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.

Stress bifurcation in large amplitude oscillatory shear of yield stress fluids

Abstract: Large amplitude oscillation shear has been an important method to investigate the yielding and flow behavior of yield stress materials. However, there are great uncertainties in determination of the yield stress from the shear stress (or shear strain) dependence of the apparent dynamic moduli or the relative harmonic intensity using Fourier transform rheology. The yield stress from these dynamic methods is also inconsistent with the steady shear and transient shear measurements. We propose a new method, namely, stress bifurcation, based on the geometric average of elastic and viscous Lissajous curves to study the yielding transition of different yield stress fluids in large amplitude oscillatory shear flow. The results prove that typical yield stress fluids such as concentrated emulsions, polymer nanocomposites, microgels, and particulate gels all exhibit stress bifurcations, both inter and intra cyclically, in large amplitude oscillatory shear experiments. Such stress bifurcation phenomena between the average stress-strain (or strain rate) curves are independent of the type of input signal, i.e., stress-controlled versus strain-controlled. A start yield stress (strain) (related to strain) and an end yield stress (strain rate) (related to strain rate), instead of a single critical variable, were suggested to characterize yielding transitions. The frequency dependences of critical stresses, critical strain, and critical strain rate determined by the new method were also investigated systematically for the different kinds of yield stress fluids. A visco-elastic-plastic model, the Kelvin-Voigt-Herschel-Bulkley model, was also adopted to understand the stress bifurcation and frequency dependencies of critical variables in large oscillatory shear flow.Large amplitude oscillation shear has been an important method to investigate the yielding and flow behavior of yield stress materials. However, there are great uncertainties in determination of the yield stress from the shear stress (or shear strain) dependence of the apparent dynamic moduli or the relative harmonic intensity using Fourier transform rheology. The yield stress from these dynamic methods is also inconsistent with the steady shear and transient shear measurements. We propose a new method, namely, stress bifurcation, based on the geometric average of elastic and viscous Lissajous curves to study the yielding transition of different yield stress fluids in large amplitude oscillatory shear flow. The results prove that typical yield stress fluids such as concentrated emulsions, polymer nanocomposites, microgels, and particulate gels all exhibit stress bifurcations, both inter and intra cyclically, in large amplitude oscillatory shear experiments. Such stress bifurcation phenomena between the av...

Entrance flow of a yield-power law fluid

Abstract: In the present work we have obtained the numerical solution of the momentum equation for a Yield-Pseudoplastic power-law fluid flowing in the entrance region of a tube. The accuracy of the numerical results is checked by comparing the asymptotic values of friction coefficients and velocity profiles with the corresponding results from the analytical solutions for the fully-developed region. The results of the entrance flow solution for the power-law exponent equal to unity (Bingham fluid) are also in agreement with the numerical solution for a Bingham fluid. Detailed results are presented for wide ranges of yield numbers and power law exponents.

Experimental and numerical investigation of a viscoplastic Carbopol gel injected into a prototype 3D mold cavity

Abstract: A numerical model for free-surface flow of a viscoplastic liquid into a cavity is presented. This flow is regarded as a basic model of injection molding, which is a widely used processing technology. Model experiments of the injection process are performed with a water-based gel with shear-thinning behavior. The filling process is visualized by tracing the free surface of the gel within the cavity. Filling times of the cavity are deduced from the experimental observations. The filling process is also analyzed by means of numerical simulation. The flow equations are integrated according to the finite-volume method. The volume-of-fluid method is employed in order to describe the flow of two incompressible, immiscible phases, the phase interface is resolved by the method of geometric reconstruction or alternatively by the method of surface compression. The Herschel–Bulkley model is used in order to describe the shear-thinning behavior of the gel and the effects of a yielding point. The governing equations of the flow are solved by means of the commercial code Fluent as well as the Open Source code OpenFOAM. The results of the numerical simulations are analyzed in detail. They are compared with the experimental findings. Cavity filling times in the experiments and the simulations are in good agreement. Different patterns of the filling flow depending on the injection parameters are evident in the experiments and the simulations. They are characterized and arranged with respect to the similarity parameters of the flow configuration. Again, the results of the simulation are found to agree well with the experimental observations.

Viscous Spreading of Non-Newtonian Gravity Currents on a Plane

Abstract: A gravity current originated by a power-law viscous fluid propagating on a horizontal rigid plane below a fluid of lower density is examined. The intruding fluid is considered to have a pure Ostwald power-law constitutive equation. The set of equations governing the flow is presented, under the assumption of buoyancy-viscous balance and negligible inertial forces. The conditions under which the above assumptions are valid are examined and a self-similar solution in terms of a nonlinear ordinary differential equation is derived. For the release of a time-variable volume of fluid, the shape of the gravity current is determined numerically using an approximate analytical solution derived close to the current front as a starting condition. A closed-form analytical expression is derived for the special case of the release of a fixed volume of fluid. The space-time development of the gravity current is discussed for different flow behavior indexes.