Computer algebra models the inertial dynamics of a thin film flow of power law fluids and other non-Newtonian fluids

Roberts, A. J. (2007) Computer algebra models the inertial dynamics of a thin film flow of power law fluids and other non-Newtonian fluids. Technical Report. University of Southern Queensland. (Unpublished)

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Abstract

Consider the evolution of a thin layer of non-Newtonian fluid. I model the case of a nonlinear viscosity that depends only upon the shear-rate; power law fluids are an important example, but the analysis is for general nonlinear dependence upon the shear-rate. The modelling allows for large changes in film thickness provided the changes occur over a large enough lateral length scale. The modelling is based on two macroscopic modes by fudging the spectrum: here fiddle the surface boundary condition for tangential stress so that, as well as a mode representing conservation of fluid, the lateral shear flow u ∝ y is a neutral critical mode. Thus the resultant model describes the dynamics of gravity currents of non-Newtonian fluids when their flow is not very slow. For an introduction I first report on an analogous case of nonlinear diffusive dissipation.


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Item Type: Report (Technical Report)
Item Status: Live Archive
Depositing User: Prof Tony Roberts
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 11 Oct 2007 00:55
Last Modified: 02 Jul 2013 22:41
Uncontrolled Keywords: thin film flow
Fields of Research (FOR2008): 01 Mathematical Sciences > 0101 Pure Mathematics > 010109 Ordinary Differential Equations, Difference Equations and Dynamical Systems
09 Engineering > 0915 Interdisciplinary Engineering > 091504 Fluidisation and Fluid Mechanics
09 Engineering > 0915 Interdisciplinary Engineering > 091508 Turbulent Flows
URI: http://eprints.usq.edu.au/id/eprint/2010

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