Viscosity Time Function

Figure 3.24 Influence of PA-6 polymerization process on relative viscosity as function of reaction time (i) atmospheric in VK column (ii) prepolymerization atmospheric followed by water removal (iii) prepolymerization at elevated pressure followed by water removal.31...

Pectins in aqueous solutions show pseudoplastic non-thixotropic behaviour, independent of their degree of methoxylation. Figure 1 shows the viscosity curve of a 2,5 % pectin solution, sheared the preselected shear rate-time function. The viscosity curves for the increasing and decreasing shear rate are superimposed. The pseudoplasticity of pectin solutions decreases with decreasing concentration. 

Usually the function [Cn) M] (intrinsic viscosity times molecular weight) is used to represent hydrodynamic volume which is plotted versus elution volume. For such a plot the calibration curves of many polymers fall on the same line irrespective of polymer chemical type. Universal calibration methodology usually requires knowledge of Mark-Houwink constants for the polymer/ temperature/solvent system under study. 

Figure 1.16 shows the relative complex viscosity as a function of conversion at 120 and 150°C. The 150°C curve shows a dramatic rise due to the simultaneous crystallization during polymerization. In addition, notice in Figure 1.13 that the complex viscosity-time curves of 150 and 160°C polymerization tend to converge. Both these effects—the nonlinear rise in relative complex viscosity in Figure 1.16 and the convergence of 150 and 160°C curves in... 

Fig. 12. Time function of viscosity in uniaxial extension for different dimensionless elongation velocities...

In a study aimed at modeling the optimum of a dynamic viscosity as functions of speed and time of mixing, this regression model has been obtained ... 

Arrhenius form, to obtain an expression which can predict viscosity-time behavior at other temperatures. If temperature is allowed to be a function of time (nonisothermal cure), Eq. 3 results, due to Roller.(J )... 

Fig. 14.— Variation of Solubility, Alkali-lability, Reducing Sugars, and Viscosity, as Function of Time, for Yellow-Farina Dextrin. ...

Figure 5. Dimensionless torque-time curves for dispersion Figure 6. Viscosity as function of frequency at T 200 C. process of artificial agglomerates using technique A (paggi=1.61 P HDPE, HDPE-30% Ti02, HDPE-30% Ti02/A0T.

Shear stress n. Force per imit area acting in the plane of the area to which the force is applied. In an elastic body, shear stress is equal to shear modulus times shear strain. In an inelastic fluid, shear stress is equal to viscosity times the shear rate. In viscoelastic materials, shear stress will be a function of both shear strain and shear rate. 

This equation can be used to describe viscosity-time profiles for any run for which the temperature can be expressed as a function of time. The activation energies can now be calculated. The plots of the natural log of the initial viscosity (determined above) versus l/T and the natural log of the apparent rate constant, k, versus l/T are used to give us the activation energies, and AEjt. Comparison of these values to the k and A.E calculated by DSC shows that this model gives larger values [82]. The DSC data are faster to obtain, but it does not include the needed viscosity information. Several corrections have been proposed, addressing dilferent orders of reaction... 

A typical profile for melt viscosity as a function of time for a polymerization reaction was shown in Figure 2. The shape of the curve reflects the kinetic processes which are occuring during the polymerization. All of the reactions were carried out neat, at a. 200 C. The viscosity/time profiles that were observed with both anionic and coordination type catalysts were essentially the same. The data not fit a normal "living" mechanism, with no side reactions. There is... 

In an inelastic fluid, shear stress is equal to viscosity times the shear rate. In viscoelastic materials, shear stress will be a function of both shear strain and shear rate. 

FIG. 24 Extensional viscosity growth function vs time for Phillips Marlex 5502, high-density polyethylene. Strain rate, s 1, 0.0022 2, 0.005 3, 0.055 4, 1.10. (Data from Ref 61.)... 

The surface-pressure history during polymer injection is predicted by Eq. 1 in the following manner. A skin/permeability quotient that is consistent with brine injectivity at 481 and 301 B/D as well as a pressure-transient test is calculated for use in the model. The shut-in-pressure difference between the injection well, P, and the observation well, Pg, is calculated to obtain the hydrostatic-pressure contribution. A viscosity/velocity functionality is assumed, and the hourly flow rates and BHP s during polymer injection are entered into the flow model to calculate injection pressure vs. time. This injection-pressure history is compared with the actual pilot data. As previously mentioned, the predicted injection pressure is inversely proportional to the area under the viscosity/velocity curve, starting at high velocities close to the wellbore and moving... 

Stressing viscosity (i, for uniaxial, biaxial, and planar extension, stressing viscosity for planar extension, and shear viscosity as functions of time ter inception of steady straining for polyisobutylene. The solid line is the low shear rate limit of. Extension and shear rates are 0.08s except the biaxial which is 0.02s-. From Retting and Lawn, 1991. 

These equations allow us to obtain an equation (in Einstein approximation, according to Landau-Lifschitz [248]) describing the time function of viscosity increase Ar (t), which occurs because of the increase of the aggregates size due to the addition of molecules activated by an external influence. 

The shear stress constant-rate flow at time 0. For a small shear rate y ( l/ii) in the linear viscoelastic regime, this stress growth is chararterized by a viscosity growth function ti t)=crs t,y)/y. As noted from eqns [21] and [22], j/ (t) is related to the relaxation modulus G(t) and/or the relaxation spectrum as... 

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