Instability of an autochemotactic active suspension

Abstract

This study examines the effects of an evolving attractant field, due to the phenomenon of autochemotaxis, on the stability of a dilute suspension of active swimmers in a channel. Motile swimmers typically exhibit an orientation bias that is dependent upon the local gradient in the attractant field. By modelling the autochemotactic behaviour of the swimmers through a non-dimensional number Da that characterizes the rate of attractant secretion, we are able to show that the active stress-driven instability predicted by Kasyap & Koch (Phys. Rev. Lett., vol. 108, issue 3, 2012, p. 038101) for a suspension of pushers is stabilized with increasing Da. We also show that the autochemotactic behaviour results in an active stress-driven flow instability for a suspension of pullers. Furthermore, we show analytically and numerically that in the absence of convective transport of the attractant, pushers and pullers undergo a simultaneous switch of stabilities at a critical Da.