Eyring viscosity relationship

As pointed out by Doolittle, the relationship between the viscosity of liquids and their free volume remained for a long time only an intuitive hypothesis though it described quite well numerous experimental results. A theoretical approach to the solution of the problem of the relationship between the viscosity of liquid and its free volume was generalized for the first time by Eyring [85] in terms of the absolute reaction rates theory. The formulas obtained by Eyring pointed to a qualitative relationship between viscosity and the ratio of the volume occupied by liquid molecules C to the volume occupied by holes through which molecules jump to the neighboring position ... 

The first application of reaction rate theory to transport phenomena was given by Eyring, 1936 (29). He assumed the liquid to have a lattice configuration and considered both diffusion and viscosity as activated rate controlled processes, taking place by molecular jumps from one position to another. When the viscosity is independent of the applied forces, i.e. Newtonian flow, Eyring derived the following relationships ... 

Temperature dependence of the fluorescence quantum yields and fluorescence lifetimes of frans-4,4 -di-fert-butylstilbene in n-hexane and n-tetradecane allowed to define the index of refraction dependence of the radiative rate constants, kf= (3.9 — 1.8) X 10 s, and fluorescence lifetime [78]. This relationship was used to calculate torsional relaxation rate constants ktp> for traws-4,4 -dimethyl- and frans-4,4 -di-ferf-butylstilbene in the n-alkane solvent series. It was found that activation parameters for ktp, based on Eyring s transition state theory, adhered to the medium-enhanced thermodynamic barrier model relationship, AHtp = AHt + aEr, and to the isokinetic relationship. The isokinetic relationship between the activation parameters for the parent frans-stilbene led to an isokinetic temperature of P = 600K and brings it into agreement with the isokinetic temperature for activation parameters based on estimated microviscosities, qp, experienced by stilbene in its torsional motion. The authors concluded that only microviscosities raflier than shear viscosities, q, can be employed in the expression ktp = ktSq — b, when a = b. These data clearly indicated the important role of the media dynamics in the stilbene cis-trans photoisomerization. 

The viscosity of the melt, which was related to the diffusion constant, was also estimated by using the Eyring relationship. It was found that the calculated viscosity agreed well with experimental data which were obtained by using an oscillating cup method except at temperatures ranging from 1550 to 1750K. 

The basic concept of the EHL model is described in [1], i. e. the non-Newtonian Ree-Eyring fluid model according to Ai cr al. [7] and the implementation of the 2D Reynolds-, elasticity- and load equation according to Venner [8]. The lubricant properties are the viscosity-pressure relationship as proposed by Mihailidis et al. [9] and the density-pressure relationship as proposed by Dowson and Higginson. The non-dimensional parameters in this work can be seen in table 1. 

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