Collective Dynamics of Catalytically Self-Propelled Particles

Colloidal motors capable of autonomously traversing liquids exhibit remarkable nonequilibrium phenomena including clustering and phase separation. Regarding motions of micron and sub-micron motors, the nature of viscous medium and the role of Brownian motions are substantial and hence, it is crucial to perceive the microhydrodynamics beside the underlying driving force for propulsion in probing the collective dynamics of the system. An increasing number of experiments on catalytically-driven (active) colloidal particles have shown that the interactions of chemically active particles are more complicated than usual interaction of two nonreactive (passive) particles. Indeed, each chemically active particle changes the distribution of product (or reactant) solutes which, in turn, alters the motion of the other particles. In this case, the motions of active particles are influenced not only by hydrodynamic interactions but also via diffusive interactions of the solute distribution generated (or consumed) at the surface of the active areas of each colloid with the boundary of other colloids.

In this research, we first present an analytical solution based on a continuum approach to address the pair interaction of two partially active colloids with arbitrary orientations. Colloids' translational and angular velocities at Stokes flow regime are obtained using Reynolds Reciprocal Theorem (RRT) based on an asymptotic approach in which the net interaction creates a slip-velocity at the surface which actuates the motion. Our analysis indicates two possible scenarios for pair trajectories of catalytic self-propelled particles: either the particles approach, come into contact and assemble or they interact and move away from each other (escape). For motions of the colloids, it is found that the direction of particle rotations is the key factor in determining the escape or assembly scenario. Next, we extend this work to account for many body interactions of a suspension of self-propelled particles by Stokesian Dynamics (SD) simulations. The phoretic interactions between the colloidal motors are short-range and hence can be taken into account in a pairwise additive fashion and the hydrodynamic and Brownian forces are taken into account according to the standard SD. We believe the proposed numerical platform can shed light in our challenging search for a fundamental understanding of reductionist systems in active matter.