Showing papers on "Herschel–Bulkley fluid published in 1981"

The impulsive motion of a flat plate in a viscoelastic fluid

Abstract: In this note the flow near a wall suddenly set in motion has been studied for a particular class of non-Newtonian viscoelastic fluids. For the description of such a fluid one has used the l~ivlin-Ericksen constitutive equation. Only the first three material constants have been taken into consideration. Because it is not possible in this cas9 to obtain similarity solutions a series expansion with respect to a non-similarity parameter will he given. Finally the velocity distribution with its separate functions will be shown.

Hydrodynamic fluctuation forces

Abstract: We consider the fluctuating hydrodynamics of Landau and Lifshitz for a fluid confined by hard walls at finite distance. By considering the non-linearity of the stochastic fluid equations of motion, we show that there can be an inhomogeneous average stress set up throughout the fluid. The average stress corresponds to a force density on the fluid which is expressed in terms of the Green's function for the fluid in the linearized theory. For simple geometries we obtain the average stress explicitly as a long range pressure field. The effect can be interpreted as a long range effective force acting between the fluid boundaries. In this sense it might have observable consequences in thin films or in suspensions of hard colloid particles. The effect is strongest in incompressible fluids. It is greatly weakened by compressibility but relaxation of the fluid viscosity prevents the effect vanishing.

Catastrophic instabilities and related results in a fluid of third grade

Abstract: Thermodynamical considerations [1] have shown that the most general form for the stress constitutive relation of an incompressible fluid of grade three is T = −p1 + μA1 + α1A2 + α2A21 + β(tr A21)A1, where A1 and A2 are the first two Rivlin-Ericksen tensors. In addition, the material parameters μ, α1, α2 and α were shown in [1] to be restricted by certain inequalities (see (1.7), (1.8)). Here we show that the condition α1 <0, which is compatible with the Clausius-Duhem inequality but not with the free energy being a minimum in equilibrium, leads to behavior which may not be physically acceptable. An explicit solution is presented for the second grade fluid, for which β =0 and μ, α1 and α2 are arbitrary, which demonstrates that if μ #62; 0 and α1 < 0 then a rotating vortex system may increase indefinitely in amplitude.

Approximate constitutive equations for slow flow of rigid plastic viscoelastic fluids

Abstract: A theory of slow flow of rigid plastic viscoelastic fluids is developed, which expresses the stress tensor in terms of a von Mises yield surface plus an expansion of acceleration tensors. The purpose of this theory is to represent the flow of concentrated suspensions of small interacting particles in polymer fluids. The 0th-order fluid turns out to be von Mises theory for perfectly plastic solids. The first-order fluid is equivalent to Oldroyd's theory of Bingham plastics. A second-order fluid theory, which is rather complex in form, is also derived.

A model equation for Non-Newtonian fluids

Abstract: A one-dimensional model for the equations of motion of a “simple fluid” according to Noll is proposed. An exterior problem for the model equation is solved by means of a transform method.

9.3. Low Reynolds Number Flows

Abstract: Publisher Summary This chapter examines the different aspects of low Reynolds number flows. The experimental methods of measuring flows in which viscous forces predominate over inertial forces and flows at low Reynolds numbers are presented. Viscous stresses usually appear in the dynamical equations as proportional to the rates of fluid strain. Viscous flow behavior has been utilized to measure both fluid physical properties and flow-field details. It is found that for the measurements of dynamic viscosity of linear fluids, the stress is measured by determining the torque needed to maintain a constant rotation rate of an outer cylinder concentric with an inner cylinder at rest. The forces, torques, and pressure distributions on rotating concentric cylinders with the fluid under study filling the annulus are sometimes measured, both for steady and oscillatory drive. The stresses in a rheologically complex fluid depend on the history of the deformation. Characterization of the constitutive constants of such a fluid is in general limited to a certain type of motion that may be produced in one apparatus, and little or no information on the same fluid's behavior in another type of apparatus may be inferred.

The Mechanical Properties of the Slurry and the Resistance Force of a Sphere Moving With Uniform Velocity in the Slurry

Abstract: It is commonly considered that the mechanical properties of the slurry are different from that of ordinary Newtonian fluid, and can be described by that of Bingham fluid. Hence its shearing stress should be described by the formula of the shearing stress of Bingham fluid. But the author holds the contrary opinion and firmly believes that the slurry is a highly viscous fluid with very long relaxation time such as those of asphalt, glass, etc. In this article, we have discussed the mechanical properties of the slurry and the resistance of a sphere moving with uniform velocity in the slurry. In the process of discussion, we use Stokes solution of the viscous fluid passing around a sphere. When the sphere is in equilibrium under the action of gravitational force, the force of buoyancy and the resistance, we get the velocity of sedimentation. When the velocity of sedimentation is equal to zero, we get the relation between the yield stress of Bingham fluid and the diameter of the particles which will not sink. The theoretical results calculated are compared with the experimental data of Northwest Institute of Hydrotechnical Research and Institute of Hydraulic Research, Yellow River Conservancy Commission. They are congruous.

Fundamental Steady F1ow of Polar Fluids

Abstract: A few fundamental steady flows of polar fluid, i.e., flow in a circular tube, flow between two parallel plates and flow between two ooaxial cylinders are analysed with the help of the theory of Eringen. Couple stress and spin angular momentum are considered in this approach. The exact solutions for velocity, micro-rotation, vortioity and shearing stress are obtained mathematically. These solutions are characterized by two parameters, i.e., the ratio of viscosities e and the size effect parameter λ which do not appear in a Newtonian fluid. e is the ratio of vortex visoosity to shear viscosity. λ means the size relation between the corpuscle and the characteristic length. The solutions are compared with those of Newtonian fluid and it is investigated how they vary with e and λ. Apparent viscosity is determined for each flow. Material constants of polar fluid can be decided from these apparent viscosities.

Some exact solutions to equations of transient flow with suction for a viscous fluid

Abstract: Self-adjoint asymptotic solutions to the equations of flow are constructed for a viscous fluid near a permeable plane boundary.

On flow of an elastico-viscous fluid past an oscillating porous plate

Abstract: A solution for the flow problem of an elastico-viscous fluid (Walters liquid B′) due to an oscillating infinite porous plate with constant suction has been obtained. It has been observed that the magnitude of velocity decreases with increase in suction velocity. The shearing stress increases with increase in suction.