Capillary interactions between spherical Janus particles at liquid-fluid interfaces

We study the interactions of spherical Janus particles at non-equilibrium orientations adsorbed at flat oil-water interfaces. At equilibrium, the orientation of Janus spheres results in each hemisphere being exposed to its more favored fluid. Experimental observations suggest that some of these particles may take a tilted orientation at the interface, giving rise to energetic inter-particle interactions. The interface shape around the particles is obtained numerically by minimizing the total surface energy of the system comprising the interface and particle-fluid regions. We quantify these interactions through evaluation of capillary energy variation as a function of the separation distance between the particles. Depending on the relative orientations of neighboring particles, attractive or repulsive forces appear between Janus spheres. The interactions are found to be dipolar in nature, with a pair potential inversely proportional to the third power of the inter-particle distance. We find that Janus spheres with similar orientations undergo a relative realignment in the interface plane in order to minimize the capillary energy. We also evaluate the dependence of capillary forces on the size and degree of amphiphilicity between two sides of the particle. This study can provide new insight into understanding the interactions and assembly of Janus particles of random orientations at liquid-fluid interfaces.