Mathematical Analysis on the PEC model for Thixotropic Fluids

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dc.contributor.authorWang, Taigeen
dc.contributor.committeechairRenardy, Michael J.en
dc.contributor.committeememberRogers, Robert C.en
dc.contributor.committeememberSun, Shu Mingen
dc.contributor.committeememberRenardy, Yuriko Y.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2016-05-04T08:01:03Zen
dc.date.available2016-05-04T08:01:03Zen
dc.date.issued2016-05-03en
dc.description.abstractA lot of fluids are more complex than water: polymers, paints, gels, ketchup etc., because of big particles and their complicated microstructures, for instance, molecule entanglement. Due to this structure complexity, some material can display that it is still in yielded state when the imposed stress is released. This is referred to as thixotropy. This dissertation establishes mathematical analysis on a thixotropic yield stress fluid using a viscoelastic model under the limit that the ratio of retardation time versus relaxation time approaches zero. The differential equation model (the PEC model) describing the evolution of the conformation tensor is analyzed. We model the flow when simple shearing is imposed by prescribing a total stress. One part of this dissertation focuses on oscillatory shear stresses. In shear flow, different fluid states corresponding to yielded and unyielded phases occur. We use asymptotic analysis to study transition between these phases when slow oscillatory shearing is set up. Simulations will be used to illustrate and supplement the analysis. Another part of the dissertation focuses on planar Poiseuille flow. Since the flow is spatially inhomogeneous in this situation, shear bands are observed. The flow is driven by a homogeneous pressure gradient, leading to a variation of stress in the cross-stream direction. In this setting, the flow would yield in different time scales during the evolution. Formulas linking the yield locations, transition width, and yield time are obtained. When we introduce Korteweg stress in the transition, the yield location is shifted. An equal area rule is identified to fit the shifted locations.en
dc.description.degreePh. D.en
dc.format.mediumETDen
dc.identifier.othervt_gsexam:7689en
dc.identifier.urihttp://hdl.handle.net/10919/70907en
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectThixotropyen
dc.subjectRegimeen
dc.subjectOscillatory Shearingen
dc.subjectSteady Shearingen
dc.subjectShear Banden
dc.subjectKorteweg Stressen
dc.titleMathematical Analysis on the PEC model for Thixotropic Fluidsen
dc.typeDissertationen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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