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Unsteady chiral swimmer in presence of an external chemical gradient

Unsteadiness occurs in the low Reynolds number swimmers' motion while they start from rest or escape from a predator or attack prey. In this paper, we study an unsteady chiral swimmer's behavior, with a prescribed surface slip velocity, in the low Reynold number regime and its response to an external chemical gradient. Using the general solution of unsteady Stokes equation and appropriate boundary conditions, i.e., slip velocity at the body surface and the ambient velocity field at the far-field, we calculate the migration velocity, rotation rate, and the ow field of the swimmer in a closed-form. We compare the velocity with some previously known results in appropriate limits. The continuous unsteady motion of the swimmer affects its tactic movement. A relevant example of this situation is chemotaxis, where the presence of chemical stimulus alters the swimmer's surface slip velocity. As a result, the swimmer either steers towards the chemical target or moves away from it, depending on the system parameters. Here, the rotation rate controls the success of the chemotaxis. In addition to the successful and unsuccessful cases, we observe a unique orbiting state where the swimmer keeps revolving around the chemical target in diffusive orbits.