Temperature dependence surface tension

TABLE 3.15 Surface Tension-Temperature Dependences of Surfactant Solutions in PTMG... 

TABLE 3.17 Surface Tension Temperature Dependences of KEP-2 Solutions in ODA... 

TABLE 3.25 Surface Tension Temperature Dependences in Systems Based on PPG-PTMG-KEP-2... 

At the critical temperature the distinction between the two phases and consequently the surface tension disappears. The absolute magnitude of the surface tension therefore depends to a great extent upon the distance from the temperature of observation to the critical point, thus we find that while the permanent gases have tensions never exceeding a few dynes per cm., in the case of liquefied metals the surface tensions may exceed a thousand. 

The dominant mechanism and transport path—or combinations thereof—depend upon material properties such as the diffusivity spectrum, surface tension, temperature, chemistry, and atmosphere. The dominant mechanism may also change as the microstructure evolves from one sintering stage to another. Sintering maps that indicate dominant kinetic mechanisms for different microstructural scales and environmental conditions are discussed in Section 16.3.5. 

The left-hand side of Eq. (8.29b) contains only quantities which are dependent on the physical quantities of the system kL depends on the surface properties between the liquid and gaseous phases, such as surface tension a depends on the degree of partitioning of gas bubbles [02]equ is constant at constant temperature and constant pressure. 

The condensate that collects on the cold surface is usually a completely homogeneous, or miscible, mixture of components. In general, the relative composition of the liquid components in the condensate is different from the composition in the vapor phase (except for an azeotropic mixture, where the condensate has the same exact molar concentration ratio as the vapor phase) [194]. The film that forms is not necessarily smooth but may show the appearance of streamers (or rivulets), waves, or droplets, depending on the particular mixture and its surface tension (which depends on the local wall temperature) [25,195,196]. If the condensate mixture is heterogeneous, or immiscible (as can occur when one component, for example, is aqueous and the other is organic), the pattern can be quite complex, looking somewhat like dropwise condensation [25,193,197]. These different condensate patterns affect the resulting fluid flow and heat transfer. 

In view of the term (jJl in Eq. (9), the Marangoni effects are hidden in the left-hand side of the interfacial momentum balance equation (8) through the surface gradients of (Ja. The thermodynamic surface tension, dJa, depends on the adsorption and temperature. The derivatives of with respect to In and InT define the Gibbs elasticity for the i-th surfactant species, Et, and the thermal analogue of the Gibbs elasticity, Ef. 

A strained, solid-like, and well-ordered liquid skin serves as an elastic covering sheet for a liquid drop or a gas bubble formation the skin is covered with locked dipoles due to charge polarization by the densely trapped core electrons. Temperature dependence of surface tension reveals the atomic cohesive energy at the surface the temperature dependence of elastic trtodulus gives the mean atomic cohesive energy of the specimen. 

The gradient model has been combined with two equations of state to successfully model the temperature dependence of the surface tension of polar and nonpolar fluids [54]. Widom and Tavan have modeled the surface tension of liquid He near the X transition with a modified van der Waals theory [55]. 

For the majority of substances the dependence of the surface tension y on the temperature can be given as ... 

The surface tension of a liquid, -y, is the force per unit length on the surface that opposes the expansion of the surface area. In the literature the surface tensions are expressed in dyn cm 1 dyn cm = 1 mN in the SI system. For the large majority of compounds the dependence of the surface tension on the temperature can be given as... 

Because the reaction takes place in the Hquid, the amount of Hquid held in the contacting vessel is important, as are the Hquid physical properties such as viscosity, density, and surface tension. These properties affect gas bubble size and therefore phase boundary area and diffusion properties for rate considerations. Chemically, the oxidation rate is also dependent on the concentration of the anthrahydroquinone, the actual oxygen concentration in the Hquid, and the system temperature (64). The oxidation reaction is also exothermic, releasing the remaining 45% of the heat of formation from the elements. Temperature can be controUed by the various options described under hydrogenation. Added heat release can result from decomposition of hydrogen peroxide or direct reaction of H2O2 and hydroquinone (HQ) at a catalytic site (eq. 19). 

Minimum Wetting Rate The minimum liquid rate required for complete wetting of a vertical surface is about 0.03 to 0.3 kg/m s for water at room temperature. The minimum rate depends on the geom-etiy and nature of the vertical surface, liquid surface tension, and mass transfer between surrounding gas and the liquid. See Ponter, et al. Int. J. Heat Mass Tran.fer 10, 349-359 [1967] Trans. Inst. Chem. Eng. [London], 45, 345—352 [1967]), Stainthorp and Allen Trans. Inst. Chem. Eng. [London], 43, 85-91 [1967]) and Watanabe, et al. ]. Chem. Eng. [Japan], 8[1], 75 [1975]). 

We expect more insight from simulations in the future, particularly in situations where these multicomponent systems show effects of coupling between the different degrees of freedom, surface tensions depending on temperature and concentration, hydrodynamic flow induced by concentration gradients in addition to thermal buoyancy. 

In a fundamental sense, the miscibility, adhesion, interfacial energies, and morphology developed are all thermodynamically interrelated in a complex way to the interaction forces between the polymers. Miscibility of a polymer blend containing two polymers depends on the mutual solubility of the polymeric components. The blend is termed compatible when the solubility parameter of the two components are close to each other and show a single-phase transition temperature. However, most polymer pairs tend to be immiscible due to differences in their viscoelastic properties, surface-tensions, and intermolecular interactions. According to the terminology, the polymer pairs are incompatible and show separate glass transitions. For many purposes, miscibility in polymer blends is neither required nor de-... 

These compounds show good solubility in acid aqueous solutions developing a sufficient depression of surface tension, but there is a strong dependence from temperature and pH value [151] (see Table 5). 

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. 

For example, for alkyl (8-16) glycoside (Plantacare 818 UP) non-ionic surfactant solution of molecular weight 390 g/mol, an increase in surfactant concentration up to 300 ppm (CMC concentration) leads to a significant decrease in surface tension. In the range 300 < C < 1,200 ppm the surface tension was almost independent of concentration. In all cases an increase in liquid temperature leads to a decrease in surface tension. This surface tension relaxation is a diffusion rate-dependent process, which typically depends on the type of surfactant, its diffusion/absorption kinetics, micellar dynamics, and bulk concentration levels. As the CMC is approached the absorption becomes independent of the bulk concentration, and the surfactant... 

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 ... 

On the meniscus surface the deviation of vapor pressure from the saturation pressure Psat depends on the surface tension a, liquid density p( gas constant R, temperature T, and radii of curvature r. When p( > -Psat(T) < (2[Pg.354]

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