A Numerical Study of Thin Liquid Film Flow over a Topographically Patterned Rotating Cylinder

Abstract

The discoveries in the field of thin liquid film flows over flat and non-flat objects have been thriving over the years. The designing and optimization of such process is quite difficult, owing to it being a complex phenomena. In the present work we are be focusing on understanding the fundamentals. We consider a thin-liquid film is flowing over a rotating cylinder with a sinusoidal pattern over the surface. To account for the intermolecular forces a body force term describing the van der Waals attraction is added to the Navier-Stokes equation. The film behaviour is studied by the application of lubrication approximation. The evolution equation for film thickness as a function of angular position and time is derived. This evolution equation studies the film behaviour under the influence of gravity, surface tension, intermolecular forces, viscous forces, surface topography and rotating rate is derived. A semi-implicit technique is used to numerically solve the evolution equation. For a thin-liquid film over the stationary cylinder at low Bond number() strong surface tension preserves the shape of the liquid film. And as the Bond number increases liquid flows towards location and a drop-like shape appears at steady state. On inclusion of intermolecular forces we are able to capture the film rupture at the thinnest region of the liquid film. The thin-liquid film over the patterned cylinder also evolves in the same manner. However, the film rupture time decreases with the increase in the frequency () of the sinusoidal pattern over the surface. In case of rotating cylinder, most of the liquid mass gets accumulated on the rotating side. Also, the liquid film over the patterned cylinder never reaches a steady state. However, the film interface attains a steady state after revolutions in the absence of pattern over the surface. The time to reach zero thickness decreases with increase in , , and Hamaker constant in van der Waals force. For rapidly spinning cylinders, continuous film over the patterned cylinder converts into drops (number equal to ) over the troughs or crests depending on the magnitude of Weber number(). The results clearly establish that the flow of thin-liquid films on rotating surfaces is affected by the presence of surface topography.