between two deformed droplets, calculated using the actual The effect of different factors (drop radius, interfacial tension, and model shapes, are in good agreement. This enables one Hamaker constant, electrolyte, micellar concentrations, etc.) on to perform easily (by using the simple model shape) extenthe interaction energy of emulsion droplets is studied theoretically. sive numerical calculations in order to reveal the effect of It is demonstrated that the deformation of the colliding droplets different factors on the behavior of an emulsion consisting considerably affects the interaction energy. The contributions of of deformable droplets. Such numerical studies can be carthe electrostatic, van der Waals, depletion, steric, and oscillatory ried out for large macroemulsion droplets (above 1 mm) as surface forces, as well as of the surface stretching and bending well as for small Brownian miniemulsion droplets (below energies, are estimated and discussed. The calculations show that 1 mm).
the droplets interact as nondeformed spheres when the attractive interactions are weak. At stronger attractions an equilibrium plane
There is some experimental evidence that the deformabilparallel film is formed between the droplets, corresponding to minity may affect the overall equilibrium properties of emulimum interaction energy of the system. For droplets in concensions. By using optical microscopy and contact angle meatrated micellar surfactant solutions the oscillatory surface forces surements, Aronson and Princen (6) observed that single become operative and one can observe several minima of the endrops coexist with aggregates of droplets. In fact, the aggreergy surface, each corresponding to a metastable state with a difgates are flocculated droplets separated by thin liquid films. ferent number of micellar layers inside the film formed between It has been established that the three-phase contact angle the droplets. The present theoretical analysis can find applications (and the film area) increase with increasing the electrolyte in predicting the behavior and stability of miniemulsions (conconcentration and decreasing the temperature in these expertaining micrometer and submicrometer droplets), as well as in iments. Hofman and Stein (7) studied experimentally the interpretation of data obtained by light scattering, phase behavior, flocculation of emulsions containing very small (of micromrheological and osmotic pressure measurements, etc. ᭧ 1995 Academic Press, Inc.
eter size) droplets and have explained some of the results Key Words: emulsion, flocculation in; thin liquid films; radial with the possible droplet deformation at certain conditions distribution function, in miniemulsions; depletion interaction; os-(high ionic strength and low interfacial tension). A similar cillatory surface force; bending energy, in emulsions; interaction idea was proposed to explain some experimental results obenergy, between emulsion drops.
tained with microemulsions (8).
A method for producing miniemulsions consisting of fairly monodisperse droplets was recently proposed (9).