Experimental results viscosity, measuring

The paper discusses the application of dynamic indentation method and apparatus for the evaluation of viscoelastic properties of polymeric materials. The three-element model of viscoelastic material has been used to calculate the rigidity and the viscosity. Using a measurements of the indentation as a function of a current velocity change on impact with the material under test, the contact force and the displacement diagrams as a function of time are plotted. Experimental results of the testing of polyvinyl chloride cable coating by dynamic indentation method and data of the static tensile test are presented. 

Of course, any set of experimental data can be described by selecting an appropriate empirical equation with an arbitrary set of constants. However, comparing a vast wealth of the known results of measurements of suspension viscosity, it should be admitted that a universal formula for ther (cp) dependence does not exist, and significant discrepancies may begin already from a linear term, so that physical reasons for exagerated values of the coefficient bt as compared to 2.5 should be looked for. 

L. L. Blyler and T. K. Kwei [39] proposed the direct opposite (to 4). In their reasoning, they proceeded from the known and generally acceptable Doolittle equation, which puts liquid viscosity in exponential dependence on the inverse value of the free volume of the latter. According to [39], gas has a volume of its own, the value of which it contributes to the free volume of the polymer when it dissolves therein as a result, viscosity falls. The theoretical formula obtained by the authors was experimentally confirmed in the same work. The authors measured pressure values at the entrance of cylindrical capillaries, through which melts of both pure polyethylene, and polyethylene with gas dissolved in it, extruded at a constant rate. 

Perrin model and the Johansson and Elvingston model fall above the experimental data. Also shown in this figure is the prediction from the Stokes-Einstein-Smoluchowski expression, whereby the Stokes-Einstein expression is modified with the inclusion of the Ein-stein-Smoluchowski expression for the effect of solute on viscosity. Penke et al. [290] found that the Mackie-Meares equation fit the water diffusion data however, upon consideration of water interactions with the polymer gel, through measurements of longitudinal relaxation, adsorption interactions incorporated within the volume averaging theory also well described the experimental results. The volume averaging theory had the advantage that it could describe the effect of Bis on the relaxation within the same framework as the description of the diffusion coefficient. 

Figure 8.7 Temperature dependences of viscosity for several solvents measured with conventional Ostwald viscometers. Markers exhibit experimental results. Data points were interpolated by polynomial function the calculated curves are drawn with lines.

Fig. 15. Comparison of the viscosities either directly measured or calculated from the spin-echo results for polyethylene melts at 509 K as a function of molecular mass ( experimental result o viscosities calculated on the basis of mode analysis). (Reprinted with permission from [52]. Copyright 1993 The American Physical Society, Maryland)...

Fig. 4.35 Right-hand side Monomeric friction coefficients derived from the viscosity measurements on PB [205]. The open and solid symbols denote results obtained from different molecular weights. Solid line is the result of a power-law fit. Dashed line is the Vogel-Fulcher parametrization following [205]. Left hand side Temperature dependence of the non-ergodicity parameter. The three symbols display results from three different independent experimental runs. Solid line is the result of a fit with (Eq. 4.37) (Reprinted with permission from [204]. Copyright 1990 The American Physical Society)...

The results and observations from the experimental methods used to study the interaction modes of RuCphen) " are compiled in Table 1. The examination of this table indicates obvious disagreements between the authors concerning the intercalation of Ru(phen)3 into DNA. Chronologically, the first spectroscopic experiments (entries 1 to 4) and the first results on DNA unwinding and dcnaturation (entries 11,12) in 1984-1986 were all consistent with intercalation. Afterwards, with the results from LD and NMR in 1988-1992 (entries 5, 7) and with the viscosity measurements in 1992 (entry 10), the intercalation of Rufphen) has become questionable. 

This second method does not lend itself to the development of quantitative correlations which are based solely on true physical properties of the fluids and which, therefore, can be measured in the laboratory. The prediction of heat transfer coefficients for a new suspension, for example, might require pilot-plant-scale turbulent-flow viscosity measurements, which could just as easily be extended to include experimental measurement of the desired heat transfer coefficient directly. These remarks may best be summarized by saying that both types of measurements would have been desirable in some of the research work, in order to compare the results. For a significant number of suspensions (four) this has been done by Miller (M13), who found no difference between laboratory viscosities measured with a rotational viscometer and those obtained from turbulent-flow pressure-drop measurements, assuming, for suspensions, the validity of the conventional friction-factor—Reynolds-number plot.11 It is accordingly concluded here that use of either type of measurement is satisfactory use of a viscometer such as that described by Orr (05) is recommended on the basis that fundamental fluid properties are more readily determined under laminar-flow conditions, and a means is provided whereby heat transfer characteristics of a new suspension may be predicted without pilot-plant-scale studies. 

Figure 4.12a shows plots of the intrinsic viscosity —in volume fraction units —as a function of axial ratio according to the Simha equation. Figure 4.12b shows some experimental results obtained for tobacco mosaic virus particles. These particles —an electron micrograph of which is shown in Figure 1.12a—can be approximated as prolate ellipsoids. Intrinsic viscosities are given by the slopes of Figure 4.12b, and the parameters on the curves are axial ratios determined by the Simha equation. Thus we see that particle asymmetry can also be quantified from intrinsic viscosity measurements for unsolvated particles. 

The practical significance of the result of this example lies in the great ease with which viscosity measurements can be made. Once the k and a values for an experimental system have been established by an appropriate calibration, molecular weights may readily be determined for unknowns measured under the same conditions. Extensive tabulations of Mark-Houwink coefficients are available, so the calibration is often unnecessary for well-characterized polymers (see Table 4.5). 

This section describes two common experimental methods for evaluating i], Fj, and IG as functions of shear rate. The experiments involved are the steady capillary and the cone-and-plate viscometric flows. As noted in the previous section, in the former, only the steady shear viscosity function can be determined for shear rates greater than unity, while in the latter, all three viscometric functions can be determined, but only at very low shear rates. Capillary shear viscosity measurements are much better developed and understood, and certainly much more widely used for the analysis of polymer processing flows, than normal stress difference measurements. It must be emphasized that the results obtained by both viscometric experiments are independent of any constitutive equation. In fact, one reason to conduct viscometric experiments is to test the validity of any given constitutive equation, and clearly the same constitutive equation parameters have to fit the experimental results obtained with all viscometric flows. 

The Mark-Houwink equation provides an indirect estimate of molar mass from a measurement of intrinsic viscosity [r ], if the two Mark-Houwink constants K and a, are known. The predictions of Mark-Houwink constants are summarized in Table 8.1. Comparison with Table 1.4 shows that the Zimm model agrees reasonably well with experimental results, as a = 0.50 is observed in 0-solvent and 0.7 < a < 0.8 is usually observed in good solvents. 

For measurements of viscosity of molten salts and glasses at high-temperatures, several methods were proposed. The selection of a particular method depends in general on the viscosity of the liquids to be measured. A broad dispersion of experimental results reflects substantial experimental difficulties connected with viscosity measurement. In general, in the measurement of viscosity of molten salts the method of torsional pendulum is most frequently used, while in the measurement of viscosity of liquids, such as molten glasses, the falling body and the rotational methods are most suitable. Methods for viscosity measurement of liquids with a very high viscosity (above 10 Pa s) will not be described here. 

Two methods of measurement are used. The first one is the classical rotational method employing the original properties of the viscosimeter. Because the measurement of viscosity of molten glasses requires a configuration with a free spindle, the determination of the angular momentum I as the function of a and the shear stress was not taken into account. Direct calibration using the experimental relation t]la =f a) showed to be very simple and relatively accurate. Based on experimental results, the linear function has been chosen in the form... 

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