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

TL;DR

This paper investigates a pressure-dependent Maxwell fluid model, revealing unique non-classical behaviors and emphasizing the importance of pressure effects in viscoelastic fluid dynamics for practical applications.

Contribution

It introduces a generalized Maxwell model with pressure-dependent viscosity and relaxation time, highlighting novel behaviors not captured by classical models.

Findings

Demonstrates non-classical features of the pressure-dependent Maxwell fluid

Solves a boundary value problem illustrating model behavior

Highlights significance of pressure effects in viscoelastic fluids

Abstract

We study a variant of the well known Maxwell model for viscoelastic fluids, namely we consider the Maxwell fluid with viscosity and relaxation time depending on the pressure. Such a model is relevant for example in modelling 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.