Plenary Lecture

Couette-Poiseuille Flow of Non-Newtonian Fluids in Concentric Annuli

Prof. Petr Filip
Institute of Hydrodynamics
Prague, Czech Republic
E-mail: filip@ih.cas.cz

Abstract: The flow of non-Newtonian fluids through an annulus is often encountered in various industrial processes such as transportation of drilling fluids in petroleum industry and extrusion of polymers (in a mandrel region).
In the annular flow one of the most difficult complications consists in the inhomogeneous distribution of shear stresses in the annular region. The analysis of annular flow originated by a combination (Couette-Poiseuille flow) of the drag (Couette flow) and pressure (Poiseuille flow) forces is further complicated by the fact that no superposition principle takes place; in other words, this flow field is not possible to obtain as a mere superposition of corresponding Couette and Poiseuille flow fields. This is a direct consequence of the dependence of fluid viscosity on velocity field invariants.
Roughly speaking there are two approaches how to cope with the description of these flow situations. The numerical approach aims at a calculation of the quantities (e.g. velocity components, flow rate) describing the concrete problem, and with an arbitrary change of the entry parameters (geometry, kinematics, rheological characteristics) it is necessary to repeat the whole procedure from the beginning.
The other approach lays emphasis on the functional participation of the individual entry parameters in the whole solution. This method enables to decide which parameters should be altered (and in which way) to obtain the more favourable results e.g. from the viewpoint of production rate. In this case the optimum approach is represented by an explicit solution or 'almost explicit' one (as e.g. so-called quasisimilarity solution) deviating negligibly from the exact one.
In the present contribution this second approach is presented for two types of Couette-Poiseuille flow in concentric annuli. For both types it is supposed that an outer cylinder is stationary and pressure is exerted in an axial direction. The difference is in kinematics of an inner cylinder - either moving along (application of the Vocadlo rheological model) or rotating round (application of the power-law model) its axis.

Brief Biography of the Speaker:
Study:
Charles University, Faculty of Mathematics and Physics, specialty applied mathematics, Prague
Ph.D. Study:
Institute of Mathematics, Czechoslovak Academy of Sciences, Prague
Dept of Partial Differential Equations
Ph.D.degree, Thesis: 'Oscillation of Wave Equation in Two Dimensions'

now with The Institute of Hydrodynamics, Academy of Sciences of the Czech Republic in Prague
Fields of interest: Rheology, Fluid Mechanics
Professional membership: The Society of Rheology, The Polymer Processing Society