State shear

Figure A3.1.5. Steady state shear flow, illustrating the flow of momentum aeross a plane at a height z.

The economics of recycling PET are more favorable than recycling HDPE. To iacrease the recycling of HDPE, the separation of bottles made of these two plastics could be omitted and a mixture processed. Coarse, light-colored powders of the two polymers have been prepared by an experimental soHd state shear extmsion pulverization process (55). The powder has been successfully injection molded without pelletization. 

Normal Stress (Weissenberg Effect). Many viscoelastic fluids flow in a direction normal (perpendicular) to the direction of shear stress in steady-state shear (21,90). Examples of the effect include flour dough climbing up a beater, polymer solutions climbing up the inner cylinder in a concentric cylinder viscometer, and paints forcing apart the cone and plate of a cone—plate viscometer. The normal stress effect has been put to practical use in certain screwless extmders designed in a cone—plate or plate—plate configuration, where the polymer enters at the periphery and exits at the axis. 

Arastoopour, H., Single-screw extruder for soUd state shear extrusion pulverization and method, US patent, 5,704,555, 1998. 

Bilgili, E., Arastoopour, H., and Bernstein, B., Analysis of rubber particles produced by the solid state shear extrusion pulverization process. Rubber Chem. Technol., 73, 340, 2000. 

Rheo-Optical Observations. The rheo-optical observations were made with a WILD stereoscope equipped with a custom made rotary optical stage using polarized light. The rotary optical stage described in detail elsewhere (9) was used for both the steady state shear and dynamic test conditions. 

Rheological Properties Measurements. The viscoelastic behavior of the UHMWPE gel-like systems was studied using the Rheometric Mechanical Spectrometer (RMS 705). A cone and plate fixture (radius 1.25 cm cone angle 9.85 x 10" radian) was used for the dynamic frequency sweep, and the steady state shear rate sweep measurements. In order to minimize the error caused by gap thickness change during the temperature sweep, the parallel plates fixture (radius 1.25 cm gap 1.5 mm) was used for the dynamic temperature sweep measurements. 

Steady state shear viscosity measurements indicate a power-law type relation for the variation of the shear viscosity with shear rate even in the lower shear rate range between 10"1 to 1 sec"l. The results at higher shear rates were questionable due to the slip between the sample and cone and plate fixtures. 

A novel approach is used to compatibilise a blend without addition of premade copolymers or functionalisation of polymers lacking functional groups. Solid-state shear pulverisation (S3P) processes polymers at temperatures below the melt transition (for semicrystalline polymers) or the glass transition (for amorphous polymers). The polymer, introduced as pellets or flakes into the pulveriser. 

For the limiting cases, N 0 and k oo, Eqs. (12-47) and (12-49) reduce to equations derived by Taylor (T2, T3) for fluid particles in steady-state shear or hyperbolic flows, i.e.,... 

Figure 7.9 Effect of pectin (DE = 76%) on (a) creaming of protein-stabilized emulsions (11 vol% oil, 0.6 wt% protein, 0.28 wt% pectin, I = 0.01 M) containing (A) asi-casein (pH = 7), (A) p-casein (pH = 7), and ( ) o i-casein (pH = 5.5) and (b) steady-state shear viscometry of casein-stabilized emulsions (40 vol% oil, 2 vt% protein). Apparent shear viscosity at 22 °C is plotted against stress pH = 7.0, / = 0.01 M, (A) -casein, (A) p-casein, ( ) ocsi -casein + 0.5 wt% pectin, ( ) p-casein + 0.5 wt% pectin, ( ) p-casein + 1.0 wt% pectin, (O) as[-casein + 1.0 wt% pectin pH = 5.5,1 = 0.01 M, (x) ocsi -casein, (O) as[-casein + 0.5 wt% pectin, ( ) oc -casein + 1.0 wt% pectin. Reproduced from Semenova (2007) with permission.

The symbols Nt and N2 denote the normal stress functions in steady state shear flow. Symmetry arguments show that the viscosity function t](y) and the first and second normal stress coefficients P1(y) and W2(y) are even functions of y. In the... 

Behavior in steady state shearing flows likewise provide values of these parameters (83) ... 

At sufficiently low shear rates the shear stress should decay at the termination of steady state shear flow according to the equation from linear viscoelasticity ... 

The total amount of shear recoil after steady state shear flow at sufficiently low shear rates is related to Je° ... 

According to the theory of linear elastico-viscous behaviour (47) the steady-state shear viscosity t] and the steady-state shear compliance Je depend in the following way on the shear relaxation modulus G (t), where t is here the time of the relaxation experiment ... 

Lodge s expression for the steady-state shear viscosity reads (10) ... 

This means that for a linear elastico-viscous liquid, the steady-state shear compliance Je must be equal to the constrained shear recovery sx which follows on a steady shear flow at unity shear stress. From this one deduces the following relation between and Je ... 

The corresponding value of the reduced steady-state shear compliance reads ... 

Unfortunately, Fixman has not yet given a value for the reduced steady-state shear compliance. However, from a comparison of eqs. (3.60a), (3.64) and (3.66) the impression is obtained that the theory of Ptitsyn and Eizner overestimates the influence of the excluded volume on 0 and JeR. As will be shown in the experimental section of this chapter, this impression is supported by flow birefringence measurements on solutions in 0- solvents and in good solvents. 

This is the well-known front factor of the reduced steady-state shear compliance as quoted by Ferry (113). In this form polydispersity factor p can be compared with the diverse molecular weight averages, as obtained from equilibrium ultracentrifugation, light-scattering and osmometry. 

Fig. 4.3. Reduced steady-state shear compliance J,B vs. volume fraction p or concentration c, according to a combination of eq. (4.10) with eqs. (4.6) and (4.9), respectively (smoothed curves). Figures below full lines... MjMp-values, figures above dashed lines. . . M/if-values (theoretical curves)...

Fig. 4.4. Concentration dependence of reduced steady-state shear compliance J,B for a series of anionic polystyrenes, as mostly provided by Pressure Chem. Corp., Pittsburgh, Pa. Except for the solutions of the three lowest concentrations of S 111 (Dow Chem. Corp.), which were prepared with methyl (4-bromo-phenyl) carbinol and used at various temperatures, all solutions were prepared with mono-bromo-benzene and used at 25° C (32). Measurement temperatures for the melts varied from 196 to 240° C (59). For the molecular weights of the polymers see Table 4.1...

Thus, the r and components of the velocity gradient are completely disregarded and Vq1 depends on those coordinates only through the r and dependence of the (radial) force density and the ground state shear velocity. The quality of this model increases with increasing kR. It is expected that the velocity perturbation is overestimated in this model and thus the hypothetical instability threshold is lowered, which makes the model appealing at least as a first attempt. 

Fig. E3.5 Steady-state shear viscosity rj and first normal stress coefficient i, obtained from dynamic measurements versus shear rate for a low-density polyethylene melt, melt I. [H. M. Laun, Rheol. Ada, 17, 1 (1978).]...

J m(t — t )y 1](t, t) dt. Consider a fluid with a single relaxation time, 20, and modulus, Go, and with h(y) = e y. Calculate the steady-state shear viscosity function... 

Fig. 11.18 (a) The steady state shear rate and (b) shear stress-dependent viscosity of carbon black... 

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