Session P14: Biological Fluid Dynamics: Collective Behavior and Microswimmers I

Collective motion of microswimmers in impure flow

We investigate through mathematical modeling, analysis and nonlinear simulations, the collective motion of micro-swimmers in fluids with resistance, which approximate a porous wet material. We use a continuum model to describe the collective dynamics of bacteria that each perform a run-and-tumble motion. The swimmer dynamics is coupled to the fluid dynamics that is modeled through a Stokes-Brinkman equation with an added active stress. The linear stability of the uniform isotropic state reveals that the suspension transitions from a long-wave instability to a finite-range one where the collective bacterial chaotic motion is weakened by the resistance. Simulations of the full nonlinear PDE system confirm the analytical results. We discuss the spread of an initial accumulation of bacteria and show that it depends non-trivially on the medium resistance which suppresses the spread. Last, we outline ongoing work on high performance simulations of the coupled motion of thousands of individually-traced swimmers in Brinkman flows.   

Semiclassical technique for computing noisy swimmer escape probabilities in fluid flows

The random fluctuations inherent to the self-propulsion of microswimmers can have a dramatic impact on their trajectories, especially near flow-induced transport barriers.  We discuss a method for calculating the probability of particular noisy swimmer trajectories in a given fluid flow, taking the hyperbolic flow as a case study.  Our approach consists of computing solutions to the time-dependent Fokker-Planck equation of a swimmer in the weak-noise limit.  This differs from traditional approaches to the swimmer Fokker-Planck equation, which are focused on the stationary (time-independent) solution and are in the Eulerian frame-of-reference.  In contrast, we construct a time-dependent swimmer probability density function by following the Lagrangian paths of a swimmer.  This procedure mirrors the semiclassical approximation in quantum mechanics and similarly involves calculating the least-action paths of a Hamiltonian system derived from the swimmer's Fokker-Planck equation.  We use this approach to quantify the tendency of noisy swimmers to cross a transport barrier in the hyperbolic flow and compare our results with Monte Carlo calculations.   

Rheotaxis in viscoleastic fluids: Experiments with swimming E. coli

The positive rheotaxis of microorganisms in Newtonian fluids encompasses the spontaneous orientation of individual swimmers against a unidirectional flow. The mechanism is governed mainly by the positioning of the swimmer at an angle in the high shear flow region close to solid boundaries. While much is known about rheotaxis in simple Newtonian liquids, our understanding of such process in complex fluids is still in its infancy. In this talk, we present experiments on positive rheotaxis of the swimming bacterium E. coli in viscoelastic fluids. We find that the flux upstream is increased by an order of magnitude in viscoelastic shear-thinning fluids as opposed to strictly Newtonian viscous fluids. The analysis of E.Coli orientation distribution allows us to quantify the relative contribution of the elastic and viscous stresses on the observed phenomena.   

Confined Collective Behavior of Aligning Self-Propelling Particles

We present a model for aligning self-propelling particles and look at the collective motion for such swimmers in non-trivial confined domains. To classify the behaviors of the swimmers in circular convex domains and racetracks, several order parameters have been considered. Based on those order parameters, we present the non-equilibrium phase diagrams of our model with respect to different geometries and sizes of confinement, the densities of swimmers, and the alignment distance. Lastly, we compare the results to experiments in active matter systems such as motile colloids, swimming bacteria or larva zebrafish, and note the qualitative similarities and differences.   

Off-center squirming in viscous flow confined by a fluid pocket

Helicobacter pylori swims through gastric mucus by locally neutralizing its acidic environment and turning surrounding gel into a fluid pocket. The size and shape of the degelled pocket strongly affects swimming speeds in such confined environments.  To study the effect of three-dimensional confinement, we develop an exact analytical solution for a spherical squirmer confined in a spherical Newtonian fluid domain with no-slip boundaries. The squirmer can be placed anywhere along the centerline of the confinement, allowing us to study off-center motility and close-range hydrodynamic interactions of the swimmer and pocket walls. We report the swimming speed and flow field for different confinement sizes and swimmer locations, for radial and tangential pusher and puller squirmers. Tangential and radial squirmers have reduced and enhanced swimming speeds, respectively, when they are located at the center of the confining pocket. Depending on the squirmer strength and pocket sizes, tangential squirmers can have enhanced swimming speeds when off-center and near a wall, and swimming speeds can even reverse. We explain our results in terms of the interaction of swimmer flow fields and the confinement boundaries.   

Active mixing of swimming bacteria in laminar shear flows

We present experiments on the motion of smooth-swimming and tumbling bacillus subtilis bacteria in steady and time-periodic laminar flows. The flows are either a channel (Poiseuille) flow in a PDMS cell or a Kolmogorov flow (alternating jets) in an acrylic cell, forced magnetohydrodynamically. For both flows, passive mixing in the flow is ordered -- even if the flow is time-periodic -- since the motion parallel to and perpendicular to the jets are decoupled from each other. For self-propelled impurities in the flow, however, the swimming  direction introduces an additional phase space variable that allows for the possibility of chaotic trajectories. We track the motion of swimming microbes in these flows and (1) investigate conditions where the trajectories are chaotic or ordered; (2) measure variations in the microbe density for both smooth-swimming and tumbling microbes; and (3) study "flights" in the microbe orientations that are predicted by the structure of the (x,y,θ) phase space.   

Invariant manifolds and barriers blocking swimming microbes in vortex flows

We present experiments on the motion of bacteria in laminar vortex chain and vortex array flows. The flows are generated by magnetohydrodynamic forcing in an acrylic, microfluidic cell, and the bacteria are a strain of bacillus subtilis mutated to express green fluorescent protein (GFP). A generalized theory of active mixing predicts "swimming invariant manifolds" (SwIMs) that split from the passive manifolds and act as one-way barriers that block the motion of smooth-swimming microbes. The same theory predicts "burning invariant manifolds" (BIMs) for the special case of bacteria that swim in a direction perpendicular to their semi-major axis; these BIMs also act as one-way barriers blocking the motion of reaction fronts in the same flow. We track the bacteria in the flow and: (1) identify curves in the flow across which the smooth-swimming bacteria cannot cross and compare those barriers to the SwIMs and BIMs predicted by the theory; (2) investigate role of BIMs as barriers that block even tumbling microbes; and (3) measure variations in the microbe density that are predicted by the theory.   

Run-and-Tumble Bacterial Chemotaxis in Confinement

Most bacteria live in complex porous materials such as tissues or soil, yet their motion and chemotaxis in confinement are still not well understood.

We present a run-and-tumble model for bacterial motion model coupled to the chemical gradient while the entire colony is inside a circular confinement. For the tumble timing, we consider a smooth transition from the `run' to `tumble' motion.The tumble angle follows a bimodal von Mises distrbution which has a one-sided mean and a reciprocal measure of dispersion. We present simulations of the collective chemotactic behavior in confinement when swimmers are either fully motile or  random mixture of motile and immotile. Finally, we will discuss the states observed for various parameters, and the phase separation of bacteria in confinement.   

Aerotactic response of bacteria: experimental characterization at the bacteria scale and population scale

Many environmental bacteria use their flagellar motility to find optimal regions for their development, they bias their swimming in response to chemical signals. The drift velocity associated to this response is proportional to the local concentration gradient of the signals and the chemotactic sensitivity coefficient. Although studied for many years, the dependence of this sensitivity coefficient with concentration is still debated. In our study, suspensions of Burkholderia contaminans are placed in a capillary sealed at one end and permeable to oxygen at the other end. The oxygen consumption of the bacteria in the capillary produces a gradient in which the bacteria move. By monitoring the concentration and velocity of bacteria, as well as the oxygen concentration along the capillary using encapsulated Ruthenium dye, we uncover the aerotactic sensitivity dependence on the oxygen concentration. In addition to this macroscopic approach, we also determine this cell sensitivity from modulation of the run-time distribution with swimming direction. Our multiscale approach sheds new light on the different theoretical models that have emerged from the Keller-Segel equations over the past fifty years.   

Reinforcement learning for pursuit and evasion of microswimmers at low Reynolds number

Most aquatic organisms can exploit hydrodynamic information to navigate, locate their preys and escape from predators. Abstracting away from specific biological mechanisms, we study a model of two competing microswimmers engaged in a pursue-evasion (zero-sum) game while immersed in a low-Reynolds-number environment. The microswimming agents have access to limited information via the hydrodynamic disturbances generated by their opponent, which provide some cues about its swimming direction and position. They can only perform simple manoeuvres: turn left, right or go straight. The goal of the predator/pursuer is to capture the evader/prey in the shortest possible time. Conversely, the prey aims at avoiding capture or delaying it as much as possible. We let the agents discover their strategies by means of an actor-critic Reinforcement Learning algorithm. We show that the agents are able to find efficient and a-posteriori physically explainable strategies which non-trivially exploit both the dynamics and the signals provided by the hydrodynamic environment. Our study provides a proof-of-concept for the use of Reinforcement Learning to rationalize prey-predator strategies in aquatic environments, with potential applications to underwater robotics.   

A lattice model of bacterial turbulence

One of the most striking difference between active and passive systems is the appearance of collective motion in self-propelled particles suspended in a fluid. The phenomenology of this transition is well established: At low densities particles move in a seemingly uncorrelated fashion, while at higher densities they organise into jets and vortices comprising many individual microswimmers. Our recent work (Stenhammar et al, PRL 119, 028005 (2017)) suggests that this transition is caused by mutual reorientation of the microswimmers and is insensitive to their translational degrees of freedom.

Motivated by this obsrevation, we develop and study a lattice model of the collective phase. We confine model microswimmers to a regular lattice and fix their positions. The dynamics of each microswimmer then comprise re-orientations in the velocity fields created by other microswimmers and random orientational changes representing bacterial tumble event. We observe that in the absence of tumbling, all dynamics cease after some initial time, yielding a 'frozen' configuration. For sufficiently often tumbling, these configurations 'melt', and we discuss the implications of this scenario for bacterial turbulence.