Surface tension variation with temperature

At the critical temperature, Tc, and critical pressure, Pc, a liquid and its vapor are identical, and the surface tension, y, and total surface energy, as in the case of the energy of vaporization, must be zero (Birdi, 1997). At temperatures below the boiling point, which is 2/3 Tc, the total surface energy and the energy of evaporation are nearly constant. The variation in surface tension, y, with temperature is given in Figure A.l for different liquids. 

The variation of surface tension with temperature will not be discussed here, except to remark that surface tension decreases with temperature and that the rate of decrease is large enough to require that the temperature of measurement of surface tension be kept constant, within the order of 0.1°C, by means of a thermostat. 

It is important to note that, for an overwhelming majority of fluids, surface tension decreases with temperature, and consequently, the inequality 0 in a certain interval of the temperature variation will also be described). 

Figure 12.3 Variation of surface tension 7 and total surface energy us with temperature for CCI4. Both 7 and us become zero at the critical temperature. Reprinted with permission from A. K. Adamson and A. P. Gast, Physical Chemistry of Surfaces. by John Wiley and Sons, Inc., 1977.

The last boundary condition on the velocity comes from the balance between the change in surface tension due to temperature variations along the surface with the tractive force induced at the free surface. Here, as in Section 10.5, the rate of change of surface tension is taken to be linear with temperature... 

During the 1870 s, Carlo Marangoni, who was apparently aware of Carra-dori s work but not of Thompson s, formulated a rather complete theory of surface tension driven flow (M2, M3). He noted that flow could result from surface tension variations as they are caused by differences in temperature and superficial concentration, and that, conversely, variations in temperature and concentration could be induced by an imposed surface flow. Marangoni ascribed several new rheological properties to the surface (notably surface viscosity, surface elasticity, and even surface plasticity), while remarking that perhaps some of these properties could be associated only with surface contamination. Most present-day authors ascribe the first explanation of surface tension driven flow to Marangoni, and term such flow a Maragoni effect. ... 

Two points stand out when Tables 59.1 and 59.2 are compared the temperature coefficients for interfacial tension are lower than those for surface tension, and there is no correlation between the interfacial tension of a polymer pair and the difference in their surface tensions. The former effect arises because the variation with temperature is a density effect. 

Typical values for the surface tension of liquids are around 70 mN.m" for polar solvents such as water and aqueous solutions, while for non-polar organic solvents such as hydrocarbons, they range between 20 and 30 mN.m" and are extremely high, in the range 100-2800 mN.m , for liquid or molten metals and to a lesser extent for molten salts, 100-300 mN.m (see Table 20.5). The addition of surfactants can decrease the surface tension of aqueous solutions. The surface tension decreases with a temperature increase, and its temperature variation can be described by the following simple equation ... 

Sugden, S. (1924), The variation of surface tension. VI. The variation of surface tension with temperature and some related functions . J. Chem. Soc., Vol. 125, p. 32. 

Fig. III-2. Variation of surface tension and total surface energy of CCU with temperature. (Data from Ref. 2.)...

The surface tension of an aqueous solution varies with the concentration of solute according to the equation y = 72 - 350C (provided that C is less than 0.05Af). Calculate the value of the constant k for the variation of surface excess of solute with concentration, where k is defined by the equation V = kC. The temperature is 25°C. 

In Fig. 2.58 (Hetsroni et al. 2001b) the dependencies of the surface tension of the various surfactants a divided on the surface tension of water ow are shown. One can see that beginning from some particular value of surfactant concentration (which depends on the kind of surfactant), the value of the relative surface tension almost does not change with further increase in the surfactant concentration. It should be emphasized that the variation of the surface tension as a function of the solution concentration shows the same behavior for anionic, non-ionic, and cationic surfactants at various temperatures. 

Brown (1967) noted that a vapor bubble in a temperature gradient is subjected to a variation of surface tension which tends to move the interfacial liquid film. This motion, in turn, drags with it adjacent warm liquid so as to produce a net flow around the bubble from the hot to the cold region, which is released as a jet in the wake of the bubble (Fig. 4.10). Brown suggested that this mechanism, called thermocapillarity, can transfer a considerable fraction of the heat flux, and it appears to explain a number of observations about the bubble boundary layer, including the fact that the mean temperature in the boundary layer is lower than saturation (Jiji and Clark, 1964). 

Experiments [43] with very high flash point fuels (JP, kerosene, Diesel, etc.) revealed that the flame propagation occurred in an unusual manner and a much slower rate. In this situation, at ambient conditions, any possible amount of fuel vapor above the liquid surface creates a gaseous mixture well outside the fuel s flammability limits. What was discovered [44, 45] was that for these fuels the flame will propagate due to the fact that the liquid surface under the ignition source is raised to a local temperature that is higher than the cool ambient temperature ahead of the initiated flame. Experimental observations revealed [45] that this surface temperature variation from behind the flame front to the cool region ahead caused a variation in the surface tension... 

Fig. 2.13. Variation of the surface tension of water with temperature.

It can be used under very high pressure and temperatures. Oil reservoirs are found typically at 100°C and 300 atm pressure. The surface tension of such systems can be conveniently studied by using high pressure and temperature cells with optical clear windows (sapphire windows 1 cm thick up to 2000 atm). For example, yof inorganic salts at high temperatures (ca. 1000°C) can be measured using this method. The variation in surface tension can be studied as a function of various parameters (temperature and pressure additives [gas, etc.]). 

All natural processes are found to be dependent on the temperature and pressure effects on any system under consideration. For example, oil reservoirs are generally found under high temperature (ca. 100°C) and pressure (over 200 atm). Actually, humans are aware of the great variations in both temperature (sun) and pressure (earthquakes) with which natural phenomena surround the earth. Even the surface of the earth itself comprises temperature variation of -50°C to +50°C. On the other hand, the center mantle of the earth increases in temperature and pressure as one goes from the surface to the center of the earth (about 5000 km). Surface tension is related to the internal forces in the liquid (surface), and one must thus expect it to bear a relationship to internal energy. Further, it is found that surface tension always decreases with increasing temperature. 

---