ISSN:
1089-7666
Source:
AIP Digital Archive
Topics:
Physics
Notes:
Local similarity solutions are presented for the stress field of a fluid described by the Oldroyd-B viscoelastic constitutive equation near the singularity caused by the intersection of a planar free surface and a solid surface along which Navier's slip law holds, the partial-slip/slip problem. For the case where the velocity field is given by Newtonian kinematics, the elastic stress field is predicted to have a logarithmic singularity as the point of attachment of the free surface is approached. Asymptotic analysis for the fully-coupled flow, where the stress and flow fields are determined simultaneously, results in a local form for the flow and elastic stress fields that is similar in form to that for the decoupled case. For both the coupled and decoupled flow problems, the strength of the singularity depends on the dimensionless solvent viscosity and the slip coefficient, but not upon the Deborah number. The asymptotic results for the coupled flow differ from the predictions with Newtonian kinematics in that the strength of the singularity in the rate-of-strain and elastic stress fields scales with the inverse of the dimensionless solvent viscosity, and suggest that calculations with decreasing solvent viscosity become increasingly difficult. The fully-coupled analysis also suggests that the asymptotic behavior in the limit of vanishing solvent viscosity, the UCM limit, is qualitatively different from that for finite values of the solvent viscosity. The structure of the flow and stress fields for both the coupled and decoupled flow problems is reproduced by finite element calculations. © 1997 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.869342
