Standard representations viscosity

Similar behavior of a certain physical property common to different material systems can only be visualized by dimensionless representation of the material function of that property (here the viscosity l). It is furthermore desirable to formulate this function as uniformly as possible. This can be achieved by the standard representation (6,11) of the material function in which a standardized transformation of the material function /i(7) is defined in such a way that the expression produced meets the requirement... 

Figure 6 shows the dependency ijl T) for eight different liquids with greatly different temperature coefficients of the viscosity, whose viscosities cover six decades within the range of T= 20-80°C. Figure 7 depicts the standard representation of this behavior. Surprisingly this proves that all these liquids behave similarly in the /r(I) respect. In addition, it proves that this standard representation is invariant to reference temperature. Water is a special juice it behaves like the other liquids only in the vicinity of the standardization range yo(2 —To) 0. 

Example 11 Standard representation of the temperature dependence of viscosity... 

Fig. 8 a Standard representation of the temperature dependence of viscosity in the form of the relationship x/[t0 =/[y0 (T- T0)]. The solid curve a represents the reference-invariant approximation by the y-fu notion (see section 8.2), whereas the dotted line corresponds to the engineering representation, eq. (8.9) from [27],... 

Fig. 11 Standard representation of the temperature dependence of viscosity of aqueous sugar solutions of different concentrations as well as their reference-invariant approximation using ip = -0.500 (solid curve). For key parameters a(x)...

In discussing Fig. 4.1 we noted that the apparent location of Tg is dependent on the time allowed for the specific volume measurements. Volume contractions occur for a long time below Tg The lower the temperature, the longer it takes to reach an equilibrium volume. It is the equilibrium volume which should be used in the representation summarized by Fig. 4.15. In actual practice, what is often done is to allow a convenient and standardized time between changing the temperature and reading the volume. Instead of directly tackling the rate of collapse of free volume, we shall approach this subject empirically, using a property which we have previously described in terms of free volume, namely, viscosity. 

As discussed in Sect. 4, in the fluid, MCT-ITT flnds a linear or Newtonian regime in the limit y 0, where it recovers the standard MCT approximation for Newtonian viscosity rio of a viscoelastic fluid [2, 38]. Hence a yrio holds for Pe 1, as shown in Fig. 13, where Pe calculated with the structural relaxation time T is included. As discussed, the growth of T (asymptotically) dominates all transport coefficients of the colloidal suspension and causes a proportional increase in the viscosity j]. For Pe > 1, the non-linear viscosity shear thins, and a increases sublin-early with y. The stress vs strain rate plot in Fig. 13 clearly exhibits a broad crossover between the linear Newtonian and a much weaker (asymptotically) y-independent variation of the stress. In the fluid, the flow curve takes a S-shape in double logarithmic representation, while in the glass it is bent upward only. 

In 1929 E. W. Dean and G. H. B. Davis,4 of Standard Oil, used this representation for viscosities to develop the VI concept for lubricant feedstocks, intermediates, and base stocks. In modified form, this method for describing the viscosity-temperature relationship for base stocks and lubricants has become one of the bedrocks of the industry. The VI of a base stock now immediately brings to mind, rightly or wrongly, other features of interest to lubricants professionals, for example, oxidation stability and chemical composition (e.g., content of isoparaffins and cycloparaffins), and more recently, volatility. It is, however, best to regard this method as a means to express the rheological properties (the science of flow) of a base stock and use other more specific tests to measure other properties. 

By convention, the most convenient and generally accepted representation of melt viscosity is the melt index , which is the amount of polymer flowing through a standard capillary viscosimeter at 190°C under a 2.16-kg load for 10 min (ASTM... 

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