Session ZC07: Biofluids: Collective Behavior and Active Matter V

Chemotactic aggregation of micro-swimmers in Brinkman flows

We study through analysis and computer simulations of a continuum model the collective dynamics and chemotactic aggregation of micro-swimmers immersed in viscous Brinkman flows. The Brinkman viscous flow approximates with a resistance or friction term the presence of inert impurities or stationary obstacles immersed in the fluid, and such an environment can be regarded as a wet porous medium.  Analysis of the linearized system reveals that resistance affects the hydrodynamic interactions between swimmers and their collective swimming. We present a parameter phase space for the distinct types of dynamics we can expect in the case of chemotactic pusher swimmers. Simulations of the full nonlinear system show that resistance impacts the collective dynamics for each of these states because it inhibits the interactions and collective motion of the swimmers. Surprisingly and unpredicted by linear analysis, we find that resistance also hampers the chemotactic aggregation of the swimmers because it impedes their ability to navigate efficiently towards chemotactic cues and assemble into clusters. We show several simulations of the complex system for various parameters sets and quantify the observed behavior through several measured quantities.    

Active assembly and transport of passive colloidal architectures

Recent experiments have demonstrated the formation of colloidal clusters in dilute bacterial suspensions and probed their emergent long-time dynamics. This clustering phenomenon is a direct consequence of enhanced colloidal diffusion and active depletion forces induced by the bacteria. We have adapted our previously developed colloid-swimmer model to study the kinetics of aggregation in collections of multiple colloids subject to short-ranged adhesive interactions and to analyze the phase behavior of the colloid-swimmer mixture. In addition, stochastic simulations are employed to estimate the effective translational and rotational diffusivities of the clusters in terms of their size and of the persistence of swimmer trajectories. We also account for the curvature in the circular trajectories of the swimming bacteria, for example E. Coli, which emerges from their interaction with solid surfaces. The long-time statistics of these colloidal aggregates exhibit slow persistent rotations, which we explain using a semi-analytical model.   

Active particles in the presence of obstacles

We consider active particles (microswimmers) moving in an environment with obstacles. These are treated using the Active Brownian Particle model (ABP), where particles move forward at constant speed but in a randomly-varying direction. We use homogenisation theory to predict their coarse-grained dynamics at long times. We present numerical solutions that describe their spatial distribution and effective diffusivity as a function of the strength of swimming and area fraction occupied by the obstacles. We then use matched asymptotic approximations to explain our numerical results in the dilute limit corresponding to small obstacle area fraction and in the dense limit, when the obstacles are nearly touching.   

Experimental studies of swimming organisms and reaction fronts in vortex array flows

We present experiments that study both the motion of swimming brine shrimp (artemia) and of reaction fronts (the excitable Belousov-Zhabotinsky chemical reaction) in an array of stationary vortices. Previous studies have already established the presence of burning invariant manifolds (BIMs) that act as one-way barriers that inhibit the motion of reaction fronts in 2- and 3-dimensional fluid flows. The same BIMs are also a special case of swimming invariant manifolds (SwIMs) that block the motion of self-propelled particles in the same flow. We

test predictions that these BIMs act as ultimate barriers even for swimmers with noisy, tumbling behavior. The striking similarities between front propagation and the motion of self-propelled particles in fluid flows leads to a prediction of the maximum combined (and averaged) speed for swimmers in the flow, based on the shape of a hypothetical reaction front in the same flow.   

Transport of Swimmers in a Periodic Vortex Lattice: A Theoretical Study with Noise

There is a large body of research on the dynamics of tracer particles in fluid flows. Most of this research focusses on the passive case, where small particles are advected by the flow. Less is known about active self-propelled tracer particles. This research is a theoretical study of the nonlinear dynamics of rigid ellipsoidal self-propelled particles (swimmers) in a two dimensional periodic vortex lattice. The system is treated with and without noise. Deterministic swimmers can undergo ballistic transport at low swimming speeds, while the motion is chaotic at high swimming speeds. The symmetries of the flow are used to produce a Poincare surface of section. Due to time reversal symmetry, periodic orbits of the Poincare map are surrounded by ballistic tori; these orbits undergo a period-doubling cascade that destroys the stable islands. These bifurcations are correlated with a ballistic to diffusive transition in ensemble simulations. Monte-Carlo simulations are used to test the robustness of these results to noise.   

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.   

Circular-Rower Model of Particle Transport by Cilia Arrays in Parallel-Wall Channels

Numerous models have been developed to investigate the mechanism of metachronal wave formation and cilia dynamics but much less is known about particle transport by cilia arrays. Our simplified circular-rower model of hydrodynamically coupled cilia is well-suited to investigate particle transport by metachronal waves. Cilia are represented by spherical beads (rowers) moving on prescribed trajectories that mimic the motion of cilia tips. The rowers are placed in a parallel-wall channel to model the particle and fluid transport in a thin fluid layer. We find that trajectories of transported particles exhibit kinks, loops, and long-time non-decaying oscillations. The loops occur above the trough or crest of metachronal waves, depending on the initial particle position, channel width, and length of the metachronal wave. However, in spite of the existence of closed fluid streamlines, no stagnation regions where particles would be trapped for a long time were found. We have determined the dependence of the particle transport rate on the system parameters and investigated the dynamics and stability of metachronal waves. Our results are relevant both for understanding particle transport by cilia arrays in vivo and development of artificial microfluidic cilia systems.   

Optimized regularized Stokeslets: calibrating reduced models of multicellular colonies with detailed single-cell models

Many microbial eukaryotes, like choanoflagellates,  are unicellular, while others form multicellular colonies. However,  the advantages or disadvantages in feeding performance or predator avoidance between single-celled versus multicellular colonies are not yet well understood.  Studying the hydrodynamics of colonies using detailed models of cells that represent flagella, microvilli, and cell bodies would be ideal.  However, given that there are hundreds of cells or more within a colony, this is not feasible.  Reduced models of swimmers are a natural choice.   Here we present a novel approach that uses the flow-field produced by a detailed computational model of a choanoflagellate to find the optimal parameters in a regularized force dipole reduced model that best fits averaged far-field flow.  This optimization also selects the regularized delta function (blob) from a given class.  We find that the optimal blob shape depends upon morphological features of the detailed cell model, like the presence of a microvilli collar. Here we use this approach, along with experimental data, to investigate the hydrodynamic advantages of flagella positioning, cell density, and the influence of colony shape on the swimming and feeding abilities of C. flexa colonies.     

Computational analysis of body shape effect in diamond fish schools

The propulsive performance of fish like swimmers in schools and individually has been studied thoroughly to understand hydrodynamic interactions found in nature. In this research, we parametrically study the effects of varying the body shape of four carangiform swimmers, schooling in a diamond shape, on their hydrodynamic performance. This study uses a class shape transformation parametrization method to create fish body shapes, independently varying the maximum thickness, location of maximum thickness along the body, leading edge radius, and boattail angle. An in-house immersed boundary method-based incompressible flow solver is then used to compute the performance coefficients and wake structure of the school. Schooling performance is defined in terms of thrust increase, drag reduction, and power consumption relative to a solo swimmer. Our results show how varying body shapes of undulating swimmers causes distinct changes in its performance and wake interactions while in a school. These results will contribute to understanding body shapes in schooling scenarios as well as adding to information used to design bio-inspired underwater robot swarms.   

Flow-coupled swimmers self-organize into energetically cooperative or greedy spatial patterns

Schooling fish interact, in addition to socially, physically through the fluid medium. Cooperative versus greedy group dynamics are often associated with social interactions, whereas flow interactions are thought to enable individuals to derive energetic benefits when swimming in groups. Here, using fluid-structure interactions models, we corroborate previous findings that flapping swimmers self-organize into stable and energy-efficient formations with only flow-interaction. Furthermore, in these stable formations, the separation distance between pairs of swimmers and the difference in flapping phase follows a universal linear relationship. Importantly, we demonstrate in larger groups that flow interactions are sufficient create versatile spatial patterns, ranging from cooperative “phalanx" patterns that favor egalitarian distribution of energy savings among group members to greedy “inline" patterns where few members get maximal benefit, leaving trailing swimmers with diminished opportunities for maintaining group coherence and gaining energetic advantage. These findings emphasize the role of flow physics in the emergence of cooperative and competitive group dynamics and hint at an intriguing prospect that, unless challenged to cooperate, fish dynamically position themselves within the school to compete over energetically favorable positions.