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dc.contributor.authorWang, Taigeen_US
dc.date.accessioned2016-05-04T08:01:03Z
dc.date.available2016-05-04T08:01:03Z
dc.date.issued2016-05-03en_US
dc.identifier.othervt_gsexam:7689en_US
dc.identifier.urihttp://hdl.handle.net/10919/70907
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_US
dc.format.mediumETDen_US
dc.publisherVirginia Techen_US
dc.rightsThis Item is protected by copyright and/or related rights. Some uses of this Item may be deemed fair and permitted by law even without permission from the rights holder(s), or the rights holder(s) may have licensed the work for use under certain conditions. For other uses you need to obtain permission from the rights holder(s).en_US
dc.subjectThixotropyen_US
dc.subjectRegimeen_US
dc.subjectOscillatory Shearingen_US
dc.subjectSteady Shearingen_US
dc.subjectShear Banden_US
dc.subjectKorteweg Stressen_US
dc.titleMathematical Analysis on the PEC model for Thixotropic Fluidsen_US
dc.typeDissertationen_US
dc.contributor.departmentMathematicsen_US
dc.description.degreePHDen_US
thesis.degree.namePHDen_US
thesis.degree.leveldoctoralen_US
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen_US
thesis.degree.disciplineMathematicsen_US
dc.contributor.committeechairRenardy, Michaelen_US
dc.contributor.committeememberRogers, Robert Cen_US
dc.contributor.committeememberSun, Shu Mingen_US
dc.contributor.committeememberRenardy, Yurikoen_US


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