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On Maxwell fluids with relaxation time and viscosity depending on the pressure

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TLDR
Using a generalized Maxwell model with pressure dependent material moduli, a variant of the well-known Maxwell model for viscoelastic fluids is considered, namely a Maxwell fluid with viscosity and relaxation time depending on the pressure.
Abstract
We study a variant of the well-known Maxwell model for viscoelastic fluids, namely we consider a Maxwell fluid with viscosity and relaxation time depending on the pressure. Such a model is relevant for example in modelling the behaviour of some polymers and geomaterials. Although it is experimentally known that the material moduli of some viscoelastic fluids can depend on the pressure, most of the studies concerning the motion of viscoelastic fluids do not take such effects into account despite their possible practical significance in technological applications. Using a generalized Maxwell model with pressure dependent material moduli we solve a simple boundary value problem and we demonstrate interesting non-classical features exhibited by the model.

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The viscosity of the earth's mantle

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On elastic solids with limiting small strain: modelling and analysis

TL;DR: In this article, implicit constitutive models for elastic solids with limiting small strain have been studied in the context of nonlinear partial differential equations, leading to new classes of challenging mathematical problems.
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On a variant of the Maxwell and Oldroyd-B models within the context of a thermodynamic basis

TL;DR: In this paper, the authors developed models within a thermodynamic standpoint that are very similar in form to the classical Maxwell and Oldroyd-B models but differ from them in one important aspect, the manner in which they unload instantaneously from the deformed configuration.
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Remarks on the notion of ``pressure''

TL;DR: In this paper, the distinction between various significations of the word "pressure" and their implications with regard to response relations for bodies is discussed, and the distinction in the meanings of the above terms assumes paramount significance when discussing properties of materials, which could possibly depend on "pressure".
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Forced convective Maxwell fluid flow through rotating disk under the thermophoretic particles motion

TL;DR: In this paper, numerical analysis is performed for incompressible Maxwell fluid model flow under the implications of thermophoresis and Cattaneo-Christov theory, where the system that comprises differential equations of partial derivatives is remodel into the system of differential equations by similarity transformations and then solved through Runge-Kutta-4 with shooting technique.
References
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Book

Viscoelastic properties of polymers

John D. Ferry
TL;DR: In this article, the authors describe the nature of Viscoelastic behavior of polymeric systems and approximate relations among the linear Viscoels and approximate interrelations among the Viscelastic Functions.
Book

A treatise on the theory of Bessel functions

G. N. Watson
TL;DR: The tabulation of Bessel functions can be found in this paper, where the authors present a comprehensive survey of the Bessel coefficients before and after 1826, as well as their extensions.
Book ChapterDOI

On the Effect of the Internal Friction of Fluids on the Motion of Pendulums

TL;DR: In this paper, the reduction to a vacuum correction is considered, which is the only correction that is necessary for a simple pendulum to swing in a vacuum environment, due to the buoyancy of the fluid.
Journal ArticleDOI

On the Dynamical Theory of Gases

TL;DR: The theory of transport processes in gases, such as diffusion, heat conduction, and viscosity, is developed on the assumption that the molecules behave like point-centres of force as mentioned in this paper.