Volume 32, Issue 1, January 1988
Index of content:
32(1988); http://dx.doi.org/10.1122/1.549961View Description Hide Description
A dilute polymer solution is modeled by linear and nonlinear dumbbells suspended in a Newtonian solvent. The Langevin equations governing the motion of the dumbbells in the tube are solved with the help of Brownian dynamics simulations consistent with the momentum balance equation. To this purpose a previously presented consistent numerical approach has to be specialized to tube flow. The models show typical features as the slip effect, the flow enhancement, and the reduction in viscosity with decreasing tube radius.
32(1988); http://dx.doi.org/10.1122/1.549995View Description Hide Description
Rheological tests based on steady‐shear and transient experiments are used to discriminate between three classes of integral constitutive equations: the K‐BKZ, the LeRoy‐Pierrard, and the Carreau equations. The tests derived from the given equations require no prior evaluation of model parameters. Reliable data obtained for steady‐shear, stress growth, and stress‐relaxation experiments conducted with various polystyrene solutions are used. The Carreau and K‐BKZ equations appear to be the most flexible, but none of the equations is capable of describing the whole spectrum of behavior observed in relaxation. The strains at which the maximum values of the shear and normal stresses are observed for the polystyrene solutions increase with the applied shear rate. This behavior can be described by the Carreau equation. This contrasts with results reported in the literature on low density polyethylene for which the strains were found to be constant.
Some Comments on the Role of Macroscopic and Molecular Inertia in the Theory and the Practicability of Transient Flow Experiments on Dilute Polymer Solutions32(1988); http://dx.doi.org/10.1122/1.549962View Description Hide Description
Two basic issues are addressed: the experimental question of whether it is practicable to generate an instantaneous jump in strain rate to a liquid, and the theoretical question of how a dissolved polymer chain will respond if the solvent around it is suddenly set into motion. It is argued that it is experimentally impossible to perform tests in which the strain rate exhibits a step change. In actual experiments the strain acceleration is bounded and the strain rate as well as the strain vary continuously. It is shown, on the basis of the equation of internal motion for a dumbbell with internal viscosity, that in idealized step strain rate flows the velocities of the beads at the very moment of inception are lower than the flow rates locally imposed on the fluid. In that case, also the mass of the beads affects the strain rate of the dumbbell. Theoretically, the stress jump at the inception of constant strain rate flows depends on φ, and where φ is the internal viscosity coefficient, f the bead‐solvent friction coefficient, and m the mass of the bead, showing that the usual omission of inertial effects in these models is permitted only if
32(1988); http://dx.doi.org/10.1122/1.549963View Description Hide Description
Often for slurries,gels,emulsions, and foams inhomogeneous fluid properties at solid boundaries create “apparent wall slip.” The reduced fluid viscosity at the boundary creates a thin layer of fluid having a large velocity gradient that can be treated as a “slipping layer”. In measurements of fluid viscosity it is necessary to correct for wall slip to determine the true deformation experienced by the bulk of the sample and the true viscosity. The classic earlier techniques for capillaries and Couette geometries were first presented by Mooney. We present a new analysis of the Couette geometry that requires only two measurements rather than the three used by Mooney. We also present a new analysis for flow between rotating parallel disks. The parallel disk geometry has several experimental advantages for measuring fluid viscosities in the presence of wall slip. The analysis of experimental data on a clay suspension and oil‐in‐water emulsion are presented to demonstrate these new techniques.
32(1988); http://dx.doi.org/10.1122/1.549964View Description Hide Description
The experimental study of foam is complicated by its inherently unstable nature and by the presence of a liquid film slip layer at the wall. A method is described for generating reproducible and stable foam capable of retaining its structure for prolonged times. An experimental technique has also been devised which eliminates problems associated with wall slippage and allows measurement of material functions without use of any empiricisms for the wall region. In a steady‐shear flow, foam behaves like a Bingham plastic with a viscosity inversely proportional to shear rate indicating the presence of a yield stress The value of the viscosity, which is significantly higher than the parent liquid viscosity, is an increasing function of gas volume fraction φ. Yield stress values obtained by extrapolating viscosity versus shear stress data agree with direct measurements obtained by using a stress relaxation technique. The yield stress is also found to increase with φ. Small amplitude oscillatory shearing experiments show foam to behave as an elastic solid for small deformations. This is evident from its frequency independent moduli, very small phase shift between strain input and stress output, and the elastic modulus's being much larger than the loss modulus. Stress growth experiments at the start‐up of steady‐shear flow reveal stress overshoots not larger than 30%. The transient viscosity divided by the steady‐state viscosity is found to be insensitive to shear rate, but is an increasing function of φ.