Steady Ostwald flow between two differentially rotating co-axial discs

Burgess, S.L.; Wilson, S. D. R.

doi:10.1007/bf00366552

Cited by 1 publication

(2 citation statements)

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“…In terms of non-Newtonian fluids, the rotating-disk configuration has attracted some attention in the context of electro-rheological flows as a fundamental boundary layer that has potential industrial/mechanical applications; see Burgess & Wilson (1996). Further interest has been directed towards this flow purely from its fluidmechanical interest, the long history of Newtonian investigations driving investigators to extend the von Kármán solution to power-law rheology fluids.…”

Section: Introductionmentioning

confidence: 99%

“…Further interest has been directed towards this flow purely from its fluidmechanical interest, the long history of Newtonian investigations driving investigators to extend the von Kármán solution to power-law rheology fluids. The analysis of Burgess & Wilson (1996) is notionally for the flow between two parallel planes; † however the large Reynolds number approximation that is applied in their work leads to the analysis being essentially that for an isolated plane (a low Reynolds number expansion is also presented that does take into account the finite axial range).…”

Section: Introductionmentioning

confidence: 99%

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

Denier

Hewitt

2004

J. Fluid Mech.

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We reconsider the three-dimensional boundary-layer flow of a power-law (Ostwaldde 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. IntroductionThe flow induced by the rotation of an infinite impermeable plane submerged in a viscous incompressible Newtonian fluid is described by a long-standing and classical (exact) solution of the Navier-Stokes equations. The solutions and their extensions have found many uses in industrial devices and processes, and they provide a test bed for the development of three-dimensional cross-flow instability theories and have applications to geophysics in Ekman pumping models and the decay of geostrophic flows.A similarity reduction of the fully nonlinear governing partial differential equations was provided by von Kármán (1921) for the flow induced by a rotating disk in a stationary fluid. This was later extended by Bödewadt (1940) to the problem of a rigidly rotating fluid above a stationary disk, with the obvious later continuation of the solutions across the intervening range of the parameter space for a rotating disk in a rotating fluid.In terms of the characteristics of the solutions to the Newtonian rotating-disk equations, it is well known that an enormously rich and detailed structure exists, spanned

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%