Showing papers on "Herschel–Bulkley fluid published in 1978"

Instability of steady shearing flows in a non-linear viscoelastic fluid

Abstract: This paper proves the non-existence of global smooth solutions to an equation for a viscoelastic fluid shearing flow. The non-existence of smooth solutions is interpreted physically as the formation of a vortex sheet and an instability in the fluid motion.

A model viscoelastic fluid

Abstract: Shear stress and first normal stress difference data are presented for materials which exhibit a constant viscosity and yet at the same time exhibit elasticity levels of the same order as polymer melts. Flow pattern observations in circular die entry flows in conjunction with independent shear and normal stress measurement strongly suggest that these fluids would make excellent model fluids for melt studies. Studies in which the influence of elasticity in the absence of shear thinning and fluid inertia can easily be made. Furthermore it is clearly shown that a realistic solution to the die entry flow problem is not obtained using second order flow theory. In the second order region the secondary cell is observed to be almost identical in size to the cell observed for an inelastic Newtonian fluid in creeping flow. Marked growth in the secondary cell as a function of elasticity is not observed until the shear rates exceed the region of second order behavior. This growth in cell size as a result of elasticity is followed at higher shear rates by a spiraling flow instability like that observed for some polymer melts.

A theory of slow fluid flow through a porous thermoelastic matrix

Abstract: Slow flow of linearly viscous fluid through a linear isotropic thermoelastic matrix is described. The interaction body force is Darcy's law, and the constitutive laws for the partial stresses assume that porosity changes of strain order occur and that porosity is a linear function of the partial pressures in matrix and fluid. A further dependence on deviatoric matrix stress allows a description of dilatancy. The laws are expressed in terms of 4 distinct compressibilities and a mixture shear modulus, and various strong inequalities between the compressibilities are examined. A consolidation theory for an incompressible fluid is derived, and the restrictions required to recover an uncoupled diffusion equation for the matrix compression are determined. Convection equations for large temperature differences across a horizontal layer are derived, allowing finite fluid expansion, and it is shown that the fluid-flow equations uncouple from the matrix equilibrium equation in the case of steady flow, but not in the case of unsteady flow. 34 references.

The effective long-time diffusivity for a passive scalar in a Gaussian model fluid flow

Abstract: The problem considered is the diffusion of a passive scalar in a ‘fluid’ in random motion when the fluid velocity field is Gaussian and statistically homogeneous, isotropic and stationary. A self-consistent expansion for the effective long-time diffusivity is obtained and the approximations derived from this series by retaining up to three terms are explicitly calculated for simple idealized forms of the velocity correlation function for which numerical simulations are available for comparison for zero molecular diffusivity. The dependence of the effective diffusivity on the molecular diffusivity is determined within this idealization. The results support Saffman's contention that the molecular and turbulent diffusion processes interfere destructively, in the sense that the total effective diffusivity about a fixed point is less than that which would be obtained if the two diffusion processes acted independently.

Erosion of cohesive soils

Abstract: The erosion of visco-plastic cohesive soils under the action of a turbulent fluid flow is studied. The equations describing a sediment bed are discussed. To solve them, the density distribution in the bed must be known at some initial time. Experimental field studies and results from the ultracentrifuge provide a clear picture of the density distribution in sediment layers. The boundary condition between the bed-fluid interface is obtained from experimental observations. It is inferred that the instantaneous physico-chemical composition at the top of the bed is uniquely related to the bed shear stress during erosion. The solution for the stationary erosion flux under a constant shear stress is obtained. The erosion flux depends on the properties of the bed and the shear stress induced by the turbulent fluid flow. The theory is shown to agree very well with the experiments performed by PARTHENIADES (1965).

Flow of an elastico-viscous fluid past an oscillating plate

Abstract: An exact solution for the flow of an elastico-viscous fluid (Walters' liquid B') due to an oscillating infinite plate has been derived. It has been observed that forgwt=0, (ω — frequency,t — time) the flow near the plate may become unstable with increasing ω whereas forωt>0, the velocity increases with increasingω. The shearing stress decreases with increasingω.

On a non-Newtonian fluid

Abstract: A non-Newtonian fluid for which the stress is supposed to be symmetrical tensor and a function of gradients of the velocity field of the first order, the second order and the third order is considered. The constitutive equation shows that an incompressible fluid of this type is characterized by two material constants. The equation of motion is a fourth order differential equation in terms of velocity and there is similarity between the present equation of motion and those of the dipolar fluid theory and the couple stress theory, although the stress is a symmetrical tensor in the present case and antisymmetric one in the dipolar fluid theory and the couple stress theory. As an illustrative example, the flow in a circular pipe is discussed. The usual no-slip boundary condition and an extra boundary condition, are used. An expression for the apparent viscosity, which may show a decreasing effect in tube diameter is obtained.

Determination of rheological constants of an elastico-viscous fluid by kinematical analysis of oscillatory motions

Abstract: This paper contains experimental and theoretical work on a rotatory oscillatory flow of an elastico-viscous fluid. Assuming a linear constitutive equation, the motion of the fluid contained in a spherical or circular cylindrical vessel is computed. In particular, the limited height of the cylinder is taken into account for the boundary conditions. The solutions yield the velocities of the fluid particles as functions of the constitutive equation parameters, everywhere in the flow field. The experimental study is essentially based upon quantitative vizualisation techniques with solid particles: the amplitude and phase of the displacements of the tracers suspended in the fluid are obtained from an analysis of the photographs. Using the above-mentioned theoretical results we deduce the measurement of characteristic coefficients and functions of the materials tested. An experimental investigation of moderately concentrated aqueous solutions of polyethylene oxide is carried out.