Mathematical Description of Janus Particles and the Generalization of the Plateau Hypothesis of a Standard Double Bubble

Janus particles represent one of the forms of existence of heterogeneous micro- and nanoparticles. A convenient mathematical prototype of Janus particles is a double bubble, which was described by Plateau when solving the problem of minimal surfaces. The main difference between a double bubble and a Janus particle is an additional condition that interfaces can have different elastic properties. The solution for this case has been obtained using the Young’s method. The limits of the existence of this solution have been revealed. The dependence of the configuration of Janus particles on the relation between the surface properties and the volumes that form the particles has been shown.