Showing papers on "Herschel–Bulkley fluid published in 1970"

Rheological properties of suspensions of spheres in non-Newtonian media

Abstract: The results of an experimental investigation of the rheologioal properties of dilute suspensions of rigid spheres 100μm in diameter in non-Newtonian pseudoplastic liquids are reported. The shear flow properties of suspensions in a solution of polyisobutylene in tetralin, in aqueous solutions of polyacrylamide and sodium carboxymethylcellulose and in a Newtonian fluid have been investigated at solid concentrations up to 10% by volume. A concentric cylinder viscometer was used, results being corrected for end effects and variations in shear rate across the gap. Results for the Newtonian fluid were not inconsistent with published data. It was found that, within the range of variables investigated, for each of the non-Newtonian fluids the relative fluidity, comparing the suspension and the suspending fluid at the same shear stress, was a function of concentration only whereas the relative fluidity comparing the suspension and the fluid at the same shear rate depended on both concentration and shear rate. The fractional decrease in fluidity produced by a given concentration of spheres in polyisobutylene solution was about double that produced by the same concentration in any of the other fluids. In what are believed to be the first reported measurements of normal stress in suspensions, the first normal stress difference (p 11-p 22 for the fluids was derived from the normal force exerted on the cone of a Rheogoniometer during steady rotation. Over ranges of concentration and shear rate limited by experimental difficulties the ratio of shear rate to normal stress for the suspension divided by the corresponding quantity for the base solution appeared to be a function of concentration only when the liquids were compared at the same normal stress but not when compared at the same shear rate. However, this conclusion was less certain than the corresponding result for relative fluidity.

Mass transfer from small capillaries with wall resistance in the laminar flow regime

Abstract: The Graetz problem in heat transfer is extended to the analysis of mass transfer in circular ducts for the cases where wall resistance is included and where non-Newtonian fluids that obey Casson's equation are considered. The eigenvalues and fluid bulk coefficients are presented for the fluid between the extremes of Newtonian and slug flow. It is found that for fluids which are only slightly non-Newtonian, such as blood, which is closely approximated by Casson's equation, the mass transfer rate can be predicted by Newtonian fluid analysis without appreciable error. Some experimental results give support to the theory.

Entrance region flow of the Bingham fluid in a circular pipe

Abstract: The laminar, isothermal entrance region flow of the Bingham fluid in a circular pipe is studied at first by using the momentum integral method and the boundary-layer equation for the Bingham fluid. In addition to the velocity boundary layer, the existence of the shear stress boundary layer is considered. The solution is valid only near the entry because of limitation of the boundary-layer model. The Campbell-Slattery method originally devised for the Newtonian fluid is also used to analyze the Bingham entrance region flow. The results are compared with those obtained through the use of the momentum integral method and those obtained through the use of the variational method by other investigators. While the results obtained in this work appear to be generally reasonable and valid, the results by the other investigators have been found to be somewhat erroneous.

Intrinsic Errors for Pressure Measurements in a Slot along a Flow

Abstract: Any rectilinear flow dynamically possible for a Newtonian fluid is shown to be possible also for a second order fluid. The stress which satisfies the condition of equilibrium is explicitly calculated. The component of stress normal to a wall bounding a shear flow is expressed in terms of the reading of a pressure gauge connected to a narrow slot in the wall, oriented in the direction of flow.

Variational Principle in Fluid Dynamics

Abstract: A variational principle is formulated for the flow of a viscous incompressible fluid taking into account the convective terms. The field of application of the variational principle is defined. A problem is solved for a time-dependent phenomenon when the fluid is a non-Newtonian pseudoplastic liquid obeying the power-law model due to its simplicity and to serve as an application of the variational principle.

Non-Newtonian flow in annuli

Abstract: An analysis of mathematical model describing the steady-state, laminar, isothermal, axial flow in ducts of annular cross-section is presented which permits a solution to be formulated which holds for any model of incompressible purely-viscous fluid (generalized Newtonian fluid).

Laminar Entry Flow of Herschel-Bulkley Fluids in a Circular Pipe

Abstract: Fargie and Martin used an elegant approach to obtain the entry region flow of Newtonian fluids in a circular pipe. They combined the differential and integral momentum equation in such a way that elimination of pressure gradient leads to a closed form solution. In this paper we extend this procedure to study the laminar entry region flow of Herschel-Bulkley fluids in a circular pipe. The solution procedure involves certain approximations. Applicability of these approximations to Herschel-Bulkley fluids has been discussed and the flow description has been obtained for various values of the flow behavior index and the Herschel-Bulkley number. Results have been illustrated graphically and compared with other available solutions: momentum integral and momentum energy integral solutions of the problem. Data displayed in the paper should be useful for design of any flow intake device involving Herschel-Bulkley fluids.

Stability of wave forms of motion of a viscous fluid layer under tangential stress

Abstract: We study the stability of wave flow of a viscous incompressible fluid layer subjected to tangential stress and an inclined gravity force with respect to long-wave disturbances.

Flow of non-Newtonian fluid between two coaxial cylinders under complex shear conditions

Abstract: The flow of a non-Newtonian fluid with an exponential rheological equation is investigated in the barrel of an extruder screw with consideration of the presence of circulating motion of the fluid in it.

Forced flow of a second-order fluid against a rotating disk

Abstract: The steady forced flow of an incompressible second-order fluid against a rotating disk is discussed here. The flow produced by the rotation of a disk in an infinite fluid which is otherwise at rest and the flow near a stagnation point occurring on a flat plate are particular cases of this problem and they have been discussed in detail. The effects of second-order terms in the constitutive equation of the fluid are (1) to decrease the thickness of the boundary layer formed near the disk, (2) to increase the magnitude of the radial and axial velocity components, and to decrease the magnitude of rotational velocity component at any point in the fluid within the boundary-layer region, and (3) to increase the dimensionless moment coefficient.

Rolling Contact Lubrication Using a Maxwell Fluid

Abstract: Pressure distribution curves are obtained for rolling cylinders lubricated by a Maxwell fluid, using a digital computer. Solutions are obtained for a ‘solid-like’ (vorticity neglected) fluid and for a fluid when vorticity is not neglected and these are compared with the Newtonian pressure distribution. A recently proposed upstream boundary condition is used throughout.