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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, the authors derived approximate analytic R-T stability criteria for both finite and infinitesimal perturbations of the driven surface of an incompressible solid plate of a given thickness, shear modulus, and von Mises yield stress uniformly accelerated by a massless fluid.
Abstract: The Rayleigh–Taylor (R-T) instability theory is usually applied to the acceleration of one fluid by a lower density one, but also becomes applicable to a solid accelerated by a fluid at very high pressure. Approximate analytic R-T stability criteria are derived for both finite and infinitesimal perturbations of the driven surface of an incompressible solid plate of a given thickness, shear modulus, and von Mises yield stress uniformly accelerated by a massless fluid. The Prandtl-Reuss equations of elastic-plastic flow are assumed for the solid. A single degree of freedom, amplitude q, is assumed for the spatial dependence of the perturbation, which is approximated to be that of the semi-infinite half-plane ideal fluid linear R-T eigenfunction. The temporal dependence of q, however, is determined self-consistently from global energy balance, following a previously published model. The (significant) effect of the unperturbed solid’s stress tensor is included and related to the converging/diverging geometrie...

23 citations

Journal ArticleDOI
TL;DR: In this paper, a steady two-dimensional flow of an electrically conducting incompressible fluid over a vertical stretching surface is considered, where the flow is permeated by a uniform transverse magnetic field.

23 citations

Journal ArticleDOI
TL;DR: In this article, the authors present a three dimensional numerical study of thermal plumes, developing from a localized heat source in a yield stress and shear thinning fluid, assuming that the fluid viscosity follows a Herschel-Bulkley law.
Abstract: We present a three dimensional numerical study of thermal plumes, developing from a localized heat source in a yield stress and shear thinning fluid. We assume that the fluid viscosity follows a Herschel–Bulkley law with a low shear rate viscosity plateau. Comparison of the plume onset time and morphology observed in the numerical study and in laboratory experiments with Carbopol shows good agreement. An extensive parameter study allows us to identify two local non-dimensional parameters that determine whether a plume rises through the fluid. The first parameter is the Bingham number, Bi, which compares the yield stress to the viscous stress. The second parameter, the yield number Ψ, compares the stress induced by the buoyancy of an equivalent hot sphere to the yield stress. We find that a plume develops only if Ψ > Ψc = 5 ± 1.2 and Bi 1. Hot fluid continues to rise from the bottom of the tank but spreads under an unyielded, high viscosity region at the top of the box.

23 citations

Journal ArticleDOI
TL;DR: In this paper, the stability of the plane Couette flow of a viscoelastic fluid adjacent to a flexible surface is analyzed with the help of linear and weakly nonlinear stability theory in the limit of zero Reynolds number.
Abstract: The stability of the plane Couette flow of a viscoelastic fluid adjacent to a flexible surface is analyzed with the help of linear and weakly nonlinear stability theory in the limit of zero Reynolds number. The fluid is described by an Oldroyd-B model, which is parametrized by the viscosity \eta, the relaxation time \lambda, and the parameter \beta, which is the ratio of solvent-to-solution viscosity; beta=0 for a Maxwell fluid and \beta=1 for a Newtonian fluid. The wall is modeled as an incompressible neo-Hookean solid of finite thickness and is grafted to a rigid plate at the bottom. The neo-Hookean constitutive model parametrized by the shear modulus G, augmented to include the viscous dissipation, is used for the solid medium. Previous studies for the Newtonian flow past a compliant wall predict an instability as the dimensionless shear rate \Gamma= $(\eta^{V/GR})$ is increased beyond the critical value $\Gamma_c$. The present analysis investigates the effect of fluid elasticity, in terms of the Weissenberg number W=$\lambda {G/\eta}$, on the critical value of the imposed shear rate $\Gamma_c$ for various parameters. The fluid elasticity is found to increase $\Gamma_c$, indicating the stabilizing influence of the polymer addition on the viscous instability. For dilute polymeric solutions with \beta \geq 0.5, the flow is stable when the Weissenberg number is increased beyond a maximum value Wmax, and Wmax increases proportional to the ratio of solid-to-fluid thickness H. For concentrated polymer solutions and melts with \beta \le0.5, the flow becomes unstable when the strain rate increases beyond a critical value for any large Weissenberg number. The weakly nonlinear analysis reveals that the bifurcation of the linear instability is subcritical when there is no dissipation in the solid. The nature of bifurcation, however, changes to supercritical when the viscous effects in the solid are taken into account and the relative solid viscosity \etar is large such that sqrt( \eta_r)/H \ge1. The equilibrium amplitude and the threshold strain energy for the solid have been calculated, and the effect of parameters H, \beta, \etar, and interfacial tension on these quantities is analyzed.

23 citations

Journal ArticleDOI
TL;DR: In this paper, an initial value investigation is made of the motion of an incompressible, viscous conducting fluid with embedded small spherical particles bounded by an infinite rigid nonconducting plate.
Abstract: An initial value investigation is made of the motion of an incompressible, viscous conducting fluid with embedded small spherical particles bounded by an infinite rigid non-conducting plate. Both the plate and the fluid are in a state of solid body rotation with constant angular velocity about an axis normal to the plate. The flow is generated in the fluid-particle system due to non-torsional oscillations of a given frequency superimposed on the plate in the presence of a transverse magnetic field. The operational method is used to derive exact solutions for the fluid and the particle velocities, and the wall shear stress. The small and the large time behaviour of the solutions is discussed in some detail. The ultimate steady-state solutions and the structure of the associated boundary layers are determined with physical implications. It is shown that rotation and magnetic field affect the motion of the fluid relatively earlier than that of the particles when the time is small. The motion for large times is set up through inertial oscillations of frequency equal to twice the angular velocity of rotation. The ultimate boundary layers are established through inertial oscillations. The shear stress at the plate is calculated for all values of the frequency parameter. The small and large-time behaviour of the shear stress is discussed. The exact solutions for the velocity of fluid and the wall shear stress are evaluated numerically for the case of an impulsively moved plate. It is found that the drag and the lateral stress on the plate fluctuate during the non-equilibrium process of relaxation if the rotation is large. The present analysis is very general in the sense that many known results in various configurations are found to follow as special cases.

23 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202341
202295
202117
202022
201920
201836