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Herschel–Bulkley fluid
About: Herschel–Bulkley fluid is a research topic. Over the lifetime, 1946 publications have been published within this topic receiving 49318 citations.
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TL;DR: In this article, a model of Bingham type taking into account inhomogeneous yield limit of the viscous fluid was chosen to describe the description of landslides, and necessary and sufficient conditions such that blocking of the fluid occurs.
Abstract: This work is concerned with the flow of a viscous plastic fluid. We choose a model of Bingham type taking into account inhomogeneous yield limit of the fluid, which is well-adapted in the description of landslides. After setting the general threedimensional problem, the blocking property is introduced. We then focus on necessary and sufficient conditions such that blocking of the fluid occurs. The anti-plane flow in twodimensional and onedimensional cases is considered. A variational formulation in terms of stresses is deduced. More fine properties dealing with local stagnant regions as well as local regions where the fluid behaves like a rigid body are obtained in dimension one.
47 citations
TL;DR: In this paper, the authors investigated the flow perturbation around a circular rigid particle during simple shear deformation for both Newtonian and non-Newtonian (power-law) fluids by finite-element modelling.
47 citations
TL;DR: In this paper, the existence of a weak solution for the Dirichlet boundary value problem for steady flows of Herschel-Bulkley fluids is proved and the rheology of such a fluid is defined by a yield stress τ* and a discontinuous constitutive relation between the Cauchy stress and the symmetric part of the velocity gradient.
Abstract: The equations for steady flows of Herschel–Bulkley fluids are considered and the existence of a weak solution is proved for the Dirichlet boundary-value problem. The rheology of such a fluid is defined by a yield stress τ* and a discontinuous constitutive relation between the Cauchy stress and the symmetric part of the velocity gradient. Such a fluid stiffens if its local stresses do not exceed τ*, and it behaves like a non-Newtonian fluid otherwise. We address here a class of nonlinear fluids which includes shear-thinning p-law fluids with 9/5 < p ≤ 2. The flow equations are formulated in the stress-velocity setting (cf. Ref. 25). Our approach is different from that of Duvaut–Lions (cf. Ref. 10) developed for classical Bingham visco-plastic materials. We do not apply the variational inequality but make use of an approximation of the Herschel–Bulkley fluid with a generalized Newtonian fluid with a continuous constitutive law.
47 citations
TL;DR: In this article, the authors present an analytical solution of interstitial fluid pressure in poroelastic materials under uniaxial cyclic loading, which contains transient and steady-state responses.
Abstract: Poroelasticity is a theory that quantifies the time-dependent mechanical behavior of a fluid-saturated porous medium induced by the interaction between matrix deformation and interstitial fluid flow. Based on this theory, we present an analytical solution of interstitial fluid pressure in poroelastic materials under uniaxial cyclic loading. The solution contains transient and steady-state responses. Both responses depend on two dimensionless parameters: the dimensionless frequency Ω that stands for the ratio of the characteristic time of the fluid pressure relaxation to that of applied forces, and the dimensionless stress coefficient H governing the solid–fluid coupling behavior in poroelastic materials. When the phase shift between the applied cyclic loading and the corresponding fluid pressure evolution in steady-state is pronounced, the transient response is comparable in magnitude to the steady-state one and an increase in the rate of change of fluid pressure is observed immediately after loading. The transient response of fluid pressure may have a significant effect on the mechanical behavior of poroelastic materials in various fields.
47 citations
TL;DR: This paper considers the immiscible displacement of a non-Newtonian fluid in a radial Hele-Shaw cell, and presents a detailed analysis of the flow, thus exposing features which until now have not been reported.
Abstract: The displacement of a high-viscosity non-Newtonian fluid by a low-viscosity Newtonian fluid in a Hele-Shaw cell is capable of producing ramified viscous-fingering patterns exhibiting fractal characteristics. Recently, it was established that interfacial tension has little influence on the formation of these fractal patterns. However, the precise mechanism behind their formation is not as yet fully understood. In this paper, we consider the immiscible displacement of a non-Newtonian fluid in a radial Hele-Shaw cell, and present a detailed analysis of the flow, thus exposing features which until now have not been reported. In particular, we find an effective length compression for the formation of viscous-fingering patterns and accelerated growth rates, which upon consideration of recent experimental results, are consistent with the formation of fractal viscous-fingering patterns.
47 citations