Pair interaction energy between deformable drops and bubbles

Abstract

The potential energy of interaction between two deformed particles, having the shape of spherical segments and separated by a planar film, is considered. An exact explicit expression for the van der Waals interaction energy between such deformed particles of arbitrary size and deformation is derived by using the microscopic approach of Hamaker [Physica 4, 1058 (1937)]. By means of Derjaguin’s approximation [Kolloid Z. 69, 155 (1934)] explicit expressions for the electrostatic, steric, depletion, and other types of interaction are derived. The relative contributions of the interaction across the planar film and between the spherical surfaces surrounding the film, are analyzed for different cases. The surface deformation energy caused by an increase of the interfacial area during the particle deformation is also considered. The implication of the obtained formulas for treatment of the particle interactions in some particular systems like emulsions,microemulsions, and vesicles, as well as for the adhesion of such particles to a solid wall is briefly discussed.