Yielding to Stress: Recent Developments in Viscoplastic Fluid Mechanics

Abstract

The archetypal feature of a viscoplastic fluid is its yield stress: If the material is not sufficiently stressed, it behaves like a solid, but once the yield stress is exceeded, the material flows like a fluid. Such behavior characterizes materials common in industries such as petroleum and chemical processing, cosmetics, and food processing and in geophysical fluid dynamics. The most common idealization of a viscoplastic fluid is the Bingham model, which has been widely used to rationalize experimental data, even though it is a crude oversimplification of true rheological behavior. The popularity of the model is in its apparent simplicity. Despite this, the sudden transition between solid-like behavior and flow introduces significant complications into the dynamics, which, as a result, has resisted much analysis. Over recent decades, theoretical developments, both analytical and computational, have provided a better understanding of the effect of the yield stress. Simultaneously, greater insight into the material behavior of real fluids has been afforded by advances in rheometry. These developments have primed us for a better understanding of the various applications in the natural and engineering sciences.

Advances in the simulation of viscoplastic fluid flows using interior-point methods

“…Such a simple model is enough to reproduce interesting physics such as the existence of stopped and rigid-body plug regions in flows or the return to rest in a finite time. For recent reviews on yield stress fluids, we refer to [1,2].…”

Localized Deformation in Plastic Liquids on Elastomers

“…These materials, also known as viscoplastic fluids, soft jammed solids, and yield stress liquids, are commonly made of concentrated emulsions, colloidal suspensions, physically crosslinked gels, granular pastes, and foams [1][2][3][4]. Their rheological behaviour has long been studied using shear rheometers [5][6][7] and extrusion channels [3,8,9].…”

Posicionamento De Tampões Em Poços De Petróleo: Uma Investigação De Escoamentos De Inversão Por Gravidade

“…O módulo de armazenamento também é conhecido como módulo elástico e o módulo de dissipação também é denominado módulo viscoso ou de perda. Tais módulos são definidos como (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16) sendo ω a freqüência, τ a a amplitude de tensão e γ a = {γ(t)/ sin(ωt) a amplitude de deformação, τ (t) = τ a sin(ωt + δ) = τ a sin(ωt) + τ a cos(ωt) a tensão senoidal aplicada, A principal função deste teste é delimitar a região viscoelástica linear, ou seja, a região em baixas amplitudes caracterizada pela dependência linear entre a tensão e a deformação. Esse teste permite correlacionar a microestrutura com a resposta linear mecânica (30).…”

“…Caso contrário (τ > τ y ), a taxa de deformação tenderá a um valor constante não nulo. A tensão medida através do teste de creep é denominada tensão limite de escoamento estática pois é a tensão acima da qual o fluido começa a escoar (15).…”

“…Este determina a correspondência entre as dimensões reais do plano do escoamento ∆y e as dimensões em pixels na imagem. Logo, Cal = ∆y px (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17) sendo ∆y = D. Para cada teste realizado, utiliza-se as marcações ao longo do eixo vertical do tubo como fator de calibração. A Figura 3.11 ilustra um exemplo desta correlação.…”