Chaotic motion of swimming microbes in laminar flows*

We present experiments on the motion of swimming algae (tetraselmis and euglena) in a time-independent vortex chain flow and a time-periodic (oscillating) channel flow. For both of these flows, trajectories of passive tracers are governed by two phase dimensions; consequently, passive mixing is solely ordered (non-chaotic). However, self-propelled particles moving in these flows have an additional, third, phase space dimension: the swimming direction of the swimmer. Consequently, chaotic trajectories are possible for active particles moving in these flows, even though passive mixing is ordered. We measure trajectories of the swimming microbes in these flows for a range of non-dimensional swimming speeds v₀ = V_swim/U where V_swim is the speed at which the microbe swims in the absence of a flow and U is the maximum flow speed. The separation of nearby trajectories is determined to look for signs of exponential separation and positive Lyapunov exponents. We also discuss the possibility of the coexistence of ordered and chaotic regions for smaller values of v₀.