Converging flows of viscoelastic materials

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Abstract
The kinematics of converging velocity fields such as those found in flows from a large duct or reservoir into a small tube are especially simple in the case of viscoelastic materials as they may be approximated by means of a diagonal deformation rate tensor. This result is shown to be valid in the present study in which aqueous polymeric solutions were utilized and is inferred as having been valid under the experimental conditions employed by Bagley in studies of molten polymers. It is suggested that asymptotic approximations based upon the diagonality of the deformation rate tensor may be of general use in analysis of flows of viscoelastic materials, that is, they could represent, potentially, simplifying approximations comparable in utility to the boundary layer approximations employed commonly in the analysis of flows of Newtonian fluids.An interesting prediction of the present analysis is that for flows from a large duct into a small one a plot of isotropic pressure vs. axial position exhibits a minimum near the inlet to the smaller duct. Experimental results are presented in partial support of this unusual behavior. The analysis also suggests that an orfice jet thrust technique for measurement of normal stresses, closely related to recent independent studies by Middleman and by Fabula, may be an indirect but especially simple and sensitive tool for measurement of material properties.