an increment in the fluid behavior index. The elevation of the Sisko surface profile decreases when the values of Sisko fluid parameter are increased, whereas it increases when the values of fluid behavior index and time are increased. The variable film thickness of four different lubricating greases is estimated by using experimental values of material constants and fluid behavior index [A. W. Sisko, Ind. Eng. Chem. Res. 50, 1789 (1958) and M. A. Delgado et al., Chem. Eng. Process. 44, 805 (2005)]. Furthermore, the flow variables studied for the Sisko fluid are also studied for the Newtonian fluid, and comparisons between both are provided.