Tandem droplet locomotion in a uniform electric field

An isolated charge-neutral droplet in a uniform electric field experiences no net force. However, a droplet pair can move in response to field-induced dipolar and hydrodynamic interactions. If the droplets are identical, the centre of mass of the pair remains fixed. Here, we show that if the droplets have different properties, the pair experiences a net motion due to non-reciprocal electrohydrodynamic interactions. We analyse the three-dimensional droplet trajectories using asymptotic theory, assuming spherical droplets and large separations, and numerical simulations based on a boundary integral method. The dynamics can be quite intricate depending on the initial orientation of the droplets line-of-centres relative to the applied field direction. Drops tend to migrate towards a configuration with line-of-centres either parallel or perpendicular to the applied field direction, while either coming into contact or indefinitely separating. We elucidate the conditions under which these different interaction scenarios take place. Intriguingly, we find that in some cases droplets can form a pair (tandem) that translates either parallel or perpendicular to the applied field direction.