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Title: Non-Newtonian fluids in complex geometries
Author: Chaffin, Stephen
ISNI:       0000 0004 6060 7613
Awarding Body: University of Sheffield
Current Institution: University of Sheffield
Date of Award: 2017
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We consider shear-dependent viscous and viscoelastic fluids in three types of geometries namely; cross-slot, snail ball and driven corner. The flow field and the stress field are solved analytically in a Hele-Shaw cross-slot geometry for weakly viscoelastic fluids, which is then corroborated using a finite element model. The analytic model further investigates the effects of asymmetry in the inlet outlet channels and the resulting elongational flow field. We found that changing the geometry from the symmetrical case reduces the uniformity in the elongation rates. For the snail ball system, two classes of solution are investigated: the rocking solution, and the runaway solution. It was found that the runaway solution still exists for both a power-law fluid and second order fluid models. The rocking solution is still possible for power-law fluid and a shear-thinning (thickening) fluid is predicted to travel less (further) than the Newtonian snail ball. The second order fluid does not allow the rocking solution but permits two constant rolling solutions, one stable and one unstable, which undergo a saddle-node bifurcation for sufficiently large viscoelastic effects. In the driven boundary problem we analyse a Carreau fluid driven by a moving plate. The problem was divided into two types of behavoir: Newtonian fluid with weak power-law dependence and a power law fluid with weak Newtonian effects. In the latter case we find that there is a break-down due to zero shear which is resolved using matched asymptomatic analysis. It is found that there are two competing effects/boundary layers: transition to Newtonian behavior and translation of the point of zero shear. In the finial section we analyze the effect of a mean field force on dumbbell dynamics under steady homogeneous velocity gradients. We find that the mean-field increases the extension of the dumbbells for both shear and elongational flow. The analysis demonstrates that there is a change in the singular extensional viscosity when the mean field term is present. Additionally, we find that the use of the Peterlin closure approximation for the spring forces leads to a dramatic over-estimation of the extension.
Supervisor: Rees, J. M. Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available