Steady state viscosity solutions

Fig. 8.3. Dynamic viscosity, absolute complex viscosity, and steady state viscosity for narrow distribution polystyrene. Data obtained at 25° C on a 0.071 gm/ml solution of polystyrene (Mw = 860000) in Aroclor (3/6)...

Many amorphous homopolymers and random copolymers show thermorheologically simple behavior within the usual experimental accuracy. Plazek (23,24), however, found that the steady-state viscosity and steady-state compliance of polystyrene cannot be described by the same WLF equation. The effect of temperature on entanglement couplings can also result in thermorheologically complex behavior. This has been shown on certain polymethacrylate polymers and their solutions (22, 23, 26, 31). The time-temperature superposition of thermorheologically simple materials is clearly not applicable to polymers with multiple transitions. The classical study in this area is that by Ferry and co-workers (5, 8) on polymethacrylates with relatively long side chains. In these the complex compliance is the sum of two contributions with different sets of relaxation mechanisms the compliance of the chain backbone and that of the side chains, respectively. 

Ctmcentrated stdutions of polypeptides sbow the Weisenbei effect 77). It is known that the extinction angle, of such solutitais can he calculated by substituting the trahies of the total normal stress,/, and of the steady-state viscosity, tj, of the solution with the equation in the form (75) ... 

Figure 5.20 Steady-state viscosity T] y) and dynamic complex viscosity rj u)) as functions of reduced shear rate (j>r) or frequency cox), for a 1.5% w/v solution of the associative thickener described in the caption to Fig. 5-18. (From Annable et al. 1993, with permission from the Journal of Rheology.)...

Figure 11.8 The steady-state viscosity for solutions of poly(l,4-phenylene-2,6-benzobisthiazole) (PBZT) with viscosity-averaged molecular weight 37,400 (molecular length 170 nm), in methane sulfonic acid at concentrations of 1.5 ( ), 2.52(H), 3.0(A), 3.43(0), 6.11(0). 8.2(Q)% (by...

It can be shown that for most dilute solutions there exists a simple correlation between dynamic and steady state flow characteristics (16). For most detergent solutions the magnitude of the complex viscosity 1 n I at a certain angular frequency CO coincides with the steady state viscosity n, at the corresponding shear rate "f (12, 17). 

Measurements of steady-state viscosity rj (at zero shear rate) on many species of flexible linear polymers in concentrated solutions and melts have established that a simple empirical equation [3]... 

Figure 12.3 Steady-state viscosity vs. shear rate for micellar solutions of 0.06 M ChEOio-Ci2E03 systems at various mole fractions of CizEOj (X) (A) 0 (B) 0.09 (C)...

Feng and Michaelides [7] resolved energy equation in the continuous phase by using a finite-difference method with their own numerical velocity field. In this work, steady-state numerical solutions were obtained for Reynolds number, viscosity ratio, and Peclet number ranges of 0 < Re < 500, 0 < K < 00 and 0 < Pe < 1000, respectively. 

Rheological properties under steady state and oscillatory shear flow of isotropic and nematic solutions of PpPTA, PBT and PBO were studied by Baird [70] and Berry et al. [46]. Baird observed shear thinning for a series of PpPTA solutions in sulfuric acid (4-15%). These results also suggest that at higher shear rates very little difference exists between the anisotropic and isotropic phases. Steady-state viscosities as a function of the temperature observed for solutions of PBO in methane sulfonic acid showed a sharp increase near T,, a behavior which has also been reported for PpPTA and PpBA solutions [46],... 

Fig. 1 The concentration dependence of steady-state viscosities at a shear rate of 1 sec" and 30 C for the HPC (O) and EC ( ) solutions.

Dynamic measurements taken on a polymer solution at a frequency 1 radian/s give values of G = 5.0 X 10 Pa and G" = 2.0 x 10 Pa. On the basis of these data, what quantitative statement (if any) can you make about the steady-state viscosity of this material at the same temperature ... 

The polymerization system for which experiments were performed is represented by the mathematical model consisting of Equations 1 and 7. Their steady state solutions are utilized for kinetic evaluation of rate constants. Dynamic simulations incorporate viscosity dependency. 

Molecular Rotational Diffusion. Rotational diffusion is the dominant intrinsic cause of depolarization under conditions of low solution viscosity and low fluorophore concentration. Polarization measurements are accurate indicators of molecular size. Two types of measurements are used steady-state depolarization and time-dependent (dynamic) depolarization. 

Flow Tests. Results of the flow tests are shown in Figures 3 through 6. Figure 3 shows the results of a typical run with a brine saturated sand pack wherein a 300 ppm polymer solution in 1 wt% NaCl was injected at a pH of 8.26. Before this, steady state conditions were established in the core by injecting 1 wt% NaCl. The pH values were stabilized at 8.0 and viscosity at around 1.1 cp. The pressure drop across the core stayed constant up to about 8 PV of polymer injection, the pH stayed in the acidic range, and effluent viscosity was consistently lower than the influent value. At about 8 PV the pressure drop started to build and within 2 PV, increased up to about 100 psi essentially plugging the core. No polymer was eluted until the end of the run. 

Fig. 8. Dependence of (A) corrected diffusion coefficient (D), (B) steady-state fluorescence intensity, and (C) corrected number of particles in the observation volume (N) of Alexa488-coupled IFABP with urea concentration. The diffusion coefficient and number of particles data shown here are corrected for the effect of viscosity and refractive indices of the urea solutions as described in text. For steady-state fluorescence data the protein was excited at 488 nm using a PTI Alphascan fluorometer (Photon Technology International, South Brunswick, New Jersey). Emission spectra at different urea concentrations were recorded between 500 and 600 nm. A baseline control containing only buffer was subtracted from each spectrum. The area of the corrected spectrum was then plotted against denaturant concentrations to obtain the unfolding transition of the protein. Urea data monitored by steady-state fluorescence were fitted to a simple two-state model. Other experimental conditions are the same as in Figure 6.

Photosensitization of diaryliodonium salts by anthracene occurs by a photoredox reaction in which an electron is transferred from an excited singlet or triplet state of the anthracene to the diaryliodonium initiator.13"15,17 The lifetimes of the anthracene singlet and triplet states are on the order of nanoseconds and microseconds respectively, and the bimolecular electron transfer reactions between the anthracene and the initiator are limited by the rate of diffusion of reactants, which in turn depends upon the system viscosity. In this contribution, we have studied the effects of viscosity on the rate of the photosensitization reaction of diaryliodonium salts by anthracene. Using steady-state fluorescence spectroscopy, we have characterized the photosensitization rate in propanol/glycerol solutions of varying viscosities. The results were analyzed using numerical solutions of the photophysical kinetic equations in conjunction with the mathematical relationships provided by the Smoluchowski16 theory for the rate constants of the diffusion-controlled bimolecular reactions. 

All steady state fluorescence experiments were conducted with the sample placed in a thermostated cell with temperature maintained at 30°C. The concentrations of anthracene and initiator used were 0.000505 and 0.00608 moles per liter, respectively. The relative quantities of solvents (n-propanol and glycerol) were adjusted from 0 to 100% to achieve solutions of different viscosities, while maintaining the same molar concentration of the reactive solutes. 

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