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Showing papers on "Herschel–Bulkley fluid published in 1968"


Journal ArticleDOI
TL;DR: In this paper, the authors considered the propagation of harmonic pressure waves through a Newtonian fluid contained within a thick-walled, viscoelastic tube, and the results indicated that the fluid impedance is smaller than predicted by the rigid tube model or by Womersley's constrained elastic tube model.

81 citations


Journal ArticleDOI
TL;DR: In this article, a new constitutive equation is proposed for viscoelastic fluids based on the time derivatives of the left Cauchy-Green strain tensor and is thus believed to characterize a new material.
Abstract: In this paper a new constitutive equation is proposed for viscoelastic fluids. It is based on the time derivatives of the left Cauchy-Green strain tensor and is thus believed to characterize a new material. From this constitutive equation, a second-order approximation is derived and it is shown that this second order fluid has a bounded and unique solution to the initial value problem of cessation of steady shear flow. This stability is in direct contrast with the presently well known second order models. Further, the natural time of the fluid is positive, making the theory consistent with the intuitive notion that phenomena in dissipative materials should depend on the past rather than the future. Finally, a test is proposed to distinguish the present second-order model from the earlier version.

50 citations


Journal ArticleDOI
TL;DR: In this paper, a combination of Galerkin's method and variational principle was used for the approximate solution of creeping flow of power-law fluid over a Newtonian fluid sphere.
Abstract: A technique which is a combination of Galerkin's method and variational principle was developed and used for the approximate solution of creeping flow of power-law fluid over a Newtonian fluid sphere. The stream functions (both internal and external) and drag coefficient are expressed in terms of three parameters: the flow behavior index of the power law fluid, the external Reynolds number, and a viscosity ratio parameter . Comparisons with existing experimental data are also given.

39 citations


Journal ArticleDOI
TL;DR: In this paper, an alternative constitutive relation, which takes account of the entire strain-history of the motion, leads to the more reasonable result that the equilibrium is stable whenever the fluid has a "fading memory".
Abstract: A recent analysis by Gupta (1967) suggests that a layer of elastico-viscous fluid at rest between parallel plane boundaries may be in unstable equilibrium. This surprising result is attributable to the inadequacy of the constitutive equation adopted by Gupta as the basis for his analysis. An alternative constitutive relation, which takes account of the entire strain-history of the motion, leads to the more reasonable result that the equilibrium is stable whenever the fluid has a ‘fading memory’.

33 citations


Journal ArticleDOI
13 Jan 1968-Nature
TL;DR: The power law equation is open to the logical objection that it is dimensionally inconsistent unless the constant of proportionality, k, is not a true constant at all but has variable dimensions which depend on the properties of the sample under observation as discussed by the authors.
Abstract: THE power law equation, between shear stress, τ, and strain rate, ɣ, may be written ɣ=kτα: it has often been shown1,2 to be in accordance with experimental data obtained for many non-Newtonian fluids. The equation is open to the logical objection that it is dimensionally inconsistent unless the constant of proportionality, k, is not a true constant at all but has variable dimensions which depend on the properties of the sample under observation. Nedonchelle and Schutz3 have shown experimentally that for one particular non-Newtonian system there is a relationship between the constant of proportionality, k, and the exponent, α, such that the equation may be reduced to a dimensionless form containing three dimensionally stable constants which are independent properties characterizing the material in its environment.

5 citations


Journal ArticleDOI
TL;DR: In this paper, the stability of plane-Poiseuille flow of a slightly viscoelastic fluid with a constant viscosity and normal stress differences varying nearly with the shear rate was investigated.
Abstract: Consideration is given to the stability of planePoiseuille flow of a slightly viscoelastic fluid which has a constant viscosity and normal stress differences varying nearly with the shear rate. It is shown that the presence of elasticity lowers the criticalReynolds number at which instability occurs.

3 citations


Journal ArticleDOI
TL;DR: In this paper, a simplified model was used for calculating the time-dependent velocity of polymeric fluid in an extruder, and the flow properties of the fluid were characterized by a simple constitutive equation based on two parameters: a constant viscosity μ and a constant elasticity modulus G.
Abstract: A simplified model is used for calculating the time-dependent velocity of polymeric fluid in an extruder. The flow properties of the fluid are characterized by a simple constitutive equation based on two parameters: a constant viscosity μ and a constant elasticity modulus G. It was found that the transient velocity fluctuates periodically, and the time tt needed to restore the steady-state velocity from a disturbance varies with the ratio G/μ and the dimensionless group ρH2G/μ2, where ρ is the density of the fluid and H is the screw depth of the extruder.

3 citations


Journal ArticleDOI
B.D. Dore1
TL;DR: In this article, a general formula for the viscous damping of small amplitude waves in a non-homogeneous fluid of infinite depth was derived and shown to be identical to that for a homogeneous fluid.

2 citations


Journal ArticleDOI
TL;DR: In this paper, the dynamic response of a one degree of freedom spherical structural system immersed in viscous fluid media is studied with the fluid forces obtained by Basset included in the differential equation of motion.

1 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown how to determine the flow curve f(τ) of an arbitrary time-independent non-Newtonian fluid in a cone and plate viscometer from the known relationship between the torque M and the angular velocity \varOmega.
Abstract: It is shown how to determine the flow curve f(τ) of an arbitrary time-independent non-Newtonian fluid in a cone and plate viscometer from the known relationship between the torque M and the angular velocity \varOmega. The general formula for the flow curve has been applied to a Newtonian fluid.

1 citations