Flow Characteristics of a “Multiconfigurational”, Shear Thinning Viscoelastic Fluid with Particular Reference to the Orthogonal Rheometer
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This paper deals with the flow characteristics of a class of nonsimple viscoelastic fluid models developed by Rajagopal and Srinivasa (1999). The central feature of these models is that the stress response is elastic from a changing natural configuration with the viscous dissipation occurring due to changes in the natural state. The class of models considered are characterized by three independent parameters that represent respectively the elasticity, the viscosity and the shear thinning index. The stress relaxation response of the material is compared with experimental data reported by Bower et al. (1987) for polyisobutelene in cetane, and parameters that fit the data are calculated. The flow of such a fluid between parallel disks rotating about noncoincident axes (the orthogonal rheometer) is then studied. It is shown that the assumed velocity field leads to a system of second-order nonlinear ordinary differential equations (Rajagopal, 1982). A parametric study is then undertaken to see the effect of the various material, geometrical, and flow parameters on the flow characteristics. It is observed that inertial effects and shear thinning effects are roughly complementary in the range of parameters considered. While it is well known that boundary layers occur in these flows due to inertial effects, it is demonstrated that these boundary effects are insensitive to the Reynolds number but rather are determined by the absorption number. Finally, in the range of parameters that are commonly observed in such rheometers, it is shown that neglect of inertia causes significant discrepancies in the calculation of the boundary shear rates.
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