McArdle, Catriona and Pritchard, David and Wilson, Stephen (2012) The Stokes boundary layer for a thixotropic or antithixotropic fluid. Journal of Non-Newtonian Fluid Mechanics, 185-186. pp. 18-38. ISSN 0377-0257Full text not available in this repository. (Request a copy from the Strathclyde author)
We present a mathematical investigation of the oscillatory boundary layer in a semi-infinite fluid bounded by an oscillating wall (the so-called ‘Stokes problem’), when the fluid has a thixotropic or antithixotropic rheology. We obtain asymptotic solutions in the limit of small-amplitude oscillations, and we use numerical integration to validate the asymptotic solutions and to explore the behaviour of the system for larger-amplitude 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 long-term average; or it may behave hysteretically. The regime boundaries depend on the precise specification of structure build-up and breakdown rates in the rheological model, illustrating the subtleties of complex fluid models in non-rheometric 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.
|Keywords:||Stokes boundary layer, thixotropic fluid , antithixotropic fluid, Probabilities. Mathematical statistics, Materials Science(all), Chemical Engineering(all), Mechanical Engineering, Applied Mathematics, Condensed Matter Physics|
|Subjects:||Science > Mathematics > Probabilities. Mathematical statistics|
|Department:||Faculty of Science > Mathematics and Statistics|
|Depositing user:||Pure Administrator|
|Date Deposited:||09 Aug 2012 13:21|
|Last modified:||22 Mar 2017 12:16|