ANTIFOAMS 113 interaction in this case is between dissimilar bodies and is therefore more complicated. Details of the calculation allowing the construction of energy/distance plots have been presented elsewhere (8) only the main conclusions will be given here. It was shown that, depending upon the test solution conditions, as an antifoam droplet approaches a foam bubble surface, it can experience either an attractive or repulsive interaction and thereby the antifoaming process will be directly influenced. In particular, in systems containing ionic foaming surfactants the repulsive interactions are important. As pointed out before, the repulsive interaction depends not only on the nature of the surfactants but also on their concentration. It is related (8) to the potential and distance of the particle (subscript 1) and bubble (subscript 2) by the expression EE = 2.23 7K 10 -•ø R•(•-•24-•'•2)( 2P (14-exp(-- KA)) ) ' (1 4- p2)In (1 -- exp(-- KA)) 4- ln(1 -- exp(-- 2KA)) where the symbols have the same significance as in the previous expression for EE and P is the zeta potential ratio (•'•/•'2). The role of van der Waals' interactions is more complex and is described in detail in the aforementioned publication (8). In short, these interactions will favor antifoaming if the Hamaker constants of the surfactant (As), antifoam droplet (ap) medium (A,,) are such that A,, • As and Ap, or A m • A5 and Ap. However if A5 A m • Ap, or Ap • A m • As, then one expects an overall repulsive van der Waals' interaction which would diminish the foam inhibition. Having considered some of the factors governing transport of the antifoam droplet to the bubble interface, it is now appropriate to consider the forces involved during entry into the interface, spreading and rupture. The first two of these are governed ultimately by short range, interfacial energies, as can be inferred from the definition of the so-called "entering" coefficient (e) of the droplet into the interface and its "spreading" coefficient (s) along the interface (19): e=7w--70 4-7ow S=7w--70--7ow where 3/w is the surface tension of the foaming solution, 3/0 is that of the antifoam liquid equilibrated with this solution, and 3/ow is the interfacial tension between the two equilibrated liquids. For effective antifoaming to occur it is a prerequisite that the antifoam liquid spread spontaneously at the bubble interface, i.e., that s be positive. If s is positive, e must also be positive, i.e., entry of the droplet into the interface is automatically facilitated. A positive spreading coefficient is favored by a high 3/w value and low values of 3/0 and 3/ow. The first and third terms, viz., 3/w and 3/ow, are both reduced by the presence of (foaming) surfactant it is the relative effect of the surfactant which is important. It is, however, a matter of experience that the spreading of a liquid tends to decrease as the surface tension of the aqueous subphase is decreased. This fact is in line with our previous statements concerning the requirements of antifoams, which, in fact, become more rigorous the lower the surface tension of the foaming solution. One of the

114 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS principle attributes of silicone liquids is their ability to spread on virtually all aqueous surfactant solutions this ability is directly connected with their low surface tension ('¾o• 20 dynes/cm). We come now to the last step involved in the antifoaming process, i.e., bubble rupture. In silicone oil-based antifoams it has been clearly shown that the presence of hydrophobic filler particles markedly improves the defoaming ability of the antifoam fluid. It is now believed, with some experimental supporting evidence, that these finely divided hydrophobic filler particles directly participate in the process of bubble rupture. Thus, in the five listed steps of antifoaming, the first four are primarily affected by the properties of the antifoam fluid, but the final step involves the filler in the following way: once the antifoam droplet enters the bubble and spreads, the AIR III!1111111111 SOLUTION /•.•-- HYDROPHOBIC SILICA PARTICLE 3 SOLUTION '• IIIII SOLUTION AIR SOLUTION IIII SOLVATED SILICA PARTICLE RUPTURE Figure 3. Schematic representation of the mechanism of bubble film rupture by hydrophobic silica particles.