On the Flows of Fluids Defined through Implicit Constitutive Relations between the Stress and the Symmetric Part of the Velocity Gradient
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In this paper, a new class of algebraic implicit constitutive relations that can be used to describe the response of fluids and solids is presented, which can describe phenomena that the classical theory, wherein the stress is expressed explicitly in terms of kinematical variables, is incapable of describing, and also present a sensible way to approach important practical problems, such as the flows of colloids and suspensions and the turbulent flows of fluids, and that of the fracture of solids.Abstract:
Though implicit constitutive relations have been in place for a long time, wherein the stress, the strain (or the symmetric part of the velocity gradient), and their time derivatives have been used to describe the response of viscoelastic and inelastic bodies, it is only recently purely algebraic relationships between the stress and the displacement gradient (or the velocity gradient) have been introduced to describe the response of non-linear fluids and solids. Such models can describe phenomena that the classical theory, wherein the stress is expressed explicitly in terms of kinematical variables, is incapable of describing, and they also present a sensible way to approach important practical problems, such as the flows of colloids and suspensions and the turbulent flows of fluids, and that of the fracture of solids. In this paper we review this new class of algebraic implicit constitutive relations that can be used to describe the response of fluids.read more
Citations
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Journal ArticleDOI
Analysis of the Shear-Thinning Viscosity Behavior of the Johnson–Segalman Viscoelastic Fluids
T. Bodnár,Adélia Sequeira +1 more
TL;DR: In this article , a numerical comparison of viscoelastic shear-thinning fluid flow using a generalized Oldroyd-B model and Johnson-Segalman model under various settings is presented.
Journal ArticleDOI
Channel flows of shear-thinning fluids that mimic the mechanical response of a Bingham fluid
TL;DR: The linear stability of channel flows driven by pressure drops is carried out for fluids that exhibit a yield stress, the mechanical response of which is prescribed by the Bingham constitutive relation or two of its regularizations: the model due to Allouche and co-workers that is usually referred to as the "simple model" and Papanastasiou model as mentioned in this paper.
References
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