Interfacial tension prediction

The matter of rfi is of some importance to the estimation of solid interfacial tensions and has yet to be resolved. On one hand, it has been shown that the Giralfco and Good model carries the implication of rr being generally significant [10], and on the other hand, both Good [193] and Fowkes [145] propose equations that predict... 

The use of the harmonic mean often leads to better predictions of interfacial tensions between polymers and better contact angles between liquids and polymer solids, but the criterion for maximization of the work of adhesion is the same as... 

The presence of calcium and magnesium ions increases the adsorption of the surfactants at the water-air interface and leads to a corresponding lowering of the surface tension at the CMC as shown by the data in Table 4. A C16 branched AOS gives a lower surface tension than a linear C16 AOS this too is in agreement with other model studies and theoretical predictions [42, and Sec. 2 on interfacial tension). 

It is advantageous with a new drug substance to be able to estimate what its solubility will be prior to carrying out dissolution experiments. There are several systems of solubility prediction, most notably those published by Amidon and Yalkowsky [14-16] in the 1970s. Their equation for solubility of p-aminobenzo-ates in polar and mixed solvents is a simplified two-dimensional analog of the Scatchard-Hildebrand equation and is based on the product of the interfacial tension and the molecular surface area of the hydrocarbon portion of a molecule. 

The Gibbs equation relates the extent of adsorption at an interface (reversible equilibrium) to the change in interfacial tension qualitatively, Eq. (4.3) predicts that a substance which reduces the surface (interfacial) tension [(Sy/8 In aj) < 0] will be adsorbed at the surface (interface). Electrolytes have the tendency to increase (slightly) y, but most organic molecules, especially surface active substances (long chain fatty acids, detergents, surfactants) decrease the surface tension (Fig. 4.1). Amphi-pathic molecules (which contain hydrophobic and hydrophilic groups) become oriented at the interface. 

Quantities useful for predicting phase continuity and inversion in a stirred, sheared, or mechanically blended two-phased system include the viscosities of phases 1 and 2, and and the volume fractions of phases 1 and 2, and ij. (Note These are phase characteristics, not necessarily polymer characteristics.) A theory was developed predicated on the assumption that the phase with the lower viscosity or higher volume fraction will tend to be the continuous phase and vice versa (23,27). An idealized line or region of dual phase continuity must be crossed if phase inversion occurs. Omitted from this theory are interfacial tension and shear rate. Actually, low shear rates are implicitly assumed. 

The interfacial tension yAB between two liquids with surface tension yA and yB is of interest in such systems as emulsions and wetting (Adamson and Gast, 1997 Chattoraj and Birdi, 1984 Somasundaran, 2006). An empirical relation was suggested (Antonow s rule), by which one can predict the surface tension yAB ... 

Microemulsions are thermodynamically stable mixtures. The interfacial tension is almost zero. The size of drops is very small, and this makes the microemulsions look clear. It has been suggested that microemulsion may consists of bicontinuous structures, which sounds more plausible in these four-component microemulsion systems. It has also been suggested that microemulsion may be compared to swollen micelles (i.e., if one solubilizes oil in micelles). In such isotropic mixtures, short-range order exists between droplets. As found from extensive experiments, not all mixtures of water-oil-surfactant-cosurfactant produce a microemulsion. This has led to studies that have attempted to predict the molecular relationship. 

The slow formation of a drop at a submerged circular orifice or nozzle will result in a drop size, predicted by equations for determining interfacial tension by the drop-weight method. At the instant a slowly forming drop breaks away from a nozzle, the force balance may be written... 

While the shape of a large fluid particle cannot be predicted accurately from first principles, the terminal velocity can be obtained from the observed shape. Interfacial tension forces are ignored. Flow is considered only in the neighborhood of the nose, where the external fluid is assumed to flow as an inviscid... 

The preceding discussion dealt with membrane-bearing systems. In the case of acellular systems, i.e. with crude cell extracts or purifled enzymes, the validity of logKow as a criterion for biocompatibility is questionable. As a result, other parameters, such as interfacial tension, have been suggested to predict the effect of solvents on enzyme stability [30]. 

Figure 3.6 shows trajectories for several values of the interfacial tension o0 in the metastable region that are predicted by using a NG model [2], For a0 < 0.01 mN/m, all the trajectories are equivalent (i.e., the value of a0 has no effect on the phase separation process) however, if a0 is higher than 0.1 mN/m, then spinodal decomposition is rapidly attained. For a0 = 0.4 mN/m practically no phase separation occurs by the NG mechanism, and demixing proceeds by SD. 

Phase separation through NG mechanism cannot be observed for polymer-polymer blend systems that show interfacial tension lying in the range 0.5-11 mN/m. In addition, they predicted that a secondary phase separation could take place inside dispersed rubber particles in the case when the average composition of dispersed domains lies in the unstable region at the end of the phase separation [2], They were not able to observe a phase separation inside dispersed domains with TEM micrographs however, they concluded that there are two phases inside the dispersed domains by the fact that the glass transition temperature of the rubber-... 

Figure 3.6 Trajectories in the metastable region predicted by using a nucleation growth model for several values of the interfacial tension

The flow phenomena in TBR are not easy to predict, because of the large number of variables such a bed porosity, size and shape of the catalyst, viscosity, density, interfacial tension, flowrates, and reactor dimensions. 

This reversible and ideal relationship predicts that the more effective depressants of interfacial tension tend to accumulate in the interface to the exclusion of others. Actually, in many cases the amount of material concentrated at the interface is greater than would be predicted by the Gibbs equation, and the system is not reversible or only sluggishly so. 

Recent theoretical studies indicate that thermal fluctuation of a liquid/ liquid interface plays important roles in chemical/physical properties of the surface [34-39], Thermal fluctuation of a liquid surface is characterized by the wavelength of a capillary wave (A). For a macroscopic flat liquid/liquid interface with the total length of the interface of /, capillary waves with various A < / are allowed, while in the case of a droplet, A should be smaller than 2nr (Figure 1) [40], Therefore, surface phenomena should depend on the droplet size. Besides, a pressure (AP) or chemical potential difference (An) between the droplet and surrounding solution phase increases with decreasing r as predicted by the Young-Laplace equation AP = 2y/r, where y is an interfacial tension [33], These discussions indicate clearly that characteristic behavior of chemical/physical processes in droplet/solution systems is elucidated only by direct measurements of individual droplets. 

It is now time to reconsider the simple case of a two-phase system that contains two different types of molecules. If molecules of phase a are polar and molecules of phase [3 are nonpolar, the introduction of amphiphilic molecules that are capable of associating with either one of the two bulk phase molecules will result in an accumulation at the interface. Hence, these molecules will have a true excess concentration at the interface. Figure D3.5.4 illustrates that once surfactants adsorb at interfaces, the concentration within the interface may be larger than in any of the other phases. In order to predict the influence that these adsorbed surfactant molecules can have on the properties of the bulk system, interfacial chemists must be able to quantify the number of molecules that are adsorbed at the interface, that is, they must be able to measure the interfacial coverage. Unfortunately, it is extremely difficult, if not impossible, to directly measure the concentration of surface-active molecules adsorbed in a two-dimensional plane. This is where the thermodynamic concepts discussed earlier prove to be very useful, because a relationship between the interfacial coverage (G) and the interfacial tension (y) can be derived. 

The wetting theory is applicable to liquid bioadhesive systems. According to this theory, the ability of a bioadhesive material to spread and determine an intimate contact with the biological substrate plays a major role in bond formation [44], This theory uses interfacial tensions to predict spreading and, in turn, bioadhesion. In the past, the surface energy of both bioadhesive materials and tissues or mucus have been extensively studied to predict the bioadhesive performance [47-49]. 

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