Session T41: Swimming, Motility and Locomotion

Undulatory swimming on a free surface

A wide variety of swimmers in nature use body undulations to generate a propulsive force, in part owing to the relative insensitivity of the principle of undulatory swimming to the value of the Reynolds number $Re=UL/\nu$, which measures the relative importance of viscous and inertial forces in the flow considered ($U$ and $L$ being the typical speed and length of the animal, and $\nu$ the kinematic viscosity of the surrounding fluid). Here we study a flexible filament forced to oscillate by imposing a harmonic motion to one of its extremities (using magnetic interactions) and propelling itself at the surface of a water tank. This experiment serves as a canonical model for studying the interactions between an elastic structure undergoing complex deformations and the surrounding fluid.   

Geometry, Curvature, and Locomotion

Many animals and robots locomote by undulating their bodies in traveling waves. Together with the generally inextensible nature of such systems, the large deformations involved in these motions introduce significant nonlinearities into their analysis. As a result, the equations of motion for these systems are often treated as black boxes -- the displacement resulting from a given input (e.g., wave amplitude) can be calculated, but the relationship between the inputs and the net displacement over a period of the wave is hidden inside the nonlinearities. Drawing on results from the geometric mechanics community, we have developed an analysis framework for high-deformation locomotion that looks inside this black box, based on three core principles: (1) Working in terms of body curvature provides a linear basis for describing nonlinear high-deformation shapes. (2) Lie bracket analysis (the exploitation of system nonlinearities through oscillatory inputs) captures the nonlinearity of the system interaction with the world. (3) Systematically optimizing the coordinate choice transforms the system nonlinearity into a form that can be geometrically analyzed over the space of body curvatures to characterize the system's ultimate locomotory capabilities.   

Optimizing turning for locomotion

Speed and efficiency are common and often adequate metrics to compare locomoting systems. These metrics, however, fail to account for a system's ability to turn, a key component in a system's ability to move a confined environment and an important factor in optimal motion planning. To explore turning strokes for a locomoting system, we develop a kinematic model to relate a system's shape configuration to its external velocity. We exploit this model to visualize the dynamics of the system and determine optimal strokes for multiple systems, including low Reynolds number swimmers and biological systems dominated by inertia. Understanding how shape configurations are related to external velocities enables a better understanding of biological and man made systems. Using these tools, we can justify biological system motion and determine optimal shape configurations for robots to maneuver through difficult environments.   

Effect of confinements: Bending in Paramecium

Paramecium is a unicellular eukaryote which by coordinated beating of cilia, generates metachronal waves which causes it to execute a helical trajectory. We investigate the swimming parameters of the organism in rectangular PDMS channels and try to quantify its behavior. Surprisingly a swimming Paramecium in certain width of channels executes a bend of its flexible body (and changes its direction of swimming) by generating forces using the cilia. Considering a simple model of beam constrained between two walls, we predict the bent shapes of the organism and the forces it exerts on the walls. Finally we try to explain how bending (by sensing) can occur in channels by conducting experiments in thin film of fluid and drawing analogy to swimming behavior observed in different cases.   

Enhanced swimming motion of nematode in a non-Newtonian fluid

Small organisms navigate their complex terrestrial substrates, which have the property of non-Newtonian complex fluids. Although a large body of literature exists on the locomotion of these organisms, the previous studies are mostly limited in simple Newtonian systems. Here we present experimental results on the locomotion of Caenorhabditis elegans (C. elegans), especially investigated in colloidal suspensions that exhibit the behavior of shear thinning fluid in the range of shear rate of undulating nematode. Interestingly, we observed that the swimming speed of nematodes was gradually increased with an increase of particle volume fraction in suspensions, and this enhanced motion of nematode is closely related to the shear thinning in the fluid viscosity.   

Hydrodynamic Optimality in the Bacterial Flagellum

Most bacteria swim through fluids by rotating helical flagella which can take one of 12 distinct polymorphic shapes, the most common of which is the normal form used during forward swimming runs. To shed light on the prevalence of the normal form in locomotion, we have gathered all available experimental measurements of the various polymorphic forms and computed their intrinsic hydrodynamic efficiencies. The normal helical form is found to be the most efficient of the 12 polymorphic forms by a significant margin--a conclusion valid for both the peritrichous and polar flagellar families, and robust to a change in the effective flagellum diameter or length. Hence, although energetic costs of locomotion are small for bacteria, fluid mechanical forces may have played a significant role in the evolution of the flagellum.   

Characterisation of metachronal waves on the surface of the spherical colonial alga \textit{Volvox carteri}

\textit{Volvox carteri} is a spherical colonial alga, consisting of thousands of biflagellate cells. The somatic cells embedded on the surface of the colony beat their flagella in a coordinated fashion, producing a net fluid motion. Using high-speed imaging and particle image velocimetry (PIV) we have been able to accurately analyse the time-dependent flow fields around such colonies. The somatic cells on the colony surface may beat their flagella in a perfectly synchronised fashion, or may exhibit metachronal waves travelling on the surface. We analyse the dependence of this synchronisation on fundamental parameters in the system such as colony radius, characterise the speed and wavelength of the observed metachronal waves, and investigate possible models to account for the exhibited behaviour.   

Collective dynamics of active suspensions in confined geometries

We discuss the collective dynamics of suspensions of self-propelled particles confined in confined geometries. First, we revisit the conventional description of the hydrodynamic couplings between swimmers living in thin films or in shallow channels. We show that these hydrodynamic interactions are chiefly set by the particle size and shape irrespective of the microscopic propulsion mechanism. Second, we use kinetic theory to study the phase behavior of dilute suspensions. Finally, we exploit these results to show that the hydrodynamic interactions destabilize isotropic suspensions of polar particles, thereby yielding spontaneous collective motion at large scales. In contrast, suspensions of apolar particles only display weakly cooperative motion at small scales. We also investigate the case of aligned suspensions. Their behavior is very similar to the bulk phase of dipolar swimmer. They display generic instabilities at all scales. Comparisons of our theoretical findings with experiments on artificial swimmers will be shown.   

Giant number fluctuations in self-propelled particles without alignment

Giant number fluctuations are a ubiquitous property of active systems. They were predicted using a generic continuum description of active nematics, and have been observed in simulations of Vicsek-type models and in experiments on vibrated granular layers and swimming bacteria. In all of these systems, there is an alignment interaction among the self-propelled units, either imposed as a rule, or arising from hydrodynamic or other medium-mediated couplings. Here we report numerical evidence of giant number fluctuations in a minimal model of self-propelled disks in two dimensions in the absence of any alignment mechanism. The direction of self-propulsion evolves via rotational diffusion and the particles interact solely via a finite range repulsive soft potential. It can be shown that in this system self propulsion is equivalent to a non Markovian noise whose correlation time is controlled by the amplitude of the orientational noise.   

Chemotactic Self-Organization of Bacteria in Three-Dimensions

Self-assembly with cellular building blocks represents an important yet relatively unexplored area of research. In this talk, we describe the self-assembly of motile cells using three-dimensional (3D) patterns of chemical (such as chemoattractants) that guide cellular and organization. These 3D chemical patterns are created when chemicals are released via diffusion from lithographically patterned self-assembled polyhedral containers. We show that a number of conceptually different strategies can be utilized for chemical patterns creation. In one such strategy, the overall shape of the container can be chosen to closely match the desired 3D spatial profile. As a part of a different strategy, we discuss how the chemical patterns can be engineered by specific placement of pores on the polyhedral containers. Combining these two strategies allows chemicals to be released in a variety of spatial patterns. To demonstrate applicability of our concept to in vitro organization of living cells in specific 3D geometries, we describe chemotactic self-organization of E. coli bacteria in a variety of well-defined shapes and space curves. We link the parameters that characterize the patterns of cells and the patterns of chemicals and describe how one can engineer the spatial shape of the multicellular constructs.   

Collective Dynamics of a Laboratory Insect Swarm

Self-organized collective animal behavior is ubiquitous throughout the entire biological size spectrum. But despite broad interest in the dynamics of animal aggregations, little empirical data exists, and modelers have been forced to make many assumptions. In an attempt to bridge this gap, we report results from a laboratory study of swarms of the non-biting midge {\it Chironomus riparius}. Using multicamera stereoimaging and particle tracking, we measure the three-dimensional trajectories and kinematics of each individual insect, and study their statistics and interactions.   

Dimensional transitions for coupled rotational/translational diffusion in powered nanorotors

Small colloidal particles in fluids are well-known to engage in rotational and translational Brownian motion. Over the past several years, experimentalists have developed a new class of colloidal particles which exhibit autonomous powered motion due to consumption of chemical fuels. Two such classes of nanomotor that have been developed are linear and rotary motors. Nanorotors engage in cyclical motions due to asymmetries in the distribution of force on the surface of the particles. We have analyzed the diffusion of powered rotary motors, considering how the addition of a powered component to their motion affects their diffusional properties.   

Swimming of bio-inspired micro robots in circular channels

In recent years, bio-inspired micro swimming robots have been attracting attention for use in biomedical tasks such as opening clogged arteries, carrying out minimally invasive surgical operations, and carrying out diagnostic tasks. There have been a number of experimental and modeling studies that address swimming characteristics of micro swimmers with helical tails attached to magnetic heads that rotate and move forward in rotating external magnetic fields. We carried out experimental studies with millimeter long helical swimmers in glass tubes placed in between Helmholtz coils, and demonstrated that swimming speed increases linearly with the frequency of the external field up to the step-out frequency. In order to study interaction of the swimmer with the circular boundary we used a computational fluid dynamics model. In simulations we compared swimming speeds of robots with respect to the frequency of the external magnetic field, wavelength and amplitude of the helical tail, and distance to the channel wall. According to simulation results, as the swimmer gets closer to the boundary swimming speed and efficiency improve. However step-out frequency decreases near the wall due to increased torque to rotate the swimmer.   

Bristle-Bots: a model system for locomotion and swarming

The term {\em swarming} describes the ability of a group of similarly sized organisms to move coherently in space and time. This behavior is ubiquitous among living systems: it occurs in sub-cellular systems, bacteria, insects, fish, birds, pedestrians and in general in nearly any group of individuals endowed with the ability to move and sense. Here we address the problem of the origin of collective behavior in systems of self-propelled agents whose only social capability is given by aligning contact interactions. Our model system consists of a collection of Bristle-Bots, simple automata made from a toothbrush and the vibrating device of a cellular phone. When Bristle-Bots are confined in a limited space, increasing their number drives a transition from a disordered and uncoordinated motion to an organized collective behavior. This can occur through the formation of a swirling cluster of robots or a collective dynamical arrest, according to the type of locomotion implemented in the single devices. It is possible to move between these two major regimes by adjusting a single construction parameter.