Viscosity experimental results

Given in terms of viscosity, experimental results confirm the theoretical Einstein formula relating the diffusion coefficient to viscosity ... 

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. 

Our approach in this chapter is to alternate between experimental results and theoretical models to acquire familiarity with both the phenomena and the theories proposed to explain them. We shall consider a model for viscous flow due to Eyring which is based on the migration of vacancies or holes in the liquid. A theory developed by Debye will give a first view of the molecular weight dependence of viscosity an equation derived by Bueche will extend that view. Finally, a model for the snakelike wiggling of a polymer chain through an array of other molecules, due to deGennes, Doi, and Edwards, will be taken up. 

In the foregoing discussions of theoretical models and experimental results, we have focused on linear polymers. We have seen the effect of chain substituents on viscosity. All other things being equal, bulky substituents tend to decrease f and thereby lower 17. The effect is primarily due to the opening up of the liquid because of the steric interference with efficient packing arising from the substituents. With side chains of truly polymeric character, the picture is quite different. 

We must be careful in assessing the experimental results on the viscosity of branched polymers. If we compare two polymers of identical molecular weight, one branched and the other unbranched, it is possible that the branched one would show lower viscosity. Two considerations enter the picture here. First, since the side chains contribute to the molecular weight, the backbone chain... 

The molecules used in the study described in Fig. 2.15 were model compounds characterized by a high degree of uniformity. When branching is encountered, it is generally in a far less uniform way. As a matter of fact, traces of impurities or random chain transfer during polymer preparation may result in a small amount of unsuspected branching in samples of ostensibly linear molecules. Such adventitious branched molecules can have an effect on viscosity which far exceeds their numerical abundance. It is quite possible that anomalous experimental results may be due to such effects. 

Whea there are reactants with three or more functionahties participating ia the polymerization, branching and the formation of iatermolecular linkages, ie, cross-linking of the polymer chains, become definite possibiUties. If extensive cross-linking occurs in a polymer system to form network stmctures, the mobiUty of the polymer chains is greatiy restricted. Then the system loses its fluidity and transforms from a moderately viscous Hquid to a gelled material with infinite viscosity. The experimental results of several such reaction systems are collected in Table 6. 

A comparison of values of yield stress for filled polymers of the same nature but of different molecular weights is of fundamental interest. An example of experimental results very clearly answering the question about the role of molecular weight is given in Fig. 9, where the concentration dependences of yield stress are presented for two filled poly(isobutilene)s with the viscosity differing by more than 103 times. As is seen, a difference between molecular weights and, as a result, a vast difference in the viscosity of a polymer, do not affect the values of yield stress. 

Qu et al. (2000) carried out experiments on heat transfer for water flow at 100 < Re < 1,450 in trapezoidal silicon micro-channels, with the hydraulic diameter ranging from 62.3 to 168.9pm. The dimensions are presented in Table 4.5. A numerical analysis was also carried out by solving a conjugate heat transfer problem involving simultaneous determination of the temperature field in both the solid and fluid regions. It was found that the experimentally determined Nusselt number in micro-channels is lower than that predicted by numerical analysis. A roughness-viscosity model was applied to interpret the experimental results. 

Computer simulations therefore have several inter-related objectives. In the long term one would hope that molecular level simulations of structure and bonding in liquid crystal systems would become sufficiently predictive so as to remove the need for costly and time-consuming synthesis of many compounds in order to optimise certain properties. In this way, predictive simulations would become a routine tool in the design of new materials. Predictive, in this sense, refers to calculations without reference to experimental results. Such calculations are said to be from first principles or ab initio. As a step toward this goal, simulations of properties at the molecular level can be used to parametrise interaction potentials for use in the study of phase behaviour and condensed phase properties such as elastic constants, viscosities, molecular diffusion and reorientational motion with maximum specificity to real systems. Another role of ab initio computer simulation lies in its interaction... 

For a given film thickness, we can get the effective viscosity from Eq (17), then the ratio can be obtained from Eq (18). The relation between the ratios versus the film thickness is plotted in Fig. 18. Interestingly, this figure is very close to the experimental results (see, for example. Fig. 7 in Chapter 5). In the thick film regime, the ratio approaches unity. In the thin film regime, however, it increases with the diminishing film thickness. Therefore, microrotation and... 

The effective viscosity predicted with micropolar theory is in very close agreement with that found by experimental results in a previous work. This does not adequately assure that it is the only possible way to explain the traits of thin him lubrication, but it shows the roles the microstructure and microrotation of the particles will play in the lubrication process in the very thin him EHL situation. 

To compare with experimental results, the parameters corresponding to real conditions were used in our computation cases. The lubricant used in the experiment is polyglycol oil. The diameter of the steel ball is 25.4 mm, elastic modulus of the balls is 2.058 X 10 Pa, and the elastic modulus of the glass disk is 5.488 X 10 ° Pa. The circumstance temperature is 28 1 °C. The oil viscosity-pressure index is taken as 1.5 X10- Pa-. ... 

Ekambra etal. [21] compared the results from ID, 2D, and 3D simulations of a bubble column with experimental results. They obtained similar results for holdup and axial velocity, while eddy viscosity, Reynolds stresses, and energy dissipation were very different in the three simulations as shown in Figure 15.7. This example also illustrates the importance of selecting the right variables for model vahdation. A 2D model will yield good results for velocity but will predict all variables based on turbulent characteristics poorly. 

The Stokes-Einstein equation predicts that DfxITa is independent of the solvent however, for real solutions, it has long been known that the product of limiting interdiffusion coefficient for solutes and the solvent viscosity decreases with increasing solute molar volume [401]. Based upon a large number of experimental results, Wilke and Chang [437] proposed a semiempirical equation,... 

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. 

A shift in the velocity constant such as is observed in bulk esterification is the exception rather than the rule. A source of more general concern is the enormous increase in viscosity which accompanies polymerization. Both theory and experimental results indicate that this factor usually is of no importance except under the extreme conditions previously mentioned. Consequently, the velocity coefficient usually remains constant throughout the polymerization (or degradation) process. Barring certain abnormalities which enter when the velocity coefficient is sensitive to the environmental changes accompanying the polymerization process, application of the ordinary methods of chemical kinetics to polymerizations and other processes involving polymer molecules usually is permissible. 

TREATMENT OF EXPERIMENTAL RESULTS INTRINSIC VISCOSITIES OF NONIONIC POLYMERS ... 

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.

Illustration Satellite formation in capillary breakup. The distribution of drops produced upon disintegration of a thread at rest is a unique function of the viscosity ratio. Tjahjadi et al. (1992) showed through inspection of experiments and numerical simulations that up to 19 satellite drops between the two larger mother drops could be formed. The number of satellite drops decreased as the viscosity ratio was increased. In low-viscosity systems p < 0(0.1)] the breakup mechanism is self-repeating Every pinch-off results in the formation of a rounded surface and a conical one the conical surface then becomes bulbous and a neck forms near the end, which again pinches off and the process repeats (Fig. 21). There is excellent agreement between numerical simulations and the experimental results (Fig. 21). 

Fig. 24. Experimental results for drop breakup in a journal bearing flow. The Figure on the right shows repeated stretching and breakup, which is observed for low-viscosity drops (Tjahjadi and Ottino, 1991).

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)...

The model proposed by Menger et al. (Fig. 2) shows two extreme conformations, one in which the hydrocarbon chains are fully extended and another in which they are folded [18, 19], The surface of Menger s micelle is less defined than in the classical model and the surfactants that form the micelle are randomly orientated. The water can penetrate and enter in contact with the hydrophobic part of the surfactants. This model, apart from being more acceptable from an esteric point of view, gives a better explanation than the classical model of a series of experimental results such as viscosity, polarity, or kinetics. 

The correlation derived by Dombrowski and Johns covers a large range of liquid viscosity and agrees favorably with experimental results. Crapper et al.[236] further applied second order and large amplitude theories to achieve better predictions. In addition, the effects of surface tension, and viscosity of a liquid sheet as well as the radial spreading and the resultant changes in the sheet thickness on the stability have been examined by Weihs.[257]... 

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