Graduate Thesis Or Dissertation
 

Generalized measures of deformation-rates in torsional flows of viscoelastic fluids between two infinite parallel planes

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  • An introduction to the generalized measures of deformation- rates involving not only velocity gradients but also acceleration gradients is given and constitutive equations using these measures have been discussed. These new constitutive equations are then used to study torsional flows of viscoelastic fluids between two infinite parallel planes. In order to assess the advantage of this theory over the existing theories, a brief review of the existing nonlinear theories of continuous media has been made. In this review, it has been pointed out that the existing theories involve a number of terms in powers and products of the ordinary measures of strain or strain-rate and several unknown response functions of invariants of kinematic matrices. This is owing to the fact that the order of the measures of strain and strain-rates have not been fixed and their generalized measures have not been used in the formulation of constitutive equations. In the present investigation we have, by fixing a priori the orders of the measures of the deformation-rates mentioned above, developed the concept of the generalized measures and been able to obtain a suitable constitutive equation for viscoelastic fluids. The orders of the measures are so chosen that the resulting constitutive equation describes pseudoplastic fluids, for which the apparent coefficient of viscosity decreases with the increase in rate of shear. These new constitutive equations have been found to contain only four terms in the deformation-rate tensors and four rheological constants, and no unknown functions of the invariants. The constitutive equation obtained thus is applied to torsional flows of a viscoelastic fluid between two infinite parallel planes. The velocity components and pressure have been expanded in power series of a small parameter, and first- and second-order approximations to the velocity components have been obtained. The normal stress differences, velocity profiles, apparent coefficient of viscosity and their behavior depending on the rheological constants nave been investigated. The phenomena of reversed flows have also been discussed. Besides the freedom to choose the order of the measures, the rheological parameter entering the constitutive equations can also be suitably varied so as to correlate the theory with experiments. It is found that the behavior of a viscoelastic fluid depends on the sign as well as the magnitude of the rheological constants. Thus, the constitutive equations based on the concept of combined generalized measures predict adequately qualitative as well as quantitative information on the behavior of viscoelastic fluids and eliminate the need for assuming unknown response coefficients.
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