Unsteady chiral swimmer and its response to a chemical gradient

Abstract

Unsteadiness occurs in the motion of swimmers while they start from rest or escape from a predator, or attack prey. In this paper, we study the behaviour of an unsteady chiral swimmer, with a prescribed surface slip velocity, in the low-Reynolds-number regime, and its response to an external chemical gradient. In the first part, by solving the unsteady Stokes equation, we calculate the migration velocity ( $\boldsymbol {U}$ ), rotation rate ( $\boldsymbol {\varOmega }$ ) and flow field of the unsteady swimmer in a closed form. We compare these results with some previously known results in appropriate limits. In the second part, we investigate the response of the unsteady chiral swimmer to an external chemical gradient, which can influence the swimmer's surface slip velocity. Consequently, the swimmer either steers towards the source of the chemical gradient or moves away from it, depending on the strengths of $\boldsymbol {U}$ and $\boldsymbol {\varOmega }$ , and the corresponding angle ( $\chi$ ) between them. Interestingly, the swimmer swims in a closed orbit in the vicinity of the chemical target, depending on the strengths of $\boldsymbol {\varOmega }$ and $\chi$ . We present a complete state diagram representing the successful, unsuccessful and orbital states for various strengths of $\boldsymbol {\varOmega }$ and $\chi$ . This study is useful to understand the unsteady propulsion of ciliated microorganisms and their response to external gradients.