Eotvos’ constant

It is probably more than a coincidence that this value for k is of the same order of magnitude as the observed values of the Eotvos constant n, the number of molecules in the thickness of the surface, being unknown, though certainly small, a closer comparison is not possible. 

Thus additional possibilities of motion in the surface molecules, capable of affecting F, may increase the Eotvos constant. In the next section we shall see evidence that such additional degrees of freedom probably come into play in the case of the triglycerides. 

Thus, besides association, the orientation and shape of the surface molecules, their number of degrees of freedom for thermal motion, and their mutual attractions and details of their shape, size, and packing, and also the number of molecules in the thickness of the surface layer, may all affect the value of the Eotvos constant. It is not surprising that experience has already shown that this constant varies enormously, and that it cannot be used for drawing trustworthy conclusions as to the degree of molecular association. 

Freund found the Eotvos constant abnormally high for high molecular weight oils it increased regularly with the mol. wt. and could be calculated from this. For liquid helium the constant is abnormally small, 1464 the value of for liquid helium is a Unear function of temperature down to... 

Values closer to 2-12 are found if allowance is made for dissociation in calculating M. This would indicate that no change in association is produced by the presence of the electrolyte in the water. The Eotvos constants of binary mixtures seem to depend on the concentration and temperature. The effect of temperature is either (i) normal, when d[a MvY>mdt is about 2-1, or (ii) abnormal, when this coefficient is less than 2-1 ljut increases with temperature from these results, conclusions have been drawn as to the molecular weights of dissolved substances. Light (including ultraviolet) has no influence on the surface tension of solutions. ... 

Eotvos constant—contd. metals, 161 for fused salts, 161 for high molecular weight substances, 160 in homologous series, 160 for liquid helium, 160 for normal substances, 160, 162 for oils, 160... 

If the excess components of y and dueto orientational entropy, are, respectively, 61 and i.e., excess surface entropy over that corresponding to a normal Eotvos constant [17]—Equation 1 becomes... 

I have registered his Nhq values (for 20 C, 1 atm) on the 760 mm Hg horizontal in Fig. 92. Several values cluster on each side of the R-line, and those for benzene and toluene indicate that the JVhq vs Phq plot would be concave upward. The value for ethyl bromide, Nhci = 0.102, gives a line over on the right, near the PhOMe line (see later). Hamai (1935) " looked for a correlation between the solubility of HCl in four halogeno-carbon compounds and the polarity, as measured by the dielectric constant, molecular symmetry, electric moment, and Eotvos constant (see Table 20). 

A very remarkable theorem respecting the constant B was found empirically by Eotvos (6) (1886). Let a mol of a liquid... 

We have so far succeeded in establishing connections between surface tension and a number of physical properties, but have not yet found a relation between the former and any chemical constant. A very simple and general relation of this kind was first pointed out by the Hungarian physicist Eotvos and confirmed experimentally, for a large number of liquids, by Ramsay and Shields. If M is the molecular weight of a liquid and p its density, then... 

MECHMOD A utility program written by Turanyi, T. (Eotvos University, Budapest, Hungary) that manipulates reaction mechanisms to convert rate parameters from one unit to another, to calculate reverse rate parameters from the forward rate constant parameters and thermodynamic data, or to systematically eliminate select species from the mechanism. Thermodynamic data can be printed at the beginning of the mechanism, and the room-temperature heat of formation and entropy data may be modified in the NASA polynomials. MECHMOD requires the usage of either CHEMK1N-TT or CHEMKIN-III software. Details of the software may be obtained at either of two websites http //www.chem.leeds.ac.uk/Combustion/Combustion.html or http //garfield. chem.elte.hu/Combustion/Combustion. html. 

Equation (12-46) implies that the Eotvos number cannot exceed a value of about 16. Since the spherical-cap regime requires Eo > 40 (see Fig. 2.5), stability considerations explain why drops falling in gases and drops in many liquid-liquid systems never attain the spherical-cap regime. Moreover, since We = 4Eo/3Cd and is nearly constant for large drops in air, it is also possible to... 

Eotvos having previously given a rather less accurate equation in which the constant 6° was not subtracted from the critical temperature. Mv is the molecular volume and Tc the critical temperature. 

Yet another cause for deviation from Eotvos s law may be found in Bom and Courant s theory1 of the motions of the molecules of liquids, which follows the lines of Debye s theory of the specific heat of solids. Assuming three degrees of freedom for the motions of the molecules, they obtained good agreement with experiment for several liquids for which the constant is about 2-1. If the number of degrees of freedom is n, the constant is altered on their theory in the ratio (n/3). ... 

The accuracy of (5) is within the limits of experimental error for many liquids. As the linear relation does not usually hold near the critical temperature, (6) is less accurate, though it is preferable theoretically as containing one less arbitrary constant. Refinements of the linear equation have usually been made along one of two lines the first is to follow Eotvos s plan of introducing the twro-thirds power of the molecular volume, as in equation (1) of Ramsay and Shields, or Katayama s modification2... 

For capillary rise the significant forces are gravit) and surface tension of the fluid. Therefore, from Table 13.1 we see that the important force ratio is gpL lcr, the Eotvos number. Here in the gravity force indicates three perpendicular directions. The L in the surface tension force cancels one of them, but the remaining refers not to one dimension squared, but rather to two perpendicular dimensions. Setting this force ratio equal to a constant and solving for one of these dimensions] we find... 

Holdup volume fraction liquid 0.05-0.25. Static liquid holdup is constant for low Eotvos number, o < 4 (Eo = density liquid X gravitational constant X particle diameter squared/liquid-gas surface tension). Liquid holdup increases with Eo for Eo > 4. Dynamic liquid holdup increases with liquid flow-rate but is independent of gas flowrate. 

The surface tension of many liquids decreases, almost linearly, with increasing temperature. In other words, the quantity dy/dT is negative and almost constant for most pure materials. A well-known relation is the Eotvos rule... 

The model species, total mass, momentum, and energy continuity equations are similar to those presented in Section 13.7 on fluidized bed reactors. Constant values of the gas and liquid phase densities, viscosities, and diffusivities were assumed, as well as constant values of the interphase mass transfer coefficient and the reaction rate coefficient. The interphase momentum transfer was modelled in terms of the Eotvos number as in Clift et al. [1978]. The Reynolds-Averaged Navier-Stokes approach was taken and a standard Computational Fluid Dynamics solver was used. In the continuous liquid phase, turbulence, that is, fluctuations in the flow field at the micro-scale, was accounted for using a standard single phase k-e model (see Chapter 12). Its applicability has been considered in detail by Sokolichin and Eigenberger [1999]. No turbulence model was used for the dispersed gas phase. Meso-scale fluctuations around the statistically stationary state occur and were explicitly calculated. This requires a transient simulation and sufficiently fine spatial and temporal grids. 

The Eotvos law links surface area, surface energy crand temperature T, with two constants critical temperature Tc and constant k ... 

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