Applying Perturbation Analysis to the Helical Flows of Generalised Non-Newtonian Fluids

Host Institution:

RMIT University

Title of Seminar:

Applying Perturbation Analysis to the Helical Flows of Generalised Non-Newtonian Fluids

Speaker's Name:

John J. Shephard (School of Mathematics and Geospatial Science, RMIT University)

Time and Date:

Friday 24 August 2012, 3.30pm (EST)

Seminar Abstract:

When an incompressible viscous fluid flows in the gap between infinitely long coaxial cylinders, with an axial fluid velocity superimposed on a transverse rotational flow, the resulting fluid motion is termed a helical flow. Such flows are of interest in applications, particularly in modelling the action of a cup and bob rheometer modified to allow axial flow, in order to carry out measurements on slurries and other settling mixtures.

When the fluid is Newtonian, such helical flow is well understood, and is widely represented in the literature. However, when the fluid is generalized Newtonian, with the fluid stress a nonlinear function of the rate of shearing, the task of obtaining the velocity profile and associated fluid properties is considerably more difficult, and usually, numerical solutions must be resorted to.

In view of the above rheometer application, two situations are of significance to the present analysis. In many applications, the intercylindrical gap is small, to minimize experimental side effects. In such cases, a perturbation procedure based on some normalized form of the intercylindrical gap as perturbation parameter is indicated to solve the nonlinear equations of motion. On the other hand, in another important class of flows, the axial flow rate, Q, is relatively small; so that a perturbation analysis based on some scaled form of Q may be employed.
In this talk, we will analyse both the situations above and appropriate perturbation methods will be applied to obtain approximate expressions for the flow field and other related quantities for a selection of significant generalized Newtonian fluids.

We will also extend these techniques to examine the flow field in the intercylindrical gap when such a fluid has a yield stress property, i.e., it changes from behaviour as a rigid body at low stress to that of a viscous fluid at higher stresses.

Seminar Convenors:

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