Disjoining forces

An illustration of the effect of micelle/nanoparticle volume fraction on contact line motion is found in [57]. They used 0.1 M NaCl solution to reduce the electrical double layer thickness surrounding the NaDS micelle. At a given number concentration of micelles, decreasing the size of each micelle decreases the volume fraction greatly, since the volume of each spherical micelle varies as the third power of the radius. Thus, the addition of electrolyte effectively reduced the micellar volume fraction in the aqueous medium. The authors found that the oil droplet that would otherwise become completely detached from the solid surface, came back to reattach itself to the solid when electrolyte was present. They rationalized this finding as being caused by the inability of the weakened structural disjoining forces to counteract the attraction of the oil drop to the solid surface. 

Clarke and co-workers developed a model to calculate the thickness of the amorphous film observed in polycrystalline ceramics.37,38 The model is based on a force balance between an attractive van der Waals dispersion force that acts across the grain boundaries, any capillary forces present, and repulsive disjoining forces (such as steric forces and electrical double-layer forces) in the amorphous film.37,38 The repulsive steric force is based on the... 

Theoretical considerations by Clarke and co-workers (Clarke, 1987 Clarke etal., 1993) show that an equilibrium film thickness arises from the competition between attractive dispersion forces determined by the dielectric properties of the grains and repulsive disjoining forces which can be steric forces and/ or double-layer forces. Wetting will occur when the solid-solid boundary energy, yb, is less than that of the wetted boundary, 2y, where y is the liquid-solid interfacial energy (Clarke, 1985), provided that there is a suitable source of liquid, for example as a consequence of liquid-phase sintering at high temperatures. 

A detailed treatise on the fundamentals and applications of thin films, i.e., lamella plus smface film, is found in Ivanov (147). The two major forces involved in the lamella behavior are thermodynamic (disjoining forces) and hydro-dynamic. Further in-depth studies on the thermodynamics are presented in de Feijter (148) and Hirasaki (149) and on the hydrodynamics in Maldarelli and Jain (150). Because of the complexity of this topic, which is not within the scope of this chapter, the following discussions will be limited to the understanding that this research brought about concem-... 

Mysels was the first to suggest that micelles can contribute to the disjoining forces in foam films (14, 15). The first treatment describing this phenomena within a theoretical thermodynamic framework was by Pollard and Radke (16), who utilized density functional theory (DFT) to calculate a micellar contribution to the disjoining pressure, Omic. This method sums the force exerted on the interfaces by the micelles in the film, as follows ... 

Thickness perturbations, of a thermal or mechanical nature, may be considered to be of a wavelike nature. A symmetrical sinusoidal perturbation is shown in Figure 1.11. Here the thin part of the film is subject to two opposing forces. Thus, a capillary pressure due to the surface tension tends to suck liquid back into the thin part of the film, and a disjoining force tends to push liquid away. 

Here the limit h = °° represents a duplex pseudoemulsion film where disjoining forces are absent so = 0 and the surface tensions of the film surfaces are... 

Bridging configurations with these stable orientations of the particles in foam films are now created as another ensemble and subjected to incremental changes in an applied capillary pressure, expressed as an increased curvature of the film surfaces. At each increase in the capillary pressure, the overall surface energy is minimized and the film searched for any points where the opposite sides are touching, indicating film rupture. This procedure therefore makes no allowance for disjoining forces in the film. 

Despite these complications, it seems reasonable to suppose that the disjoining forces across aqueous films on hydrophobic solids (or those rendered hydrophobic)... 

Measurements of the disjoining forces in films prepared from 1 wt.% solutions of this perfluoroester in dodecane reveal no repnlsion until the film thickness becomes 17.5 nm. Bergeron et al. [29] suggest that this behavior represents strong evidence of positive contributions to the disjoining pressnre isotherm from steric interactions. They find that such air-dodecane-air films do not rupture even with an external capillary suction pressure of >30 kPa (which corresponds to > 0.3 bar). 

As evaporation occurs and solid surfaces are brought together, repulsive forces arising from electrostatic repulsion, hydration forces, and solvent structure resist contraction of the gel. The pore liquid will diffuse or flow from the swollen interior of the gel toward the exterior to allow the surfaces to move further apart. The disjoining forces thus produce an osmotic flow. Since these forces become important when the separation between surfaces is small, they are most likely to be important near the end of drying, when the pore diameter may approach 2 nm. 

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