Hostname: page-component-588bc86c8c-zwqp5 Total loading time: 0 Render date: 2023-11-30T14:34:27.007Z Has data issue: false Feature Flags: { "corePageComponentGetUserInfoFromSharedSession": true, "coreDisableEcommerce": false, "useRatesEcommerce": true } hasContentIssue false

Asymptotic matching constraints for a boundary-layer flow of a power-law fluid

Published online by Cambridge University Press:  20 October 2004

School of Mathematical Sciences, The University of Adelaide, South Australia, 5005, Australia
Department of Mathematics, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK


We reconsider the three-dimensional boundary-layer flow of a power-law (Ostwald–de Waele) rheology fluid, driven by the rotation of an infinite rotating plane in an otherwise stationary system. Here we address the problem for both shear-thinning and shear-thickening fluids and show that there are some fundamental issues regarding the application of power-law models in a boundary-layer context that have not been mentioned in previous discussions. For shear-thickening fluids, the leading-order boundary-layer equations are shown to have no suitable decaying behaviour in the far field, and the only solutions that exist are necessarily non-differentiable at a critical location and of ‘finite thickness’. Higher-order effects are shown to regularize the singularity at the critical location. In the shear-thinning case, the boundary-layer solutions are shown to possess algebraic decay to a free-stream flow. This case is known from the existing literature; however here we shall emphasize the complexity of applying such solutions to a global flow, describing why they are in general inappropriate in a traditional boundary-layer context. Furthermore, previously noted difficulties for fluids that are highly shear thinning are also shown to be associated with the imposition of incorrect assumptions regarding the nature of the far-field flow. Based on Newtonian results, we anticipate the presence of non-uniqueness and through accurate numerical solution of the leading-order boundary-layer equations we locate several such solutions.

© 2004 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)