110 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS The discussion so far has suggested that there are several conditions under which one can expect to produce foams with indefinite stability. These are, however, seldom encountered because there are, in addition, several factors which can cause local fluctuations in the film thickness, resulting in force imbalances and consequent film rupture. These factors include: (1) evaporation of the liquids, (2) gas diffusion and corresponding changes in the size and size distribution of the bubbles, (3) thermal motions, (4) mechanical disturbances, (5) interactions involving the absorption of sound or electromagnetic radiation and (6) local compositional fluctuations. Foams derive stability against such local fluctuations by their ability to resist thinning and their ability to heal weak spots. Surface viscosity and surface elasticity are two primary properties which enable a foam to restore itself and resist rupture from local stressing. Gibbs' surface elasticity is defined as: e = 2d3'/d In A •- -- 2P (d3'/dP) where 3' is the surface tension of the foaming solution, A is the area per molecule of the surfactant, and I' its adsorption density, at the interface. The higher e, the higher the restoring force to a local surface concentration fluctuation and, hence, the higher will be the film stability. Mechanistically, this implies that any external perturbance which either dilates or contracts the surface film, i.e., decreases or increases the surfactant adsorption density, will be opposed by a corresponding change in surface tension thereby minimizing the effect of the perturbance. These aspects have been dealt with in some detail by Mysels (3). However, direct proof is limited owing to experimental diflSculties. A high level of surface viscosity or viscoelasticity represents another factor affecting film stability by its influence on film drainage. A higher surface viscosity implies a lower rate of liquid drainage within the lamellae and the movement of a layer of subsurface solution during the healing of a locally thinned film. Films with viscoelastic properties will, in addition, stabilize foams because film thinning can be practically stopped owing to the high restoring force accompanying a local displacement together with a reduction in drainage rates. The latter is especially significant when the shear stress, due to the drainage, falls below the yield stress of the film. Scheludko (6) postulated that the film rupture is caused by surface ripples which are generated primarily by thermal motion. He derived an expression for the critical thickness, hr, which a single film must reach before rupture can occur. Vrij (7), by light scattering experiments, found evidence of such fluctuations and modified Scheludko's equation for hr, obtaining the expressions {A ro• •/4 = ] when E v • • EH and IA 2 r hr = 0.267[-- •o / \f3' when E H • • E v. Here r o is the radius of the single film, A and 3' are the Hamaker constant of the film and its surface tension, respectively, and f is a parameter, depending on H and 3', which decreases with thickness.

ANTIFOAMS 111 The above equation yielded satisfactory values of hr for some foaming systems but there were large discrepancies for other systems, particularly in those where damping of surface ripples was expected to occur through Gibbs-Marangoni elasticity and/or surface viscosity effects. However if rapid adsorption of surfactant from the bulk was possible, the equation again became applicable. ANTIFOAMING The phenomenon of antifoaming has been thought of as an interfacial or "spreading" phenomenon in a rather restricted sense. However it generally involves the prior dispersing of the active compound, often a silicone base fluid, into fine droplet form in the foaming system in which antifoaming is desired. For these droplets to be effective, they should possess very low solubility and a positive "spreading coefficient" over the foaming solution (8,14-20). The ultimate process of antifoaming is thus thought to be the displacement of an adsorbed foaming surfactant monolayer by a more surface- active layer which does not support foaming (14-20). This simple view of antifoaming, based on interfacial energies, provides only a partial description of the phenomenon but forms an excellent basis for initial selection of antifoaming compounds. It cannot, however, explain the relative effectiveness of various antifoams in different foaming systems, nor the marked improvement in the antifoaming performance attending the incorporation of small amounts of colloid-size hydrophobic particles in the antifoam, as is now commercial practice (8-10). In other words, much concerning the mechanisms of antifoaming is imperfectly understood. This situation results from the restricted view of antifoaming as essentially an interfacial phenomenon involving the liquid/gas (L/G) interface. Recently, however, we have emphasized (8-10) that the process involves not only spontaneous spreading of antifoam but also the prior step of bringing the antifoam droplet to the bubble surface in a process which can be likened to heterocoagulation. The interfacial forces governing the spreading behavior are all short-range and therefore are not expected ,to participate in the process unless the droplet and bubble have approached each other to within small (Angstrom) distances. The transport of a droplet to such a distance from the bubble is influenced by other forces in the system such as hydrodynamic, electrical and van der Waals' interactions. The latter interactions can be influenced by the fact that antifoam droplets as well as the foam bubble can adsorb foaming surfactant molecules and acquire a surface charge. The complex process of antifoaming using silicone oil-based antifoams in aqueous systems evidently involves the following steps: (1) dispersion of antifoam in the foaming solution, (2) transport of antifoam droplet from bulk to the bubble interface (heterocoagulation), (3) entry of the droplet into the gas/liquid interface, (4) spreading and (5) bubble rupture. Up until recently the details of the second step have never been considered and also the last two steps were considered synonymous inasmuch as spreading of the (appropriate) antifoam was felt automatically to lead to bubble rupture. We now have evidence that even though spreading is necessary for antifoaming, it does not necessarily cause rupture. Studies on the change in sensitivity of solutions of ionic surfactants to defoaming by standard silicone antifoams, carried out as a function of the concentration of the