  The dynamics and pair trajectory of two self-propelled colloids are reported.
The autonomous motions of the colloids are due to a catalytic chemical reaction
taking place asymmetrically on their surfaces that generates a concentration
gradient of interactive solutes around the particles and actuate particle
propulsion. We consider two spherical particles with symmetric catalytic caps
extending over the local polar angles $\theta^1_{cap}$ and $\theta^2_{cap}$
from the centers of active sectors in an otherwise quiescent fluid. A combined
analytical-numerical technique was developed to solve the coupled mass transfer
equation and the hydrodynamics in the Stokes flow regime. The ensuing pair
trajectory of the colloids is controlled by the reacting coverages
$\theta^j_{cap}$ and their initial relative orientation with respect to each
other. 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 arbitrary motions of the colloids, it is found that the direction of
particle rotations is the key factor in determining the escape or assembly
scenario. Based on the analysis, a phase diagram is sketched for the pair
trajectory of the catalytically active particles as a function of active
coverages and their initial relative orientations. We believe this study has
important implications in elucidation of collective behaviors of
auotophoretically self-propelled colloids.
