Journal of Fluid Mechanics



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


ROGER E. KHAYAT a1 and KYU-TAE KIM a2
a1 Department of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, Canada N6A 5B9 rkhayat@uwo.ca
a2 Industrial Materials Institute, National Research Council of Canada, Boucherville, Quebec, Canada

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

Abstract

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)



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