Constructing micro-chains: a study of self-phoretic torus-sphere interactions

Self-phoretic particles are capable of propulsion in liquid solution by catalyzing the decomposition of chemical "fuel." Recent studies have focused on the self-organization of self-phoretic particles into larger assemblies , i.e., so-called "machines from machines." For instance, Nasouri et al. (JFM 2020) have shown that two spheres can form stable bound pairs for specific choices of the particle design parameters. Particle shape and topology may hold the key for achieving greater control over pairwise interactions. In particular, increasing the topological genus of one of the particles could increase pair stability and even allow for a "lock-and-key" assembly mechanism. Here, we study the pairwise interaction between a self-phoretic torus and a self-phoretic sphere. We analytically calculate the concentration field for the torus-sphere pair and discuss the resulting motion of the pair. We consider both stable configurations as well as configurations in which the sphere passes through the torus. Finally, we show that the results can straightforwardly be extended to a self-phoretic spheroid-torus pair.