The inertial dynamics of thin film flow of non-Newtonian fluids

Roberts, A. J. (2008) The inertial dynamics of thin film flow of non-Newtonian fluids. Physics Letters Section A: General, Atomic and Solid State Physics, 372 (10). pp. 1607-1611. ISSN 0375-9601

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Abstract

Consider the flow of a thin layer of non-Newtonian fluid over a solid surface. I model the case where the viscosity depends nonlinearly on the shear-rate; power law fluids are an important example, but the analysis here is for general nonlinear dependence. The modelling allows for large changes in film thickness provided the changes occur over a relatively large enough lateral length scale. Modifying the surface boundary condition for tangential stress forms an accessible foundation for the analysis where flow with constant shear is a neutral critical mode, in addition to a mode representing conservation of fluid. Perturbatively removing the modification then constructs a model for the coupled dynamics of the fluid depth and the lateral momentum. For example, the results model the dynamics of gravity currents of non-Newtonian fluids when the flow is not creeping.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Deposited in accordance with the copyright policy of the publisher.
Depositing User: Prof Tony Roberts
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 19 Feb 2008 03:19
Last Modified: 02 Jul 2013 22:58
Uncontrolled Keywords: thin fluid flow; non-Newtonian fluid; inertia; power law rheology
Fields of Research (FOR2008): 09 Engineering > 0904 Chemical Engineering > 090408 Rheology
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
Socio-Economic Objective (SEO2008): E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering
Identification Number or DOI: doi: 10.1016/j.physleta.2007.10.014
URI: http://eprints.usq.edu.au/id/eprint/3862

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