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Showing papers on "Herschel–Bulkley fluid published in 1975"


Journal ArticleDOI
TL;DR: In this article, the motion of a slender axisymmetric rod-like particle is investigated for translation through a quiescent second-order fluid and for rotation in a simple shear flow of the same material.
Abstract: The motion of a slender axisymmetric rod-like particle is investigated theoretically for translation through a quiescent second-order fluid and for rotation in a simple shear flow of the same material. The analysis consists of an asymptotic expansion about the limit of rheologically slow flow, coupled with an application of a generalized form of the reciprocal theorem of Lorentz to calculate the force and torque on the particle. It is shown that an arbitrarily oriented particle with fore-aft symmetry translates, to a first approximation, at the same rate as in an equivalent Newtonian fluid, but that the motion of particles with no fore-aft symmetry may be modified at the same level of approximation. In addition, it is found that freely translating particles with fore-aft symmetry exhibit a single stable orientation with the axis of revolution vertical. In simple shear flow at small and moderate shear rates, the non-Newtonian nature of the suspending fluid causes a drift through Jeffery orbits to the equilibrium orbit C = 0 in which the particle rotates about its axis of revolution. At larger shear rates, the particle aligns itself in the direction of flow and ceases to rotate. Comparison with the available experimental data indicates that the measured rate of orbit drift may be used to determine the second normal stress difference parameter of the second-order fluid model. Finally, in an appendix, some preliminary observations are reported of the motion of slender rod-like particles falling through a quiescent viscoelastic fluid.

217 citations


Journal ArticleDOI
TL;DR: In this article, a theory for roll coating of a fluid onto a moving sheet is developed utilizing the usual lubrication approximations, and the effects of fluid and operating parameters on coating thickness and pressure distribution are determined for a Newtonian fluid, and for a purely viscous non-Newtonian fluid obeying the Power Law.
Abstract: A theory for roll coating of a fluid onto a moving sheet is developed utilizing the usual “lubrication approximations.” The effects of fluid and operating parameters on coating thickness and pressure distribution are determined for a Newtonian fluid, and for a purely viscous non-Newtonian fluid obeying the Power Law. The results for these cases are obtained analytically, and are rather straightforward. A viscoelastic fluid is considered, of a type which shows typical non-Newtonian shear behavior observed in polymer melts and solutions and which also exhibits normal stress behavior. Analytical solutions are not possible, but a perturbation method, using a viscoelastic perturbation parameter related to a Deborah number, yields an approximate solution. Only terms to first order in the perturbation parameter are given. Subject to that degree of approximation, the following conclusions are drawn: 1 Non-Newtonian shear behavior reduces the pressure distribution, and increases the coating thickness. 1 Elasticity of the type usually observed in polymer solutions makes only a minor contribution to the roll-separating (load-carrying) force. The contribution is positive, but smaller than the corresponding negative contribution due to the non-Newtonian shear effects. 1 An increase in load-carrying capacity would require a different viscoelastic fluid than the type considered here—one that is essentially Newtonian in shear but, independently, capable of developing significant normal stresses.

67 citations


Journal ArticleDOI
TL;DR: It is shown that the motion of a slightly compressible fluid is near that of an incompressible fluid, and the minimum of the potential energy function becomes sharper if the equation of state of the compressable fluid is changed so that the sound speed increases.
Abstract: We show that the motion of a slightly compressible fluid is near that of an incompressible fluid. That is, for a given initial velocity field, the motion of a compressible fluid with large sound speed is near to that of an idealized incompressible fluid. We consider the compressible fluid motion in Lagrangian coordinates and show that it can be defined by two functions giving the kinetic and potential energies. The minimal set for the potential energy is the configuration space of incompressible fluid motion. If the equation of state of the compressible fluid is changed so that the sound speed increases, the minimum of the potential energy function becomes sharper. The compressible fluid motion approaches a curve in the minimal set and this curve defines an incompressible fluid motion.

21 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that the dynamics of a deformed spherical body in a fluid medium is significantly different from the motion of an undeformed spherical bodies in the same medium.
Abstract: The motion of a deformed spherical body in a fluid medium is significantly different from the motion of an undeformed spherical body in the same medium. It is shown in this work that a bubble moving in a viscoelastic fluid takes the shaper=a+U 0η0/σa(λ 1−λ 2)(180R 3+240R 2+816R+672)P 2(cosθ)/960(1+R)3 and so one must expect the dynamics of a bubble moving in a non-Newtonian fluid to be significantly different from that of a bubble moving in a purely viscous fluid.

13 citations


Journal ArticleDOI
TL;DR: In this article, the results of the entrance flow in a tube for the case of zero yield stress are compared with the solution for a Newtonian fluid for a wide range of yield numbers.
Abstract: The numerical solution of the entrance flow in a tube has been obtained for a Bingham fluid. The numerical procedure used is that of Patankar and Spalding [1]. The accuracy of the numerical results is demonstrated by comparing the fully-developed velocity profiles with analytical exact solutions. The results of the entrance flow in a tube for the case of a zero yield stress are compared with the entrance flow solution for a Newtonian fluid. Detailed results are presented for a wide range of yield numbers (=τ y D/ūμ).

11 citations


Journal ArticleDOI
TL;DR: In this paper, a theoretical analysis of the velocity-, pressure-and shear stress distributions in the flow field is given, and the roll-separating forces are described in terms of the geometrical and kinematical parameters of the system.
Abstract: Fluid flow between a pair of rotating cylinders with non-equal sized rolls and/or non-equal speeds of the rolls is considered for aNewtonian fluid at constant temperature. The lubrication approximation is applied as usual in the theory of calendering. A theoretical analysis of the velocity-, pressure- and shear stress distributions in the flow field is given. Processing parameters as volumetric flow rate, total power required to drive both rolls, and roll-separating forces are calculated and described in terms of the geometrical and kinematical parameters of the system.

11 citations


Journal ArticleDOI
TL;DR: In this paper, the momentum equation for a Casson fluid flowing in the entrance region of an annular tube has been obtained for a large range of radii ratio and dimensionless yield stress.
Abstract: The solution of the momentum equation for a Casson fluid flowing in the entrance region of an annular tube has been obtained. The results have been presented for a large range of radii ratio and dimensionless yield stress. The mathematical accuracy of the numerical procedure is demonstrated by comparing the asymptotic velocity profiles at large axial distance with fully developed solution [1]. In addition, the results of the numerical solution for the case of yield stress equal to zero are compared with the entrance flow solution for a Newtonian fluid [2].

7 citations


Journal ArticleDOI
TL;DR: In this paper, a simple approximative formula for the friction correlation of a viscoelastic fluid in laminar region is derived, which is applicable on flow in pipe, annulus and parallel slit.
Abstract: In polymer extrusion, in fluid transport and in heat exchangers the flow through an annulus is of some importance, as for flow rate reducing or hose forming. A simple approximative formula for the frictioncorrelation of a viscoelastic fluid in laminar region is derived. Of special importance is the possibility of determining the flow-curve especially at high shear rates. Turbulent flow characteristics give knowledge about elastic parameters of the fluid. In all cases formulas are applicable on flow in pipe, annulus and parallel slit.

5 citations


Journal ArticleDOI
TL;DR: In this paper, a solution to the boundary value problem for the transient development of the velocity profile in a viscoelastic fluid subjected to the sudden onset of shearing in an idealized viscometer is presented.
Abstract: A solution is presented to the boundary value problem for the transient development of the velocity profile in a viscoelastic fluid subjected to the sudden onset of shearing in an idealized viscometer. A differential Oldroyd type of constitutive equation is used to describe the mechanical behavior of the fluid. The results indicate that the elastic nature of the fluid significantly increases the length of time required for the steady‐state velocity profile to be established. A solution is also presented for the drainage of a viscoelastic fluid off a vertical plate. The predicted initial elastic overshoot or rapid drainage of the fluid is in qualitative agreement with reported experimental results.

5 citations


Journal ArticleDOI
TL;DR: In this article, the indentation of the free surface of a Newtonian fluid in a finite cylindrical container by a right circular cylinder is considered and it is assumed that weight and inertia effects are negligible compared to viscous effects.
Abstract: The indentation of the free surface of a Newtonian fluid in a finite cylindrical container by a right circular cylinder is considered. It is assumed that weight and inertia effects are negligible compared to viscous effects.

1 citations


Journal ArticleDOI
01 Apr 1975
TL;DR: In this paper, the effects of fluid elasticity on flow were brought out by comparing the results with those obtained in case of a Newtonian fluid, limited to fluids with short memories.
Abstract: Oscillatory flow of an elastico-viscous fluid (Walters fluid B′) over a flexible surface is analysed. The study is limited to fluids with short memories. The effects of fluid elasticity on flow are brought out by comparing the results with those obtained in case of a Newtonian fluid.