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.

From stress-induced fluidization processes to Herschel-Bulkley behaviour in simple yield stress fluids

Abstract: Stress-induced fluidization of a simple yield stress fluid, namely a carbopol microgel, is addressed through extensive rheological measurements coupled to simultaneous temporally and spatially resolved velocimetry. These combined measurements allow us to rule out any bulk fracture-like scenario during the fluidization process such as that suggested in [Caton et al., Rheol Acta, 2008, 47, 601–607]. On the contrary, we observe that the transient regime from solid-like to liquid-like behaviour under a constant shear stress σ successively involves creep deformation, total wall slip, and shear banding before a homogeneous steady state is reached. Interestingly, the total duration τf of this fluidization process scales as τf ∝ 1/(σ − σc)β, where σc stands for the yield stress of the microgel, and β is an exponent which only depends on the microgel properties and not on the gap width or on the boundary conditions. Together with recent experiments under imposed shear rate [Divoux et al., Phys. Rev. Lett., 2010, 104, 208301], this scaling law suggests a route to rationalize the phenomenological Herschel-Bulkley (HB) power-law classically used to describe the steady-state rheology of simple yield stress fluids. In particular, we show that the steady-state HB exponent appears as the ratio of the two fluidization exponents extracted separately from the transient fluidization processes respectively under controlled shear rate and under controlled shear stress.

Non-Newtonian fluids with a yield stress

Abstract: A modified Herschel–Bulkley model [E. Mitsoulis, S.S. Abdali, Flow simulation of Herschel–Bulkley fluids through extrusion dies, Can. J. Chem. Eng. 71 (1993) 147–160] predicts an infinite apparent viscosity at vanishing shear rate. Furthermore, the dimensions of one parameter depend on another parameter. In this contribution, we propose a generalized model based on earlier work by De Kee and Turcotte [D. De Kee, G. Turcotte, Viscosity of biomaterials. Chem. Eng. Commun. 6 (1980) 273–282] and on the work of Papanastasiou [T.C. Papanastasiou, Flows of materials with yield, J. Rheol. 31 (1987) 385–404] to solve the problems associated with the modified Herschel–Bulkley model. Compared to the responses of the Papanastasiou model and the modified Herschel–Bulkley model, the proposed generalized model provides the expected improvements and is capable of predicting successfully the rheological behavior (viscosity and yield stress) of Carbopol 980 dispersions.

Peristaltic transport of a power-law fluid in a porous tube

Abstract: Peristaltic transport of a power-law fluid in an axisymmetric porous tube is studied under long wavelength and low Reynolds number assumptions The slip boundary conditions given by Beavers–Joseph and Saffman type are considered in obtaining solutions for the flow and resulting pumping characteristics are compared Trapping and reflux phenomena are discussed for various parameters of interest governing the flow like Da Darcy number, α Beavers–Joseph constant and n the fluid behavior index The novel feature arising in pumping due to a straight section dominated (SSD) wave form other than sinusoidal wave is discussed The time mean flow becomes negative in free pumping for a shear thickening fluid or shear thinning fluid for an expansion or contraction SSD wave, respectively The pressure rise increases for the increasing of Da against which the peristalsis acts as a pump and decreases for an increase in α Peristalsis works as a pump against a greater pressure rise for a shear thickening fluid and the opposite happens for a shear thinning fluid, compared with Newtonian fluid The trapped bolus volume for sinusoidal wave is observed to decrease as the fluid behavior index decreases from shear thickening to shear thinning fluid, whereas it increases for increasing Darcy number The rheological property of the fluid, wave shape and porous nature of the wall play an important role in peristaltic transport and may be useful in understanding transport of chyme in small intestines

Flow through Porous Media of a Shear-thinning Liquid with Yield Stress

Abstract: Darcy's law for the laminar flow of Newtonian fluids through porous media has been modified to a more general form which will describe the flow through porous media of fluids whose flow behavior can be characterized by the Herschel-Bulkley model. The model covers the flow of homogeneous fluids with a yield value and a power law flow behavior. Experiments in packed beds of sand were carried out with solutions of paraffin wax in two oils and with a crude oil from the Peace River area of Canada. The model fitted the data well. A sensitivity analysis of the fitting parameters showed that the model fit was very sensitive to errors in the flow behavior index, n, of the Herschel-Bulkley model. A comparison of the “n” values calculated from viscometer measurements and from flow measurements agreed well. A more general Reynolds number for flow through porous media, which includes a fluid yield value, was developed. The data were fitted to a Kozeny-Carman type equation using this Reynolds number. The constant in the Kozeny-Carman equation was determined for the two packed beds studied using Newtonian oils. The data could all be represented, within the experimental error, by the relationship f* = 150/Re*. Since the mean volume to surface diameter of the packing was determined by the measurement of its permeability to a Newtonian oil, assuming C' = 150, the new definition of the Reynolds number allows the direct use of the Kozeny-Carman equation with Herschel-Bulkley type fluids.