Van der Waals Interaction between Two Truncated Spheres Covered by a Uniform Layer (Deformed Drops, Vesicles, or Bubbles)

Abstract

In this paper, we derive explicit expressions for the van der Waals interaction energy and force between two truncated spheres covered by a thin layer of uniform thickness. These expressions can be used for description of the interactions in dispersions of deformable particles (emulsions, vesicle suspensions, and foams). As an illustration of the applicability of these formulas to real systems, we consider the interaction between micrometer-sized oil drops, covered by a protein adsorption layer, in oil-in-water emulsions. The Hamaker constants for the interactions between protein, oil, and water are calculated from literature data. The equilibrium radius and thickness of the liquid film, which forms upon the collision of two emulsion drops, are determined as functions of the drop size and electrolyte concentration. From the parameters of the equilibrium films, we calculate the total interaction energy between the drops. The numerical results show that both factors, the presence of the protein layer and the drop deformation, have a significant effect on the pair interaction energy.