A perturbation analysis of the flow of a Powell--Eyring fluid between coaxial cylinders

Abstract

The Powell--Eyring generalised viscous fluid model was developed to model the flow of viscous inelastic shear thinning fluids, such as polymer melts and suspensions of solids in non-Newtonian solvents. We consider the helical flow of a Powell--Eyring fluid between infinitely long coaxial cylinders. Such a flow is of relevance to a number of applications, including rheometry. We show that a perturbation approach to the flow problem yields simple explicit expressions for the fluid velocity field, which may then be applied to obtain approximations to other features of the flow. References C. Chiera, H. J. Connell and J. J. Shepherd, Perturbation analysis of the helical flow of non-Newtonian fluids with application to a recirculating coaxial cylinder rheometer, Mathematical and Computer Modelling, 18, No. 10: 131--140, 1993. B. D. Coleman and W. Noll, Helical flow of General Fluids, J. App. Phys., 10: 1508--1512, 1959. R. I. Tanner, Engineering Rheology, Oxford University Press, Oxford, 1988. M. T. J. Farrugia, A Perturbation Analysis of the Flow of a Powell--Eyring Fluid between Coaxial Cylinders, Honours Thesis, Mathematics Department, RMIT, 1999. R. B. Bird, R. C. Armstrong and D. Hassager, Dynamics of Polymetric liquids, Vol. 1, John Wiley and Sons, 1987.