Mathematical modelling of thixotropic and antithixotropic fluids

In this thesis we consider two fundamental flow problems, the Stokes problem and flow in a slowly-varying channel, for complex fluids. Specifically, we investigate these problems for thixotropic and antithixotropic fluids described by Mewis and Wagner's [Advances in Colloid and Interface Science, 147-148, 214-227 (2009)] general structure parameter model together with a version of the constitutive law proposed by Moore [Transactions and Journal of the British Ceramic Society, 58, 470-494 (1959)]. In certain limits, this model reduces to the generalised Newtonian power-law model, which we also consider. In chapters 2 and 3 we consider the Stokes problem for power-law, and thixotropic and antithixotropic fluids, respectively. Our main motivation for studying the Stokes problem is to investigate the interplay between the timescales of the fluid response and the forcing. Therefore, the emphasis of our investigations is on the periodic oscillatory behaviour of the systems, rather than on the transient initial phase during which the system adjusts to the attracting periodic solution. In chapter 4 we consider the two-dimensional flow of a thixotropic or antithixotropic fluid along a slowly-varying channel. Although previous studies have considered similar geometries, ours appears to be the first systematic development of a thin-film theory for a thixotropic or antithixotropic fluid. Like the conventional lubrication approach for a Newtonian fluid, our approach is based on an asymptotic expansion in powers of the aspect ratio δ in the limit δ - 0. Under appropriate assumptions concerning the Reynolds number and the dimensionless structure response rates, we obtain the governing equations for the velocity, pressure and structure parameter up to O(δ). In contrast to the Newtonian case, the lubrication equations include terms at O(δ), and it is at this order that thixotropic and antithixotropic effects occur.

Name dc:type.qualificationname

phd

Level dc:type.qualificationlevel

doctoral-pg

Grantor dc:publisher.institution

University of Strathclyde

Year dc:date.issued

2013

Author dc:creator

• McArdle, Catriona R.

DOI

10.48730/frfc-7375

Identifier

T13552

OAI identifier oai:identifier

oai:strathclyde:qj72p716m