Session T04: Active Matter III: Swimming and Nonlinearity

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While many active-matter systems reside in fluids (solution, blood, ocean, air), so far, studies that include hydrodynamic interactions have focussed either on microscopic scales in Stokes flows, or on large scales at high Reynolds numbers. What happens in between? In this talk, I will present my group's work on simple model swimmers we use to understand the transition from Stokes to intermediate Reynolds numbers, first for a single swimmer, then for pairwise interactions and finally for collective behavior and active matter. We show that, even for simple models, inertia can induce hydrodynamic interactions that generate novel phase behavior, steady states and transitions.   

Collective behavior of schooling fish in confined domain

Collective phenomena occur across nature, from insect swarms to bird flocks and fish schools. Fish schools are a typical example where collective dynamics emerge from individual-level interactions. Here we construct a model that integrates, under geometric confinement, phenomenological behavioral rules based on vision with hydrodynamic interactions based on the flows generated by swimming fish. Using a systematic approach to study the collective dynamics over the entire parameter space, we show that a new multi-stability phase emerges in which the group of fish intermittently switches between schooling and milling. We analyze the intermittency regime with multivariate Fokker-Planck equation and dimensionality reduction based on coarse-grained order parameters. We find that this intermittency regime is sensitive to both school size and confining strength, and will break into bistability under certain circumstance. We conclude by commenting on the extendibility of these techniques in studying general collective dynamics.   

Long-range active mixing of swimming microbes in a vortex chain flow

We present results of experiments that track the motion of swimming tetraselmis and euglena algae in a flow composed of a chain of alternating vortices. Trajectories of active particles in this two-dimensional flow can be chaotic, even though the flow is time-independent. Swimming invariant manifolds (SwIMs) can be calculated for the flow; these SwIMs not only act as barriers impeding the motion of the swimming microbes but also result in ``chutes'' that carry microbes between adjacent vortices. The flux of microbes between vortices in the experiments agrees with predictions based on these chutes. We also measure the growing variance of an ensemble for different microbe swimming speeds and interpret those results in terms of the SwIM geometry. Comparing the transport of elongated euglena versus the almost-circular tetraselmis microbes enables us to ascertain the role of microbe shape in the transport process.

    

The Geometry of Swimming Invariant Manifolds Mediates Long-Range Transport of Micro-swimmers in a Vortex Array

We analyze the kinematics of micro-swimmers in an imposed microchannel flow consisting of alternating fluid vortices.  These swimmers could be biological (e.g. bacteria or algae) or artificial (e.g. Janus particles).  Using dynamical systems techniques, we show that transport from one vortex down the channel to another vortex is mediated by Swimming Invariant Manifolds (SwIMs); SwIMs have previously been emphasized as one-way barriers to swimmer transport, but they also form chutes which guide swimmer passage between vortices.  The SwIM geometry thus plays a critical role in determining transport rates of swimmers between vortices.  Here, the SwIM geometry is analysed via a two-dimensional surface-of-section, which simplifies the analysis and leads to a topological classification of swimmer orbits. Our theoretical framework is applied to experiments on algae in microfluidic channels.

    

An adjoint-based approach to study the hydrodynamic schooling of heaving-pitching swimmers

The hydrodynamic schooling of swimmers presents fascinating flow physics with complex flows generated by individuals and their interactions. However, its further study is often hindered by the large parametric space proportionally increased with the number of individual swimmers, not to mention designing an optimal schooling for man-made underwater vehicles. An adjoint-based approach is developed here for its unique feature that the computational cost for optimization keeps almost the same with the increase of control parameters, and makes an idea choice to study hydrodynamic schooling. The preliminary study focuses on a model problem where the leading foil moves with a prescribed heaving-pitching motion, and the motion of multiple trailing foils are optimized for better hydrodynamic performance. The control parameters include the heaving amplitude, pitching amplitude, and the phase delay of each trailing foils. The optimal solution for the drag reduction of trailing foils shows that some degree of synchronization is achieved among all foils, though a small phase delay remains.   

Hydrodynamic interactions between mother and calf whales under optimized positioning and motion

From the onset of life, a whale calf swims in formation with its mother for not only shelter and nurturing but also for beneficial hydrodynamic interactions. However, the dynamic interactions exhibited by formations of moving solid bodies in a three-dimensional domain poses a complex and computationally intensive problem. In this study, the whales are approximated as echelon pairs of spheroids. The leading spheroid oscillates in the vertical direction under fixed parameters to mimic a mother whale's aquatic motion. The reduced size trailing spheroid, mimicking a calf whale, is optimized over multiple control parameters: position in a 3D space and amplitude and phase of bi-axial oscillatory motion. Due to the complexity by the large parametric space, an adjoint-based optimization is developed to concurrently optimize all control parameters while the computational cost remains a feasible level. This adjoint-based approach allows for in-depth understanding of the vortical structures and interactions generated between mother and calf pairs in various configurations often seen in nature, and the optimal solution may potentially go beyond the natural configurations for engineering purpose.   

Schooling of Antarctic krill in a novel annular flume

Schooling is a key behavior of Antarctic krill, an ecologically important species in the Southern Ocean. Proposed benefits for school membership include increased hydrodynamic efficiency and improved awareness of external environmental signals, such as those created by predators, prey, or mates. Here we describe a novel annular flume used for exposing Antarctic krill schools at Palmer Station, Antarctica to various levels of flow, light, and odor. An annular design allows for continuous schooling without the animals encountering an up- or down-stream barrier as would occur in a linear flume. The tank inner and outer diameters are 0.3 m and 1.2 m, respectively. Variable flow in the range of 1-100 mm s^-1 is generated by rotating the inner cylinder and by submersible pumps and flow conditioners positioned along the outer wall and is characterized using particle image velocimetry (PIV). An overhead stereophotogrammetry system with near-infrared backlighting illumination beneath the flume allows three-dimensional measurements of krill positions at all ambient light levels. We report school polarity, swimming speed, and nearest neighbor distance results from experiments in which 700 krill were subjected to flow speeds of approximately 15 and 30 mm s^-1 at two different light levels.   

Diel Vertical Migration of Mesozooplankton: Large Mixing by Small Animals?

Diel Vertical Migrations (DVM) of mesozooplankton aggregations are hypothesized to trigger biogenic mixing. Lab studies have shown that the vertical migration of swarms of model organisms results in large-scale momentum and scalar transport via flow instabilities. However, it is unclear how to scale these results to inform the physics of the upper ocean. Here we outline a new approach for assessing DVM effects by: (1) characterizing DVM from ocean-color satellite observations; (2) developing a lab-based, continuum model parameterization of fluid transport by DVM; and (3) implementing the acquired DVM characteristics and swimmer parameterization in a global-ocean biogeochemistry model with a realistic representation of mesozooplankton physiology and behavior. Focusing on (2), we measured the flow field of individuals and aggregations of relevant copepod species using bright-field and 2-D PIV, respectively. We discuss the effects of aggregation density,  migrating direction, and the energetic length scales on the induced fluid transport and mixing. Our study will provide a unique framework for incorporating vertically-migrating organism behavior and the associated physical processes into state-of-the-art ocean circulation models to quantify marine ecosystem structure accurately.   

Complex Emergent Dynamics in Fish Schools - Insights from a Flow-Physics-Informed Model of Collective Swimming in Fish

Complex collective behavior emerges in fish schools due to a combination of behavioral imperatives (such as safety from predators, improved foraging, etc.) propulsive forces, and the hydrodynamic forces induced by the complex flow field encountered by fish swimming in a school. Hydrodynamics also plays a key role in enabling a fish to sense the position/velocity of neighbors and to control its own velocity and heading. Finally, hydrodynamic interactions can be exploited by fish in schools to improve swimming performance. In the current study, we employ a new model of collective swimming of fish that has three key features: (a) the model is based on the balance of forces and moments on the fish; (b) the model includes interaction with the vortex wakes of fish; (c) the model is parametrized via data from direct numerical simulations (DNS) of a swimming fish. The model is used to examine emergent topologies and dynamical behavior of fish schools, as well as the effect of key parameters on swimming efficiency, and visual and lateral line sensing in fish schools.   

Simulating the Motion of High-Density Human Crowds as a Low Reynolds Number Newtonian Fluid

The synchronized movement of large crowds of people are common at both sporting events and in response to traumatic events (such as active shooters) in crowded venues. Proper understanding of high-density crowd movement and behavior can be used to design safer building layouts to reduce the risks of suffocation and trampling in crowds. Due to the independent thinking of individuals, it is typically difficult to model crowd motion due to the inability to accurately predict what individuals may do within the crowd. However, if the density of the crowd is very high and the goal of the majority of the crowd members is similar, then it is feasible to treat a high-density crowd as a low Reynolds number Newtonian fluid. In this work, a bifurcating hallway was simulated at several crowd velocities and densities. In all cases, the Reynolds number based on hallway width was between 45 and 77. High-pressure regions in the hallway were identified, and the layout of obstructions and diversions in the path were adjusted to reduce the pressure difference, resulting in a reduced risk of death by suffocation.

    

Author not Attending

Recently, it has been experimentally discovered, and analytically proved, that the stationary velocity distribution function of an active ideal gas is bimodal. In this work, we analytically reveal the condition under which a bimodal velocity distribution arises, and the condition under which this bimodal distribution will become Gaussian. This condition is seen to depend on two important time scales in the problem, namely, reorientation and inertial time scales. Briefly, when the inertial time is larger than the orientation time, the active Fokker-Planck stationary solution admits a bimodal structure. The inverse condition is seen to admit a Gaussian structure.   

Author not Attending

Janus phoretic particles exploit chemical energy to self-propel at microscopic scale, and respond to their hydrodynamic and chemical environment. As a result, they are able to interact both hydro-dynamically and chemically with other particles, like chemotactic biological microswimmers (e.g., bacteria, algea), or with an external flow or chemical signal, leading to non-trivial collective behaviour (e.g., phoretic particles clustering or bacterial swarming). Recent experiments and analysis have demonstrated that the response of sheared active suspensions can in fact lead to significant reduction in viscosity due to the injection of energy at the microscopic scale.

Using a continuum kinetic model, we analyse numerically the response to simple shear flow of a dilute and confined phoretic suspension, focusing specifically on the dual influence of confinement and shear strength. Depending on the relative intensity of these effects to the particles’ chemotaxis and self-propulsion, different steady and unsteady regimes are observed and analysed, together with their impact on the suspension’s effective viscosity.