Squeeze Flow of Stress Power Law Fluids

Lorenzo Fusi,Andrea Ballotti

doi:10.3390/fluids6060194

Abstract

In this paper, we studied the squeeze flow between circular disks of a new class of fluids defined by an implicit relation referred to as stress power law fluids. The constitutive response of these fluids was written expressing the symmetric part of the velocity gradient as a tensorial function of the Cauchy stress. We assumed that the aspect ratio between the gap separating the disks and the radius was small so that a lubrication expansion could be adopted. We wrote the general problem and looked for a solution that could be written in terms of the small aspect ratio parameter. We obtained a sequence of problems that could be solved iteratively at each order, and we focused on the leading and first order, deriving explicit expressions for the velocity field, stress, and pressure.

Highlights

Malek et al [1] studied incompressible fluids from a new perspective, namely that in which the constitutive equation is written expressing kinematical quantities as a function of the stress
In the stress power law model, the constitutive equation is defined by the symmetric part of the velocity gradient being a function of the deviatoric part of the Cauchy stress tensor
We studied the squeeze flow between parallel circular disks of a fluid whose constitutive equation is of the type of (7) under the assumption that the gap between the squeezing disks is much smaller than their radius

Summary

Introduction

Malek et al [1] studied incompressible fluids from a new perspective, namely that in which the constitutive equation is written expressing kinematical quantities as a function of the stress. In the stress power law model, the constitutive equation is defined by the symmetric part of the velocity gradient being a function of the deviatoric part of the Cauchy stress tensor. This new class of fluids has many interesting applications, among which we must mention blood and colloidal dispersions; see [3,4,5,6]. We shall provide a graphical representation of the velocity, stress, and pressure fields, and we discuss the obtained results

Squeeze Flow

Results and Discussion

Conclusions