Surface tension dispersion forces

Surface waves at an interface between two innniscible fluids involve effects due to gravity (g) and surface tension (a) forces. (In this section, o denotes surface tension and a denotes the stress tensor. The two should not be coiifiised with one another.) In a hydrodynamic approach, the interface is treated as a sharp boundary and the two bulk phases as incompressible. The Navier-Stokes equations for the two bulk phases (balance of macroscopic forces is the mgredient) along with the boundary condition at the interface (surface tension o enters here) are solved for possible hamionic oscillations of the interface of the fomi, exp [-(iu + s)t + i V-.r], where m is the frequency, is the damping coefficient, s tlie 2-d wavevector of the periodic oscillation and. ra 2-d vector parallel to the surface. For a liquid-vapour interface which we consider, away from the critical point, the vapour density is negligible compared to the liquid density and one obtains the hydrodynamic dispersion relation for surface waves + s>tf. The temi gq in the dispersion relation arises from... 

Static mixing of immiscible Hquids can provide exceUent enhancement of the interphase area for increasing mass-transfer rate. The drop size distribution is relatively narrow compared to agitated tanks. Three forces are known to influence the formation of drops in a static mixer shear stress, surface tension, and viscous stress in the dispersed phase. Dimensional analysis shows that the drop size of the dispersed phase is controUed by the Weber number. The average drop size, in a Kenics mixer is a function of Weber number We = df /a, and the ratio of dispersed to continuous-phase viscosities (Eig. 32). 

The continuum model, in which solvent is regarded as a continuum dielectric, has been used to study solvent effects for a long time [2,3]. Because the electrostatic interaction in a polar system dominates over other forces such as van der Waals interactions, solvation energies can be approximated by a reaction field due to polarization of the dielectric continuum as solvent. Other contributions such as dispersion interactions, which must be explicitly considered for nonpolar solvent systems, have usually been treated with empirical quantity such as macroscopic surface tension of solvent. 

The surface tension 7 is a measure of the work required to create unit area of surface from molecules in the bulk it is expressed in ergs per square centimeter or dynes per centimeter. The surface tension is a bulk property, not a molecular property. There appears to be some trend of y with other measures of polarity, but a lower limit of y is reached with very nonpolar liquids this limit (evidently about 15 dyn/cm) reflects the ever-present dispersion force between the molecules of liquid. 

Atomization generally refers to a process in which a bulk liquid is disintegrated into small drops or droplets by internal and/or external forces as a result of the interaction between the liquid (dispersed phase) and surrounding medium (continuous phase). The term dispersed phase represents the liquid to be atomized and the atomized drops/droplets, whereas the term continuous phase refers to the medium in which the atomization occurs or by which a liquid is atomized. The disintegration or breakup occurs when the disruptive forces exceed the liquid surface tension force. The consolidating... 

As shown by Fowkes (1968) the interfacial energy between two phases (whose surface tensions - with respect to vacuum - are y1 and y2) is subject to the resultant force field made up of components arising from attractive forces in the bulk of each phase and the forces, usually the London dispersion forces (cf. Eq. 4.2) operating accross the interface itself. Then the interfacial tension (energy) between two phases y12 s given by... 

Under noncoalescing conditions, the size of gas bubbles in gas-liquid dispersions can be obtained by balancing the surface-tension forces with those due to turbulent fluctuations, which results in (C3, H3) ... 

It is probable that numerous interfacial parameters are involved (surface tension, spontaneous curvature, Gibbs elasticity, surface forces) and differ from one system to the other, according the nature of the surfactants and of the dispersed phase. Only systematic measurements of > will allow going beyond empirics. Besides the numerous fundamental questions, it is also necessary to measure practical reason, which is predicting the emulsion lifetime. This remains a serious challenge for anyone working in the field of emulsions because of the polydisperse and complex evolution of the droplet size distribution. Finally, it is clear that the mean-field approaches adopted to measure > are acceptable as long as the droplet polydispersity remains quite low (P < 50%) and that more elaborate models are required for very polydisperse systems to account for the spatial fiuctuations in the droplet distribution. 

As is known, if one blows air bubbles in pure water, no foam is formed. On the other hand, if a detergent or protein (amphiphile) is present in the system, adsorbed surfactant molecules at the interface produce foam or soap bubble. Foam can be characterized as a coarse dispersion of a gas in a liquid, where the gas is the major phase volume. The foam, or the lamina of liquid, will tend to contract due to its surface tension, and a low surface tension would thus be expected to be a necessary requirement for good foam-forming property. Furthermore, in order to be able to stabilize the lamina, it should be able to maintain slight differences of tension in its different regions. Therefore, it is also clear that a pure liquid, which has constant surface tension, cannot meet this requirement. The stability of such foams or bubbles has been related to monomolecular film structures and stability. For instance, foam stability has been shown to be related to surface elasticity or surface viscosity, qs, besides other interfacial forces. 

Surface Active Agents Chemicals which alter the forces of surface tension between adjacent molecules generally decrease the surface tension of a fluid such as an oil, used to facilitate its dispersion throughout the water column. 

The same logic that we used to obtain the Girifalco-Good-Fowkes equation in Section 6.10 suggests that the dispersion component of the surface tension yd may be better to use than 7 itself when additional interactions besides London forces operate between the molecules. Also, it has been suggested that intermolecular spacing should be explicitly considered within the bulk phases, especially when the interaction at d = d0 is evaluated. The Hamaker approach, after all, treats matter as continuous, and at small separations the graininess of matter can make a difference in the attraction. The latter has been incorporated into one model, which results in the expression... 

An expression for the Hamaker constant analogous to Equation (67) had been proposed by Fowkes (1964) for the case when only dispersion forces determine the surface tension. The Fowkes equation... 

For An = A22, A2l2 = 0, and =0, from the viewpoint of van der Waals forces, this condition corresponds to no net interaction between particles. By using experimental criteria to identify this state of affairs, it is possible to vary the medium in a disperse system until this condition is met and then use the surface tension of the medium (via Equation (67)) to evaluate Au and, therefore 422. Going further, Equation (67) can be applied again to estimate y22 for the dispersed particles. This strategy implies that suitable values for d0 are available. 

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