Journal of Fluid Mechanics


Thin-film flow of a viscoelastic fluid on an axisymmetric substrate of arbitrary shape

a1 Department of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, Canada N6A 5B9
a2 Industrial Materials Institute, National Research Council of Canada, Boucherville, Quebec, Canada

Article author query
khayat re   [Google Scholar] 
kim k   [Google Scholar] 


The interplay between inertia and elasticity is examined in this study for the transient axisymmetric flow of a thin film. The fluid is assumed to emerge from an annulus, as it is driven by axial pressure gradient and/or gravity. The substrate is assumed to be stationary and of arbitrary shape. The boundary-layer equations are generalized for a viscoelastic film obeying the Oldroyd-B constitutive model. These equations are solved by expanding the flow field in terms of orthonormal shape functions in the radial direction and using the Galerkin projection, combined with a time-stepping implicit scheme, and integration along the flow direction. It is found that the viscosity ratio and fluid elasticity can have a significant effect on steady state as well as transient behaviour. It is also found that low-inertia and/or highly elastic fluids tend to accumulate near the annulus, exhibiting a standing wave that grows with time. This behaviour clearly illustrates the difficulty associated with coating viscoelastic high-viscosity fluids. A criterion for film rupture is also established, which is based on the steepening of flow and stress gradients. The topography of the substrate has a drastic effect on the flow as well.

(Published Online March 29 2006)
(Received April 7 2005)
(Revised September 12 2005)

Related Content