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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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Ames Laboratory

^{1}TL;DR: In this paper, the Equations of Motion (EOM) and potential flow and slightly viscous flow are used to describe the gas flow in one dimension in one-dimensional space.

Abstract: Contents: The Equations of Motion.- Potential Flow and Slightly Viscous Flow.- Gas Flow in One Dimension.- Vector Identities.- Index.

1,219 citations

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TL;DR: In this article, a general relationship between impeller speed and the shear rate of a non-Newtonian fluid has been developed, and the resulting relationship was then used to interpret and correlate power-consumption data on three non-newtonian fluids by use of a generalized form of the conventional power-number-Reynoldsnumber plot for Newtonians.

Abstract: Since the shear rate of a non-Newtonian fluid is of importance in fixing the rheological or viscometric behavior of such a material, the present study has been concerned with the development of a general relationship between impeller speed and the shear rate of the fluid. The resulting relationship was then used to interpret and correlate power-consumption data on three non-Newtonian fluids by use of a generalized form of the conventional power-number–Reynolds-number plot for Newtonians.
Flat-bladed turbines from 2 to 8 in. in diameter were used exclusively. Tank diameters ranged from 6 to 22 in. and power inputs from 0.5 to 176 hp./1,000 gal. The study encompassed a 130-fold range of Reynolds numbers in the laminar and transition regions. The results to date indicate that power requirements for the rapid mixing of non-Newtonian fluids are much greater than for comparable Newtonian materials.

905 citations

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TL;DR: The effective elastic moduli of a fluid-saturated solid containing thin cracks depend on the degree of interconnection between the cracks as mentioned in this paper, which can be estimated from the crack geometry or permeability.

Abstract: The effective elastic moduli of a fluid-saturated solid containing thin cracks depend on the degree of interconnection between the cracks. Three separate regimes may be identified: (1) dry (drained), in which fluid in cracks can flow out of bulk regions of compression, (2) saturated isobaric, in which fluid may flow from one crack to another but no bulk flow takes place, and (3) saturated isolated, in which there is no communication of fluid between cracks. Transitions between these cases involve fluid flow, resulting in dissipation of energy. Relaxation of shear stresses in viscous fluid inclusions also results in dissipation. Viscoelastic moduli are derived, by using a self-consistent approximation, that describe the complete range of behavior. There are two characteristic frequencies near which dissipation is largest and the moduli change rapidly with frequency. The first corresponds to fluid flow between cracks, and its value can be estimated from the crack geometry or permeability. The second corresponds to the relaxation of shear stress in an isolated viscous fluid inclusion; its value may also be estimated. Variations of crack geometry result in a distribution of characteristic frequencies and cause Q to be relatively constant over many decades of frequency. Fluid flow between cracks accounts for attenuation of seismic waves in water-saturated rocks and attenuation observed in laboratory measurements on water-saturated rocks and partially molten aggregates. Attenuation in a partially molten upper mantle is probably due to fluid flow between cracks, although grain boundary relaxation in an unmelted upper mantle could also account for the seismic low-velocity zone. Grain boundary relaxation in the mantle may cause the long-term shear modulus to be around 20% less than that measured from seismic observations.

835 citations

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TL;DR: In this paper, two simple constitutive equations appropriate to materials exhibiting viscoelasticity are presented, one of a basic solid nature and one of basic fluid nature, and the predictions of the equations for a stress relaxation experiment are worked out.

Abstract: Two simple types of constitutive equations appropriate to materials exhibiting viscoelasticity are presented, one of a basic solid nature and one of a basic fluid nature. The predictions of the equations for a stress relaxation experiment are worked out and compared to the data from some experiments on various elastomers. The fluid theory is shown to be most appropriate in a certain sense.

624 citations