Author(s)

S. J. Baxter, H. Power, K. A. Cliffe & S. Hibberd

Abstract

Steady Stokes flow driven by gravity down an inclined plane wall around a circular cylinder attached to the wall is considered. The effects of the cylinder are examined for various flow configurations. Values for the unit normal and curvature of the free surface are found using a Hermitian radial basis function interpolation. All free surface profiles indicate an upstream peak, followed by a trough downstream of the obstacle with the peak decaying in a \“horseshoe” shaped deformation. Flow profiles are governed by four parameters; the plane inclination, the Bond number, the contact angle and the obstacle geometry. Keywords: BEM, three-dimensional, thin film, Newtonian viscous flow, cylinder. 1 Introduction Thin film flows down an inclined plane wall driven by gravity can often be modelled as an incompressible Stokes flow. Flows usually involve interaction with an obstacle either fully submerged of protruding through the film surface. Early published works considering two-dimensional film flows over obstacles utilized a variety of techniques for the numerical procedures required to obtain solutions.An overviewof these publications is presented in Blyth and Pozrikidis [1]. Hayes et al. [2] considered a three-dimensional steady, thin, viscous liquid film down an inclined plane driven by gravity and over small topographies. The lubrication approximation was used as the basis for their model and formulates a single linear inhomogeneous evolution equation. The free surface shape was then obtained by formation of the appropriate Green’s function.

Keywords

BEM, three-dimensional, thin film, Newtonian viscous flow, cylinder.