Interaction between catalytic micro motors

Starting from a microscopic model for a spherically symmetric active Janus particle, we study the interactions between two such active motors. The ambient fluid mediates a long range hydrodynamic interaction between two motors. This interaction has both direct and indirect hydrodynamic contributions. The direct contribution is due to the propagation of fluid flow that originated from a moving motor and affects the motion of the other motor. The indirect contribution emerges from the re-distribution of the ionic concentrations in the presence of both motors. Electric force exerted on the fluid from this ionic solution enhances the flow pattern and subsequently changes the motion of both motors. By formulating a perturbation method for very far separated motors, we derive analytic results for the transnational and rotational dynamics of the motors. We show that the overall interaction at the leading order, modifies the translational and rotational speeds of motors which scale as ${\cal O}\left([1/D]^3\right)$ and ${\cal O}\left([1/D]^4\right)$ with their separation, respectively. Our findings open up the way for studying the collective dynamics of synthetic micro motors.