Surface Tension Model

Several attempts were made to describe the course of the dependency of surface tension on composition in the binary and ternary systems. 

Grjotheim et al. (1972) used for calculation of the surface tension of binary mixtures three different modifications of the Guggenheim s equation (6.34). 

In this equation the molar fractions were replaced by the volume fractions 

Vi are the molar volumes of pure components, and the average surface area per molecule, A, is given by the equation 

The reason for introducing Eqs. (6.58) and (6.61) is that in Eq. (6.56) for the two components equal molar volumes and equal surface areas per molecule were originally assumed. However, these two assumptions are not valid in molten salt mixtures as can be seen from the molar volume data. 

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The solubility characteristics of surfactants (in water) is one of the most studied phenomena. Even though the molecular structures of surfactants are rather simple, their solubility in water is rather complex as compared to other amphiphiles such as long-chain alcohols, etc., in that it is dependent on the alkyl group. This is easily seen since the alkyl groups will behave mostly as alkanes. The hydrophobic alkyl part exhibits solubility in water, which has been related to a surface tension model of the cavity (see Appendix B). However, it is found additionally that the solubility... 

Surface Tension Simulation in Diffuse Interface Method Similar to surface tension modeling in the VOF method, both CSF and CSS methods are applicable, with minor adjustments, to the diffuse interface method. The CSF method is as follows ... 

Accurate surface tension modeling is also a key component of many simulations but is difficult as a surface force must be represented on a volumetric grid. In addition, the wall contact angle plays a very important role in many cases and this is often a highly uncertain parameter. 

Theories Based on Multi-Component Surface Tension Models. 71... 

In this section a brief introduction to the concept of surface tension and surface tension models for the determination of surface tension of solids is given. The surface tension (y) is the tangential stress (mNm ) in the surface layer and is a direct measure of the intermolecular forces at the surface [92]. A munber of empirical and semi empirical methods, based... 

Booth and coworkers also studied the surface tension of binary systems (dicar-boxylic acids (oxalic, malonic, succinic, glutaric, and adipic acids) and ammonium sulfate) both experimentally (at 21 °C) and using modeling to determine whether additive or thermodynamic surface tension models agreed better with experimental data [190]. Following the methodology of Topping et al. [143] they found that the LiLu model best predicted binary systems. 

Li ZB, Li YG, Lu JF (1999) Surface tension model for concentrated electrolyte aqueous solutions by the Pitzer equation. Ind Eng Chem Res 38 1133-1139... 

Table 3.1 Fitting Parameters for the Surface Tension Model... 

Kondo, M., Koshizuka, S., Suzuki, K., Taldmoto, M. (2007). Surface tension model using inter-particle force in particle method. ASME Coirference Proceedings, 2007,93-98. 

Baltussen MW, KuipersJAM, Deen NG A critical comparison of surface tension models for the volume of fluid method, Chem Eng Sd 109 65—74, 2014. 

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