McArdle, C. R. and Pritchard, D. and Wilson, S. K. (2012) The Stokes boundary layer for a thixotropic or antithixotropic fluid. Journal of NonNewtonian Fluid Mechanics . (Submitted)

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Abstract
We present a mathematical investigation of the oscillatory boundary layer (‘Stokes layer’) in a semiinfinite fluid bounded by an oscillating wall (the socalled ‘Stokes problem’), when the fluid has a thixotropic or antithixotropic rheology. We obtain asymptotic solutions in the limit of smallamplitude oscillations, and we use numerical integration to validate the asymptotic solutions and to explore the behaviour of the system for largeramplitude oscillations. The solutions that we obtain differ significantly from the classical solution for a Newtonian fluid. In particular, for antithixotropic fluids the velocity reaches zero at a finite distance from the wall, in contrast to the exponential decay for a thixotropic or a Newtonian fluid. For small amplitudes of oscillation, three regimes of behaviour are possible: the structure parameter may take values defined instantaneously by the shear rate, or by a longterm average; or it may behave hysteretically. The regime boundaries depend on the precise specification of structure buildup and breakdown rates in the rheological model, illustrating the subtleties of complex fluid models in nonrheometric settings. For larger amplitudes of oscillation the dominant behaviour is hysteretic. We discuss in particular the relationship between the shear stress and the shear rate at the oscillating wall.
Item Type:  Article 

Subjects:  D  G > General 
Research Groups:  Oxford Centre for Collaborative Applied Mathematics 
ID Code:  1555 
Deposited By:  Peter Hudston 
Deposited On:  05 Jul 2012 07:49 
Last Modified:  29 May 2015 19:15 
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