Weissenberg effect

Abstract: A statistical mechanical theory of the so-called Weissenberg effect (or, normal stress effect) is presented. We adopt the weakly coupled rubber-like network model which we have formulated and applied to investigate the shearing and the tensile viscosity of concentrated solutions of linear high polymers. When the elastico-viscous liquid is compelled to stationary shearing flow, our theory shows that an additional normal tension arises in the direction of flow owing to the orientation of the network structure in addition to the usual shearing stress. Furthermore if the fluid is in a concentric circular motion with the angular velocity gradient in the radial or the axial direction, each doughnut-shaped piece along a flow line behaves as a streched rubber loop due to the said additional tension. As the result the inner bulk of the liquid is squeezed. The pressure increases as one approaches to the rotational axis. Such pressure distribution is calculated for the instruments of three types, i.e., the coaxial c...

Abstract: This paper reports the development of practical methods of viscometry to characterize non-Newtonian fluids in slow flow. It is shown that measurements of the free surface near rods rotating in STP and polyacrylamide are accurate, reproducible, and in excellent agreement with a theory of rod climbing. Results are presented that establish the theory and experiment as a viscometer for determining the values of certain (Rivlin-Ericksen) constants that arise in the theory of slow flow. The variation of these constants with temperature in our sample of STP has been explicitly and accurately determined. The experiments in STP show that there is a range of rotational speeds for which STP may be well described by the fluids of grade four. Depth-averaged equations are derived from the equations governing steady axisymmetric flow of any incompressible simple fluid. From the depth-averaged equations, we prove a theorem about the variation of the torque required to turn the rod.

Abstract: We apply the finite element method to calculate the time-dependent velocity of a sphere falling along the axis of a circular cylinder filled with a viscoelastic fluid. The mesh surrounding the sphere translates along the cylindrical wall. For our calculations, we select an Oldroyd-B fluid with viscometric properties similar to those of the M1 Boger fluid. We then calculate the motion of spheres with variable density as one would in the laboratory. We examine the effect of the Weissenberg number and of the geometry upon the essential features of the time-dependent flow. We find that, for a given sphere and a given fluid, the viscoelastic effects are damped when the radius of the cylinder becomes much larger than the radius of the sphere. The velocity overshoot decreases when the Weissenberg number increases. We also examine the sensitivity of the flow to the magnitude of the retardation time.