Collision between chemically driven self-propelled drops

We use analytical and numerical approaches to investigate head-on collisions between two self-propelled drops described as a phase separated binary mixture. Each drop is driven by chemical reactions that isotropically produce or consume the concentration of a third chemical component, which affects the surface tension of the drop. The isotropic distribution of the concentration field is destabilized by motion of the drop, which is created by the Marangoni flow from the concentration-dependent surface tension. This symmetry-breaking self-propulsion is distinct from other self-propulsion mechanisms due to its intrinsic polarity of squirmers and self-phoretic motion; there is a bifurcation point below which the drop is stationary and above which it moves spontaneously. When two drops are moving in the opposite direction along the same axis, their interactions arise from hydrodynamics and concentration overlap. We found that two drops exhibit either an elastic collision or fusion, depending on the distance from their bifurcation point, which may be controlled, for example, by viscosity. An elastic collision occurs when there is a balance between dissipation and the injection of energy by chemical reactions. We derive the reduced equations for the collision between two drops and analyse the contributions from the two interactions. The concentration-mediated interaction is found to dominate the hydrodynamic interaction for a head-on collision.