Modeling and analysis of high shear viscoelastic Ellis thin liquid film phenomena

Abstract

In this paper, the Steady state thin layer flow of a viscoelastic Ellis fluid in contact with a vertical cylinder for drainage and lift problems is examined. Closed form solutions are obtained from the resulting differential equation using the well known binomial series technique. Furthermore, during the analysis of high shear viscoelastic Ellis liquid film, special cases including power law, Bingham plastic and Newtonian fluid film have been retrieved. The Physical quantities such as vorticity vector, thickness about the fluid film, flow rate and average velocity have been investigated for both the lift and drainage physical phenomena. The Thickness of the Ellis fluid film on cylindrical surfaces has been calculated. The velocity profiles for the phenomena are graphically sketched and during the study it is investigated that at the high shear rates the model reduces to the power law model and adequately low shear stress the model reduces to a Newtonian model. From the results it is noticed that, with increase in α and R, velocity increases for drainage case while decreases for lift case. Velocity profile for Newtonian and Bingham plastic fluids is calculated and it is observed that, the drainage velocity profile has increasing effect with the increase of r and has reverse effect for lift case with increasing r. The variation of n for power law model in drainage and lift have been plotted, where it is investigated that velocity of fluid layer grow up.