Speaker
Description
Starting from the Smoluchowski for cell density profile in both spatial and orientational coordinates, we analyze the emergence of collective elliptical motion recently observed in quasi-2D bacterial suspensions. Within this framework, a necessary condition for the instability is the phase-leading response of swimming cells against periodic shear flow, in which case energy flows from cells into the medium. This requires the swimming speed of bacteria to be sufficiently high and tumbling rate sufficiently small. Under certain simplifying assumptions, a phase diagram spanned by cell Peclet number (a measure of nonequilibriumness) and effective film thickness is constructed, delineating the transition from a passive phase-lag regime to an active phase-leading regime. Spontaneous motion further requires cell density exceeds certain threshold so that the total energy injection due to swimming offsets dissipation in the viscous fluid. These conditions are in good numerical agreement with experimental observations. Going beyond the linear response theory, we will present analytical and numerical results for the oscillation amplitudes, and more importantly, mechanisms that lift the degeneracy of linear and circularly polarized modes into elliptical orbits.