Flows of viscoplastic fluids

Abstract

Viscoplastic fluids are a class of material which behave as a rigid solid at stresses below a threshold, "yield", stress, but flow like a fluid at larger stresses. This property is common in pastes, slurries and gels and hence the theory of viscoplastic fluid flow has wide ranging applications to environmental and industrial flows. In this thesis we analyse a number of viscoplastic flow problems through the techniques of matched-asymptotic methods, shallow-layer theory, direct numerical simulation, and laboratory experiments.

A particular focus is on the inclusion of a yield stress in classical similarity solutions for viscous fluids undergoing non-trivial two-dimensional motion in wedge geometries, for which we detail the existence and structure of unyielded "plugs" and viscoplastic boundary layers as functions of the non-dimensional yield stress. These features are typical of yield-stress flows and represent qualitatively different phenomenology from the corresponding Newtonian solutions. Static unyielded regions are of particular importance to applications. For example, in the food processing industry, stagnant material can spoil and contaminate the product. We quantify the size of unyielded regions of viscoplastic fluid in recirculating corner flows and squeezing flows between hinged plates, and make general conclusions about the unyielded region that forms at a stagnation point in a planar flow.

Finally, we explore the evolution of a thin layer of viscoplastic material scraped by a translating scraper. Such a flow occurs in applications including the removal of excess plaster from a wall or of mud from a road following a mudslide. We employ shallow layer theory to derive the transient evolution of the mound of fluid in front of the scraper and of the residual material behind the scraper, and perform laboratory experiments using a commercial hair gel to test the validity of the predicted surface profiles.

Date of Award	3 Oct 2023
Original language	English
Awarding Institution	University of Bristol
Supervisor	Andrew J Hogg (Supervisor) & Vladislav Tadic (Supervisor)