Viscosity relative temperature coefficient

From [9.31], it follows that the relative temperature coefficient of viscosity = 3t / T 3T = 31nri / 3T for mixtures of chemically non-interacting liquids is described by equation ... 

The diffusion current Id depends upon several factors, such as temperature, the viscosity of the medium, the composition of the base electrolyte, the molecular or ionic state of the electro-active species, the dimensions of the capillary, and the pressure on the dropping mercury. The temperature coefficient is about 1.5-2 per cent °C 1 precise measurements of the diffusion current require temperature control to about 0.2 °C, which is generally achieved by immersing the cell in a water thermostat (preferably at 25 °C). A metal ion complex usually yields a different diffusion current from the simple (hydrated) metal ion. The drop time t depends largely upon the pressure on the dropping mercury and to a smaller extent upon the interfacial tension at the mercury-solution interface the latter is dependent upon the potential of the electrode. Fortunately t appears only as the sixth root in the Ilkovib equation, so that variation in this quantity will have a relatively small effect upon the diffusion current. The product m2/3 t1/6 is important because it permits results with different capillaries under otherwise identical conditions to be compared the ratio of the diffusion currents is simply the ratio of the m2/3 r1/6 values. 

Variations in the temperature coefficient of viscosity with solvent, which have also been presented as evidence of association in concentrated solutions (135,143), could be similarly related to differences in Ta among the solutions. When free draining behavior is a possibility, the relative viscosities in different solvents should be compared at the same value of Co f°r the mixtures (that is, at constant free volume rather than at constant temperature). In any case, it is clear that a very well planned series of experiments is necessary in order to test for the existence of additional specific effects such as association. These comments are not meant to suggest that association can not occur at moderate concentrations. Indeed, the existence of association in various forms of polymethyl methacrylate seems well established (144). The purpose is rather to advocate that less specific causes be eliminated before association is inferred from viscosity measurements alone. 

Unfortunately, there are relatively few data for transport coefficients measured under high pressure from which the coefficient (3 In rijdT)v can be calculated. Table I compares the isobaric and isochoric temperature coefficients of viscosity and binary diffusion for a number of liquids. It will be seen that the isochoric temperature coefficients are considerably smaller than those observed at constant pressure. The data of Jobling and Lawrence28 indicate that (d In rj/dT)v is more nearly proportional to (1/T2) than is (d In t]jdT)P. This observation is confirmed in an analysis of viscosity data for a number of hydrocarbons made by Simha, Eirich, and UUmann.31 The small number of substances studied and the shortness of the temperature range covered, however, do not enable us to assume a logarithmic dependence of the isochoric viscosity as a generally valid relationship. 

The relationship in this equation is relatively insensitive to temperature. Mobilities change with temperature mainly as a result of the sensitivity of the frictional resistance of the medium to temperature (the temperature coefficient of viscosity). Proportional changes in all mobilities cancel out in equation [29-1]. 

Compared with petroleum-based fluids, silicone oils show relatively small changes in viscosity as a result of temperature change (59,328). A common measure of the viscosity change with temperature is the viscosity—temperature coefficient (VTC) (341). Typical dimethylsilicone VTC is 0.6 or less. Phenylsilicones are slightly higher. Organic oils are typically 0.8 or greater. The viscosity—temperature curves follow equations 27 and 28, where a, b, and c are constants. 

Table 3.1 Comparison of selected ionic B-coefficients of viscosity, the relative self diffusion on function (1 — Z)w(E) w). and the NMR relaxation and the sign of their temperature coefficients near 25 °C... 

Geometrically, the conductivity isotherms of I and II types are similar to the % isotherms for binary liquid systems without interaction (Section 9.3.1.4). But conductivity dependencies corrected for viscosity vs. the concentration of interacted system differ from the corresponding dependencies for non-interacting systems by the presence of maximum. Also, interacting and non-interacting systems differ based on analysis of effect of the absolute and relative temperature conductivity coefficients on concentration. The relative temperature electric conductivity coefficient, (1, differs from the electric conductivity activation energy, by a constant multiplier. ... 

Above Tg, the supercooled glass-forming hquid exhibits decreasing viscosity with increasing temperature. On the one hand the glass-forming hquid of silica exhibits a relatively small and constant temperature coefficient of viscosity, e.g. decreasing from Pas... 

Supercritical fluid extraction (SFE) is a technique in which a supercritical fluid [formed when the critical temperature Tf) and critical pressure Pf) for the fluid are exceeded simultaneously] is used as an extraction solvent instead of an organic solvent. By far the most common choice of a supercritical fluid is carbon dioxide (CO2) because CO2 has a low critical temperature (re = 31.1 °C), is inexpensive, and is safe." SFE has the advantage of lower viscosity and improved diffusion coefficients relative to traditional organic solvents. Also, if supercritical CO2 is used as the extraction solvent, the solvent (CO2) can easily be removed by bringing the extract to atmospheric pressure. Supercritical CO2 itself is a very nonpolar solvent that may not have broad applicability as an extraction solvent. To overcome this problem, modifiers such as methanol can be used to increase the polarity of the SFE extraction solvent. Another problem associated with SFE using CO2 is the co-extraction of lipids and other nonpolar interferents. To overcome this problem, a combination of SFE with SPE can be used. Stolker et al." provided a review of several SFE/SPE methods described in the literature. 

Whatever the technique used, it is important to note that (i) only an equivalent viscosity can be determined, (ii) the response of a probe may be different in solvents of the same viscosity but of different chemical nature and structure, (iii) the measured equivalent viscosity often depends on the probe and on the fluorescence technique. Nevertheless, the relative variations of the diffusion coefficient resulting from an external perturbation are generally much less dependent on the technique and on the nature of the probe. Therefore, the fluorescence techniques are very valuable in monitoring changes in fluidity upon an external perturbation such as temperature, pressure and addition of compounds (e.g. cholesterol added to lipid vesicles alcohols and oil added to micellar systems). 

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