Showing papers on "Herschel–Bulkley fluid published in 1971"
TL;DR: The ICE technique for numerical fluid dynamics has been revised considerably, and generalized in such a way as to extend the applicability to fluid flows with arbitrary equation of state and the full viscous stress tensor as mentioned in this paper.
510 citations
TL;DR: In this paper, a long slender axisymmetric body is considered placed at rest in a general linear flow in such a manner that the undisturbed fluid velocity is identically zero on the body axis.
Abstract: A long slender axisymmetric body is considered placed at rest in a general linear flow in such a manner that the undisturbed fluid velocity is identically zero on the body axis. Formulae for the total force and torque on the body are found as an expansion in terms of a small parameter κ defined as the radius-to-length ratio of the body. These general results are used to determine the resistance to axial rotation of the body and also the equivalent axis ratio of the body for motion in a shear flow.
176 citations
TL;DR: In this article, the boundary-layer equations are solved for the case of two-dimensional flow of a second-order viscoelastic fluid near a stagnation point, and it is shown that the effect of visco-elasticity is not only to increase the wall-shear stress but also to cause oscillations in the velocity profile.
Abstract: The boundary-layer equations are solved for the case of two-dimensional flow of a second-order viscoelastic fluid near a stagnation point. It is shown that the effect of viscoelasticity is not only to increase the wall-shear stress but also to cause oscillations in the velocity profile. It is further shown that the constitutive equation for the second-order viscoelastic fluid is not applicable to the analysis of stagnation point flow for Weissenberg numbers greater than approximately 0.32.
27 citations
TL;DR: For the boundary value problem for creeping flow of a fluid, called "a generalized Newtonian fluid", defined by the constitutive relations τij= 2η (IIe, IIIe)eij, the uniqueness of its solution is proved, and two equivalent variational problems are formulated.
Abstract: For the boundary value problem for creeping flow of a fluid, called "a generalized Newtonian fluid", which is defined by the constitutive relations τij= 2η (IIe, IIIe)eij, the uniqueness of its solution are proved, and two equivalent variational problems are formulated. This fluid contains plastic fluids. The flow field, therefore, may consist of flow regions and stationary regions, or may include surfaces of discontinuous velocity. In stationary regions the stress field is not unique. Present work is a partial extention and development of studies by Hill and Prager.
25 citations
01 Jan 1971
22 citations
TL;DR: In this paper, the non-Newtonian behavior of kaolin has been studied at different scales of 5, 10, 20 and 20% by weight, and the dependence of the fluid properties, yield stress, and plastic viscosity on pH and concentration is characterized; both these properties increase with increase in concentration, or decrease in pH (increase in acidity).
Abstract: Bottom materials often involve clay-water suspensions which evidence complex rheology. Studies of the non-Newtonian behavior of kaolin are reported herein. Concentric viscometer analysis at concentrations of 5, 10 and 20% by weight indicate Bingham-plastic-body behavior; Newtonian fluid behavior is evidenced at low concentration and alkalinity. The dependence of the fluid properties, yield stress, and plastic viscosity on pH and concentration is characterized; both these properties increase with increase in concentration, or decrease in pH (increase in acidity). Measurements of the drag of simple bodies in this mixture are reported. The drag coefficient of spheres and discs in the laminar boundary-layer region (Reynolds numbers below 2 x 10 5 ) indicate negligible non-Newtonian effect above a Reynolds number of 1,000. At lower Reynolds number, a yield stress effect is superimposed. The dependence of this effect on the Hedstrom number is indicated for values of this parameter up to 4,000. The occurrences with spheres and discs are found to be much the same.
12 citations
TL;DR: In this paper, the torque on the inner cylinder of a second order fluid in the supercritical regime is calculated using the energy method, and it is shown that when the second normal stress difference is negative, the flow is more stable than for a Newtonian fluid and the torque is reduced.
Abstract: Using Stuart's energy method, the torque on the inner cylinder, for a second order fluid, in the supercritical regime is calculated. It is found that when the second normal stress difference is negative, the flow is more stable than for a Newtonian fluid and the torque is reduced. If the second normal stress difference is positive, then the flow is more stable and there is no torque reduction. Experimental data related to the present work are discussed.
5 citations
01 Dec 1971
TL;DR: In this paper, a two-phase solid-fluid continuum model to represent the spinal column subjected to dynamic loadings is presented, where the authors examine a simple dynamic model that has a continuum representation and offers a capability to include the inertia and pressure effects of a fluid and use this model to study what effect the presence of fluid has on the stresses in the solid material.
Abstract: : A preliminary investigation of a two-phase solid-fluid continuum model to represent the spinal column subjected to dynamic loadings is presented The two-fold purpose of this investigation is (1) to examine a simple dynamic model that has a continuum representation and offers a capability to include the inertia and pressure effects of a fluid and (2) to use this model to study what effect the presence of a fluid has on the stresses in the solid material The model consists of a uniform straight porous elastic column containing a viscoelastic fluid and supporting a mass to represent the head Loading consists of a constant acceleration at the base of the column Two types of boundary conditions for the fluid at the upper end of the column are considered The problem is formulated in terms of two coupled partial differential equations with the displacements of the fluid and the solid material treated as unknowns (Author)
4 citations
TL;DR: In this article, it was proved that the separation from a curved wall for a second-order fluid occurs earlier than that for a Newtonian fluid, and this fact was confirmed by determining the flow of a secondorder fluid past a circular cylinder and finding the location of the point of separation for various values of a nondimensional parameter formed from the material constants of the fluid, the velocity at infinity and the radius of the cylinder.
Abstract: It has been proved that the separation from a curved wall for a second-order fluid occurs earlier than that for a Newtonian fluid. This fact is confirmed by determining the flow of a second-order fluid past a circular cylinder and finding the location of the point of separation for various values of a non-dimensional parameter formed from the material constants of the fluid, the velocity at infinity and the radius of the cylinder. The dependence of the point of separation on the material constants of the fluid and the flow parameters is a peculiarity of a second-order fluid since the location of the point of separation for a Newtonian fluid is independent of these quantities.
4 citations
2 citations
TL;DR: In this paper, the apparent viscosity of a polar fluid with suspensions of rigid spherical particles undergoing a prescribed bulk motion is calculated, and it is shown that the increased rate of dissipation in a polar liquid with suspensions is greater than that of a Newtonian fluid.
Abstract: The apparent viscosity of a polar fluid with suspensions of rigid spherical particles undergoing a prescribed bulk motion is calculated. It is shown that the increased rate of dissipation in a polar fluid with suspensions is greater than that of a Newtonian fluid. It is found that the relationship between the viscosity and the concentration has a same form with that of a Newtonian fluid suspension of which ambient fluid has a shear viscosity multiplied by a factor which is greater than unity.
TL;DR: In this article, the eigenvalues of the generalized Orr-Sommerfeld equation for an elasticoviscous fluid were found for a constant velocity profile, and it was shown that the effect of elasticity is to stabilize the flow.
Abstract: The eigenvalues of the generalized Orr-Sommerfeld equation for an elasticoviscous fluid are found for a constant velocity profile. The result shows that the effect of elasticity is to stabilize the flow.
TL;DR: In this paper, the stress distribution in the inertialess flow of a viscoelastic fluid confined between two plane parallel walls, in which the upper wall moves with a constant velocity while the lower is held at rest with a uniform constant suction applied on its surface, is discussed.
Abstract: In continuation of an earlier investigation, the present paper discusses the stress distribution in the inertialess flow of a viscoelastic fluid confined between two plane parallel walls, in which the upper wall moves with a constant velocity while the lower is held at rest with a uniform constant suction applied on its surface. However, the stress field is discussed in detail for the case when the upper wall is also held at rest and the effects arising due to application of suction are pointed out. The most important difference in the behaviour of viscoelastic fluid, compared with that ofNewtonian fluid, lies in the fact that the gradient of the normal stress component in the horizontal direction depends on the distance from the walls.