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

Michael T Farrugia, John J Shepherd, Andrew J Stacey

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.

Keywords


Viscous helical flow; perturbation methods

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DOI: http://dx.doi.org/10.21914/anziamj.v52i0.3748



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