The viscous heat effect on the fluid temperature is investigated in circular tube flow. Approximate mathematical solutions are given for the temperature distribution of fluid over the cross section of a circular tube and also for the temperature rise of fluid along the tube in consideration of heat conduction through the tube wall. In the case of liquid flow, the temperature rise ΔT at the exit of the tube is related to the pressure drop Δp through the tube by the following approximate equation. _??_, where _??_, a: internal radius of tube b: external radius of tube l: length of tube Kc: thermal conductivity of tube Kf: thermal conductivity of liquid c: volumetric heat capacity of liquid η: viscosity of liquid. The temperature rises calculated by this equation generally agree with those obtained by experiments. In the case of gaseous flow where the sample gas is regarded as an ideal gas, it is concluded theoretically that the heat energy due to viscous resistance is spent in compensation for the reduction of internal energy due to the bulk expansion of flowing gas with the decrease of pressure, and consequently, temperature of flowing gas is kept constant.
The relaxation modulus G (t) and the viscosity decay function η(t) after cessation of steady flow were measured for suspensions of Aerosil in polystyrene solution with a coaxial cylinder rheometer. Particle content were from 3 to 5wt%. Measurements were performed at various magnitudes of shear strain γ ranging from 0.046 to 2.4 and at various shear rates γ ranging from 0.024 to 1.21s-1. The maximum relaxation time τ1 and the associated relaxation strength G1 were evaluated from G (t) through the Procedure X. Both τ1, and G1 decreased with increasing strain for all the suspensions studied. The Procedure X was also applicable to η(t) of 3wt% suspension, revealing that both τ1 and η1 decreased with increasing shear rate. However, it was not applicable to η(t) of 5wt% suspension, because η(t) did not decay to zero value even after very long time. As the behavior of G (t) and of η(t) were different from each other, detailed experiments were carried out. The stress relaxation after various shearing times under a constant shear rate was measured. When the shearing time was short, the stress relaxation function decreased with shearing time. On the other hand, when the suspension was sheared for more than a certain shearing time, the stress relaxation function began to increase with shearing time. And finally after long time shearing, i. e, after cessation of steady flow, it showed residual stress at the long-time region. It is suggested that G (t) and η(t) originate from two different relaxation mechanisms.
Measurements of birefringence and streamlines near the exit of a slit were carried out for the steady laminar flow of high density polyethylene Sholex 6008 melt. Distributions of deviatoric stress intensity and its direction were obtained by graphical method from the isochromatic and isoclinic trajectories, respectively. The results provided basic informations on the mechanical feature of the Barus effect, i. e., the enlargement phenomenon of the cross-sectional area of the extrudate than that of the nozzle. Observed directional change of the streamline suggested that large swelling was developable around the center plane in spite of small first normal stress difference there. On the other hand, near the slit wall, particularly near the slit edge, the polymer melt was highly stretched to the direction of flow and the positive normal stress was generated to the same direction. These observations were compared with the computer results obtained by Tanner et al. under Stokes' approximation for a particularly slow Newtonian liguid flow about the exit of a circular tube. Normal stresses normal to the duct wall surface was clearly generated in a short distance just before and after the exit plane. This was in contrast to the present observation where the normal stress varied over a wide range of distance from the exit plane. Thus the distribution of deviatoric normal stresses near the slit exit, suggests that the Barus effect is a kind of solid-like retarded elastic recovery phenomenon in response to the rapid release from the restriction of the sustaining duct wall.
The steady-flow, linear and nonlinear viscoelastic properties of disperse systems of swollen styrene-divinylbenzene copolymer particles were measured for a wide variety of the degree of cross-linking by means of a Weissenberg Rheogoniometer. The rheological properties of disperse systems in which each particle does not reach the state of equilibrium swelling, depend strongly on the boundary layers between neighboring particles. The lower the degree of cross-linking of particles, the higher the storage and loss moduli of the disperse system. The nonlinear viscoelasticity of these disperse systems are compared with those of suspensions of rigid particles.