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Title: Low Reynolds number flows of generalized non-Newtonian fluids
Author: Childs, Laura Helen
Awarding Body: University of Bristol
Current Institution: University of Bristol
Date of Award: 2013
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A Newtonian fluid is one for which the stress induced by flow is proportional to the strain rate, with the constant of proportionality being the fluid's viscosity. Fluids not adhering to this linear relationship are described as non-Newtonian. This thesis considers several problems involving flows of generalized non-Newtonian fluids - where the effective viscosity is a nonlinear function of the strain rate - experiencing negligible inertial effects. First, we consider the flow of a power-law fluid through a rectangular duct. We propose a numerical method of solution, reliant on expressing the governing equations in terms of the stress tensor components, rather than the velocity field. This results in an effective method of determining the flux of fluid through a cross-section of a duct. The calculation is extended to duct flows of regularized Herschel-Bulkley fluids, and the determination of the critical yield stress below which there is no flow. We then consider free-surface dam-break flows of power-law fluids. By utilizing a similarity scaling for the front position of the flow with time, the flux calculation of the preceding work, and laboratory experiments, we propose a method of determining the rheological parameters of a power-law fluid. The settling velocity of a spherical particle through a power-law fluid is next examined. For particles settling within a background shear flow, the settling velocity is found to have two distinct dependencies on the dimensionless flow parameters, corresponding to regimes of dominant background shear or gravitational settling. Finally, we consider the effect that a modified sedimentation law, based upon the results of the settling calculation, has on shear flows of dilute particulate suspensions. The method of characteristics is applied to investigate the sedimentation law's impact on properties such as the concentration profile, and run-out length, of a sustained intrusion of particles suspended in a power-law fluid.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available