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.

The dam-break problem for Herschel-Bulkley viscoplastic fluids down steep flumes

Abstract: In this paper we investigate the dam-break problem for viscoplastic (Herschel–Bulkley) fluids down a sloping flume: a fixed volume of fluid initially contained in a reservoir is released onto a slope and flows driven by gravitational forces until these forces are unable to overcome the fluid’s yield stress. Like in many earlier investigations, we use lubrication theory and matched asymptotic expansions to derive the evolution equation of the flow depth, but with a different scaling for the flow variables, which makes it possible to study the flow behavior on steep slopes. The evolution equation takes on the form of a nonlinear diffusion–convection equation. To leading order, this equation simplifies into a convection equation and reflects the balance between gravitational forces and viscous forces. After presenting analytical and numerical results, we compare theory with experimental data obtained with a long flume. We explore a fairly wide range of flume inclinations from 6° to 24°, while the initial Bingham number lies in the 0.07–0.26 range. Good agreement is found at the highest slopes, where both the front position and flow-depth profiles are properly described by theory. In contrast, at the lowest slopes, theoretical predictions substantially deviate from experimental data. Discrepancies may arise from the formation of unsheared zones or lateral levees that cause slight flow acceleration.

Flow of a yield stress fluid in a long domain. Application to flow on an inclined plane

Abstract: Complex isochoric flows in a domain of space that is long compared to its width are studied for a viscoplastic and perfectly rigid Herschel–Bulkley model. It is argued here that no continuous yield surface can exist along the flow direction in these either confined or open channel flows. A similarity analysis is performed that shows that normal stresses cannot be neglected. For open channel flows the influence of normal stresses can be estimated through comparison of the yield stress value to the hydrostatic pressure value at the channel bed. Generalized Barre de Saint Venant one‐dimensional equations are obtained. The influence of the yield stress value on wave velocity and on gradually varied flows and critical depth has been deduced.

Pulsatile flow of Herschel–Bulkley fluid through stenosed arteries—A mathematical model

Abstract: In this paper, the pulsatile flow of blood through stenosed artery is studied. The effects of pulsatility, stenosis and non-Newtonian behavior of blood, assuming the blood to be represented by Herschel–Bulkley fluid, are simultaneously considered. A perturbation method is used to analyze the flow assuming the thickness of plug core region to be non-uniform changing with axial distance. An expression for the variation of plug core radius with time and axial distance is obtained. The variation of pressure gradient with steady flow rate is given. Also the variation of wall shear stress distribution as well as resistance to flow with axial distance for different values of time and for different values of yield stress is given and the results analyzed.

Fluid property evaluation by piezoelectric crystals operating in the thickness shear mode

Abstract: Hydrodynamic coupling between a fluid and a planar piezoelectric crystal operating in the thickness shear mode provides a powerful, yet remarkably simple means to characterize fluid properties. Equations describing hydrodynamic coupling are developed for Newtonian fluids. This analysis takes into account, for the first time, the influence of a nonuniform piezoelectric crystal surface velocity. In particular, a Gaussian velocity distribution, suggested by other work, yields a functional relationship between hydrodynamic coupling and the fluid viscosity/density product that is in agreement with experiment. Beginning with these results, analytical methods for measuring individually the fluid visocity and density are described. Finally, it is demonstrated experimentally that the automatic gain control from the piezoelectric crystal oscillation circuit provides a ready means of fluid property characterization.