Dynamics of Deformable Active Particles

In this review we discuss the dynamics of deformable active particles mainly from the theoretical point of view. Fluid droplets in a surfactant solution undergo translational motion under certain conditions by generating a gradient of the surface tension. This migration induces shape deformation due to the nonlinear coupling between the migration and shape degrees of freedom. On the other hand, migration is induced by shape deformation in living matter. The swimming of bacteria is a pertinent example. A repeated shape change is generally necessary for the crawling motion of eukaryotic cells on substrates. We introduce a set of time-evolution equations for deformable active particles in a manner as general as possible by a symmetry argument focusing on the interplay between the shape deformation and translational motion. The spinning of a particle is also considered as the active dynamics. Our basic assumption is that the migration velocity and lower modes of the shape deformation of a spherical particle (a circular particle in two dimensions) are the relevant slow degrees of freedom of the system. It is emphasized that our theory is not purely phenomenological and that the time-evolution equations are derived by an interfacial approach in an excitable reaction diffusion system and in chemically reacting ternary fluids, the latter of which gives rise to the self-generated Marangoni effect. We also investigate the dynamics of interacting deformable particles and show numerically that a soliton-like behavior occurs in collisions of collective density waves in two dimensions. In the final section, some open problems and future perspectives are discussed.