Session L19: Biological Fluid Dynamics: Collective Behavior and Microswimmers

Microorganisms Flock in a Turbulent Flow

The understanding of collective, cooperative motion of organisms is one of the most important problems in areas spanning physical biology, soft matter, and statistical physics. Most of the work in this field has focussed on showing how flocking emerges in a collection of organisms without taking into account the typically noisy, random and spatio-temporally complex environment experienced by these individuals. We now show, for the first time, that self-organised, collective behaviour can emerge, contrary to naıve expectations, in a group of microorganisms moving in a turbulent flow. By combining ideas from the Vicsek model and turbulent transport, we show that non-trivial correlations between the flow and individual dynamics are crucial for the microorganisms to flock in, for example, a turbulent marine environment. Crucially, we show – as in nature – that the degree of flocking depends sensitively on the shape and size of the organism.   

Diverging velocity fluctuations and enhanced tracer diffusivities in interacting swimmer suspensions

Evidence from both experiments and simulations suggests that suspensions of rear-actuated micro-swimmers exhibit interesting phenomena, such as long ranged orientational order, enhanced tracer particle diffusivities as well as collective motion, among others. We present an analytical characterization of the fluid velocity correlations and tracer diffusivities in an interacting swimmer suspension. Pair-interactions lead to a logarithmically divergent velocity variance, and a non-decaying covariance, in a suspension of straight swimmers at O(nL³)²; n being the swimmer number density and L being its characteristic length (nL³ << 1). Incorporating orientation decorrelation in the form of tumbles leads to the said divergence being cut-off at distances of order the long but finite run length - Uτ, where τ represents the swimmer's mean run duration and U the swimming speed. The covariance shows a weak logarithmic decay at distances r ∼ O(Uτ), and an eventual O(1/r) decay for r >> Uτ. The O(nL³)² tracer diffusivity exhibits a linear divergence with Uτ. Interestingly, the mean square displacement exhibits a broad crossover from ballistic to diffusive regimes, with the transition extending from times of O(L/U) to O(τ), for Uτ/L >> 1, giving the impression of an anomalous exponent.
  

Torque-dipolar micro-swimmers: modeling, circling behavior and large-scale simulations

We present a new model for micro-swimmers that takes into account the counter-rotation of the body and flagella, as seen in motile bacteria or spermatozoa. The disturbance fluid flow of one such swimmer now contains a torque-dipole singularity in addition to the well-known force-dipolar singularity. We show that this head-and-flagella counter-rotation gives rise to clock-wise circling at no-slip walls just as observed in experiments of bacteria on surfaces. We discuss the scattering behavior of spermatozoa in a forest of cylindrical pillars, confirmed also by new experiments. Last, we show large scale and fast simulations of thousands of such swimmers that interact with each-other through direct collisions as well as through the fluid.   

Collective dynamics of human sperm swimming in a viscoelastic medium

We have numerically investigated collective dynamics of sperm swimming, modelling cells as superposition of regularized flow singularities, based on experimentally obtained human sperm images in watery low viscous medium and highly viscous-weakly elastic, methylcellulose medium. In both media, the time-averaged flow around the cell is that of a typical pusher-type swimmer, and the cells tend to form dynamical clustering. However, considering the temporal fluctuating contributions, it is found that the cell yaw and cell pulling dynamics inhibit clustering in low viscous media. This study therefore emphasizes that the finer-scale temporal dynamics of sperm flagellar movement can impact large-scale collective behaviors, and also motivates the need for the characterization of sperm waveform and their dynamics.