Generalized measures of deformation-rates in non-Newtonian hydrodynamics and their applications to some flow problems Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/n009w433r

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  • Integral representations for the generalized measures of deformation and deformation-rates have been obtained and suitable constitutive equations using these measures have been developed for viscoelastic materials, These new constitutive equations are then applied to study some flow problems, In order to assess the comparative advantage of this approach over the existing nonlinear theories of continuous media, a brief review of the latter has been first made. In this review, special attention has been drawn to the ever-increasing complexity of the constitutive equations which 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 complexity in these constitutive equations has arisen since generalized measures have not been used and consequently the order of the measures could not be fixed. With a view to bring simplicity and at the same time to retain generality, to ensure the effectiveness of the present theory, generalized measures of deformation-rates have been suitably extended before using them in the constitutive equations for isotropic incompressible fluids. After the orders of the generalized measures have been fixed, these new constitutive equations have been found to contain only four terms in the deformation-rate tensors and four rheological constants, but no unknown functions of the invariants, This new constitutive theory based on generalized measures has been applied in the solution of the following three types of problems: rectilinear flows, helical flows and torsional flow. The normal stress effects including swelling and thinning in Poiseuille flow, and climbing in Couette flows, velocity profiles, pressure variations, etc. have been studied in much greater detail and added precision than has been done in the literature so far. The phenomena of back flow between two parallel plates and helical flow in a narrow annular gap have also been studied. The results have been compared with the classical theory. To enhance the value of this investigation and to make it more useful for practical purposes, graphs of velocity profiles, pressure variations, etc. have also been drawn. A special feature of this analysis is to bring out important non-Newtonian effects in real fluids with an unparalleled precision and simplicity. All this has been accomplished because of the use of generalized measures. Possible scope of future work, where the idea of generalized measures may be profitably exploited, has also been discussed.
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