Surface tension temperature coefficient

Loglio G., Ficalbi A., and Cini R. (1978) A new evaluation of the surface tension temperature coefficients for water. J. Colloid Interface Sci. 64, 198. 

Element Surface tension at the melting temperature, (Tm (mN/m) Surface tension temperature coefficient, 3(7/3 r(mN/m/K)... 

Heat capacity, molar Heat capacity at constant pressure Heat capacity at constant volume Helmholtz energy Internal energy Isothermal compressibility Joule-Thomson coefficient Pressure, osmotic Pressure coefficient Specific heat capacity Surface tension Temperature Celsius... 

Extensive tables and equations are given in ref. 1 for viscosity, surface tension, thermal conductivity, molar density, vapor pressure, and second virial coefficient as functions of temperature. 

Generalized charts are appHcable to a wide range of industrially important chemicals. Properties for which charts are available include all thermodynamic properties, eg, enthalpy, entropy, Gibbs energy and PVT data, compressibiUty factors, Hquid densities, fugacity coefficients, surface tensions, diffusivities, transport properties, and rate constants for chemical reactions. Charts and tables of compressibiHty factors vs reduced pressure and reduced temperature have been produced. Data is available in both tabular and graphical form (61—72). 

Physical characteristics Molecular weight Vapour density Specific gravity Melting point Boiling point Solubility/miscibility with water Viscosity Particle size size distribution Eoaming/emulsification characteristics Critical temperature/pressure Expansion coefficient Surface tension Joule-Thompson effect Caking properties... 

Corollary 4.—The temperature coefficient of the surface tension of a liquid is inversely proportional to the molecular surface. 

Laplace had previously deduced from his theory that the temperature coefficient of surface tension should stand in a constant ratio to the coefficient of expansion this is in many cases verified, and shows that the effect of temperature is largely to be referred to the change of density (Cantor, 1892). 

In order to take into account the effect of surface tension and micro-channel hydraulic diameter, we have applied the Eotvos number Eo = g(pL — pG)d /(y. Eig-ure 6.40 shows the dependence of the Nu/Eo on the boiling number Bo, where Nu = hd /k] is the Nusselt number, h is the heat transfer coefficient, and k] is the thermal conductivity of fluid. All fluid properties are taken at the saturation temperature. This dependence can be approximated, with a standard deviation of 18%, by the relation ... 

We are naturally interested in connecting a physical constant, like surface tension, with other physical constants, and one such connection is immediately suggested by the decrease in surface tension caused by an increase in temperature. It is only natural to inquire whether there is any parallelism between this and the most obvious change produced in a liquid by increasing temperature expansion. Measurements have shown that this is indeed the case, and that there is marked parallelism between the temperature coefficient of surface tension, i.e., the decrease caused by a rise in temperature of one degree, represented by the constant a in our first equation, and the coefficient of expansion. 

The greater the latter, the greater also is the decrease in surface tension per degree, and the ratio temperature coefficient/coefficient of expansion is approximately the same—between 2 and 3—for a very large number of liquids. Some explanation of this fact, as well as many other connections between surface tension and various physical constants will be suggested by theoretical considerations, to which we now proceed. 

Van der Waals further finds a relation between the temperature coefficient of surface tension and the molecular surface energy which is in substantial agreement with the Eotvos-Ramsay-Shields formula (see Chapter V.). He also arrives at a value for the thickness of the transition layer which is of the order of magnitude of the molecular radius, as deduced from the kinetic theory, and accounts qualitatively for the optical effects described on p. 33. Finally, it should be mentioned that Van der Waals theory leads directly to the conclusion that the existence of a transition layer at the boundary of two media reduces the surface tension, i.e., makes it smaller than it would be if the transition were abrupt—a result obtained independently by Lord Rayleigh. 

The latter three factors are only relevant for the mass transfer if the Reynolds number (Re = p vr db / q) of the liquid flow around the particle is larger than 1. The size of the gas bubbles depends on liquid properties such as temperature, surface tension and viscosity but also on the dissipated power. If we have to deal with small gas bubbles in a bubble column than we can consider the gas bubbles as rigid. The mass transfer coefficient k q is then given by the equation ... 

The relationship between surface tension and temperature leads to a series of interesting results bearing upon chemical constitution and the structure of the surface layer. As we have seen the surface tension is numerically equal to the free surface energy from which with the aid of the temperature coefficient the total surface energy may be obtained. 

In an extreme case the surface tension of diphenyl is almost double that of benzene at the same temperature and it would be expected that in a mixture of these substances the benzene would be preferentially adsorbed at the surface, and any attempt to find the mean molecular weight of the two would break down. Certain mixtures of aniline and water were found by Worley (J.G.S. ov. 260, 1914) to have positive temperature coefficients of surfiice tension as exemplified in the following data for a 3-3 °/o aniliiie... 

In these examples, as one would expect, the interfacial tensions are small and diminish as the critical solution temperature is approached. The differences between the surface tensions of the two phases are generally too small to decide whether the interfacial tension approaches zero asymptotically in all cases although such appears to be the case in the phenol water system we notice however that the temperature coefficient is very small indeed, as is the case for surface tensions of liquids near their critical point, but to a still greater degree. 

The physical properties of solvents greatly influence the choice of solvent for a particular application. The solvent should be liquid under the temperature and pressure conditions at which it is employed. Its thermodynamic properties, such as the density and vapor pressure, temperature and pressure coefficients, as well as the heat capacity and surface tension, and transport properties, such as viscosity, diffusion coefficient, and thermal conductivity, also need to be considered. Electrical, optical, and magnetic properties, such as the dipole moment, dielectric constant, refractive index, magnetic susceptibility, and electrical conductance are relevant, too. Furthermore, molecular... 

Unlike most liquids, perhaps with the exception of some liquid metals, the temperature coefficients of the surface tension of B203, Ge02, and Si02 are positive (24, 50). Some possible causes of this anomaly are (1) a preferred orientation occurring in the surface layer, and (2) dissociation or... 

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