The Stokes boundary layer for a power-law fluid |
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Authors: | David Pritchard Catriona R McArdle Stephen K Wilson |
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Institution: | 1. Department of Mechanical and Aerospace Engineering, Case Western Reserve University, Cleveland, OH 44106, USA;2. NASA Glenn Research Center, Cleveland, OH 44135, USA;3. Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA 92093, USA |
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Abstract: | We develop semi-analytical, self-similar solutions for the oscillatory boundary layer (‘Stokes layer’) in a semi-infinite power-law fluid bounded by an oscillating wall (the so-called Stokes problem). These solutions differ significantly from the classical solution for a Newtonian fluid, both in the non-sinusoidal form of the velocity oscillations and in the manner at which their amplitude decays with distance from the wall. In particular, for shear-thickening fluids the velocity reaches zero at a finite distance from the wall, and for shear-thinning fluids it decays algebraically with distance, in contrast to the exponential decay for a Newtonian fluid. We demonstrate numerically that these semi-analytical, self-similar solutions provide a good approximation to the flow driven by a sinusoidally oscillating wall. |
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