We investigate the collective dynamics in array formed by self-propelling particle (SPP) under low Reynolds number (Re) condition. This system is an interesting non-equilibrium issue to be explored. In microfluidic devices, Re is low due to small characteristic length scale and low inertial effect. The above constraints lead to non-rotational flow in microfluidics devices. Bacteria, as a kind of self-propelling particles, possess molecular motors that are able to perform highly efficient flagellum rotation even under low Re condition.
In this work, we form self-propelling particle array by depositing bacteria on treated surface in a microfluidic device. The formed high density bacterial carpet renders high density ensemble of freely rotating flagella that are able to exert thrust in the surrounding fluid. The micro?uidic channel is composed of single polarly-?agellated Vibrio alginolyticus (VIO5 or NMB136) deposited glass substrates. The individual ?agellum swimming speed is tuned by varying buffer sodium concentration. Hydrodynamic coupling strength is tuned by varying buffer viscosity. Particle tracking statistics shows high ?agellum rotational rate and strong hydrodynamic coupling strength lead to collective sub-diffusive dynamics in VIO5 case, while not the case for NMB136.
The flick motions of the VIO5 could generate a thrust that propagates back to the original bacteria and exert a counteraction in the flow in between. In bacterial carpet condition, the suspended particle could experience an effectively confining action by the counteractions from all directions through hydrodynamic coupling. The NMB136 counterpart, however, could not generate strong thrust by rotational motion that could lead to strong anti-persistent motions in particle, thus no sub-diffusive dynamics.
According to the experiment observation, we find out a vertical force generated by bacterial carpet. It can be measured by optical tweezers. Interactions between neighboring ?agella and force measurement show the forces may come from the collective ?agella motion. At the low Reynolds number system, Saffman force pushes the tracer particles to the region of higher ?uid velocity in the non-uniform flow. This is a physically probable mechanism to explain the sub-diffusive behavior.
