Session V11: Focus Session: Nonlinear Hydrodynamics of Swimming Cells

The hydrodynamics of chiral micro-swimmers

Many species of bacteria utilize rotating rigid helical flagella to propel themselves in a low Reynolds number environment. Recent experiments demonstrate that artificial micro-swimming employing this kind of locomotion is realizable by using magnetic fields to rotate colloidal structures that possess chiral symmetry. We perform a series of numerical simulations to investigate the hydrodynamics of the helical shapes found in natural swimmers as well as those developed for artificial systems. We quantify the dependence of the rotation-translation coupling on the geometry of the swimmer and assess the hydrodynamic efficiency for different chiral shapes. From this analysis, we identify optimal shapes and provide insight into artificial micro-swimmer design.   

Paramecium swimming in a capillary tube

Micro-organisms exhibit different strategies for swimming in complex environments. Many micro-swimmers such as paramecium congregate and tend to live near wall. We investigate how paramecium moves in a confined space as compared to its motion in an unbounded fluid. A new theoretical model based on Taylor's sheet is developed, to study such boundary effects. In experiments, paramecia are put inside capillary tubes and their swimming behavior is observed. The data obtained from experiments is used to test the validity of our theoretical model and understand how the cilia influence the locomotion of paramecia in confined geometries.   

Experimental measurement of the flow field around a freely swimming microorganism

Despite their small size, the fluid flows produced by billions of microscopic swimmers in nature can have dramatic macroscopic effects (e.g. biogenic mixing in the ocean). Understanding the flow structure of a single swimming microorganism is essential to explain and model these macroscopic phenomena. Here we report the first detailed measurement of the flow field around an isolated, freely swimming microorganism, the spherical alga Volvox, and discuss the implications of this measurement for other species.   

Swimming Microorganisms in Gels

Many swimming microorganisms must move through viscoelastic fluids and gels. In this talk I focus on swimming through gels. First, unlike incompressible fluids, a gel can have compressional modes with relative motion between polymer and solvent fractions. In a continuum model for a gel, we show that compressibility can increase the swimming speed of Taylor's swimming sheet. The zero-frequency shear modulus of a gel requires altered boundary conditions on the swimmer. Second, many biological gels are heterogeneous on the lengthscale of swimming microorganisms, necessitating non-continuum models that treat the gel network and swimmer on equal footing. We show that a random network modeled as dilute, immobile spherical obstacles increases the average swimming speed of a Golestanian three-sphere swimmer.   

Model for hydrodynamic synchronization of beating cilia in a viscoelastic fluid

The synchronization of beating flagella or cilia is important for swimming microorganisms such as Chlamydomonas as well as transport processes such as the clearing of foreign bodies from the airway. Many of these situations involve Newtonian fluids, but some such as the airway involve viscoelastic fluids. A hypothesis currently under intense investigation is that hydrodynamic interactions between nearby beating cilia lead to synchronization. Theoretical studies of simple models consisting of orbiting spheres in Newtonian liquids show that the spheres lock phases when they are subject to suitable normal forces. This talk describes a theoretical study of how synchronization arises in viscoelastic fluids.   

Viscosity of suspension of swimming bacteria

Measurements of the shear viscosity in suspensions of swimming \textit{Bacillus subtilis} in free standing liquid films have revealed that the viscosity can decrease by up to a factor of seven compared to the viscosity of the same liquid without bacteria or with non-motile bacteria. The reduction in viscosity is observed in two complimentary experiments: one studying the decay of a large vortex induced by a moving probe and another measuring the viscous torque on a rotating magnetic particle immersed in the film. The viscosity depends on the concentration and swimming speed of the bacteria. The viscosity reduction is attributed to the effect of self- propulsion of swimming bacteria.   

Flagellated bacteria trace out a parabolic arc under low shear condition

The measurement and prediction of bacterial transport of bacteria in aquatic systems is of fundamental importance to a variety of fields such as groundwater bioremediation ascending urinary tract infection. The motility of pathogenic bacteria is, however, often missing when considering pathogen translocation prediction. Previously, we reported that flagellated E. coli can translate upstream under low shear flow conditions (Hill \textit{et al}., 2007). The upstream swimming of flagellated microorganisms depends on hydrodynamic interaction between cell body and surrounding fluid flow. In this study, we use a breathable microfluidic device to image swimming \textit{E. coli} and \textit{P. aeruginosa} at a glass surface under low shear flow condition. We find the dominant experimental variables that lead to upstream swimming are: fluid shear, bacterium velocity, and bacterium length. We will present data showing that the sum of forces and torques acting on a bacterium lead to them tracing out a parabolic arc as they turn into the flow to swim upstream.   

The Stampeding Crowd: Guiding Micro-Organisms in Microfabricated Environments

Custom-made microstructures are used to influence the motion of micro-organisms. By exploiting the runs-and-tumble swimming dynamics of bacteria, we show that their motion can be rectified using asymmetric funnel-shaped structures [Galajda et al. J. Bact. 2007]. However, a large enough population of cells is able to chemotactically ``escape'' an array of funnel barriers by collectively modifying their chemical micro-environment[Liao and Lambert, Submitted 2009]. This invasion-like behavior relates to that of metastatic cancer cells: cells leave an initially confined environment to populate neighboring tissues. We extend the use of microstructured devices to the study of cancer cells motility. We use microscopic channels and funnel-shaped barriers to physically constrain and guide mammalian cells. Cells with different motility are inoculated inside the devices and their collective motion is studied. We find that the difference in cell motility between cancer cells at different stages of progression may be used to sort them. These studies could prove important to the understanding of the dynamics of tissue invasion and metastasis.   

Hydrodynamic Synchronization in a Multiple-Paddle Model System

Hydrodynamic synchronization is important in many biological systems such as beating cilia and cell motility. Here we study a model problem, in which flexible paddles rotate in a viscous liquid. We examine a three-paddle system and show that, depending on the arrangement, paddles can exhibit either a periodic phase difference variation or converge to a synchronization state. The phase difference in the synchronized state is determined not only by the symmetry of the paddle but also by the paddles' relative position. Measurement of paddles' rotational speeds shows that the drag between paddles is minimized during synchronization. Theoretical approaches developed for two-paddle systems are extended to the current geometries, and numerical simulations, using the method of regularized stokeslets, are also used to explore the dynamics of multiple paddle systems.   

Swimming bacteria power microscopic gears

While the laws of thermodynamics prohibit extraction of useful work from the Brownian motion of particles in systems at equilibrium, under non-equlibrium conditions their motions can be ``rectified'', for example, in the presence of asymmetric geometrical obstacles. We describe a class of systems in which aerobic bacteria \textit{Bacillus subtilis} moving randomly in a fluid film power submillimeter gears and primitive systems of gears decorated with asymmetric teeth. The directional rotation is observed only in the regime of collective bacterial swimming and the gears' angular velocities depend on and can be controlled by the amount of oxygen available to the bacteria. The ability to harness and control the power of collective motions appears an important requirement for further development of mechanical systems driven by microorganism.   

Fluid Mixing by Active particles

For systems with low Reynolds number, mixing is efficient only via chaotic advection. We investigate the dynamics of active particles suspended in chaotic two-dimensional, incompressible fluid flows. The spheroidal particles have their own intrinsic velocity and they strongly affect the bulk mixing dynamics. We observe that swimmers break transport boundaries in the flow that fluid elements could not cross. We also show that in some limits, swimming can lead to interesting phenomena like particle trapping and formation of patterns.   

The fidelity of adaptive phototaxis

Along the evolutionary path from single cells to multicellular organisms with a central nervous system are species of intermediate complexity which move in ways suggesting high-level coordination, yet have none. Instead, organisms within this category possess many autonomous cells which are endowed with programs that have evolved to achieve concerted responses to environmental stimuli. We examine the main features of the program underlying high-fidelity phototaxis in colonial algae which spin about a body-fixed axis as they swim. Using micromanipulation and particle image velocimetry of flagella-driven flows in {\it Volvox carteri}, we show that there is an adaptive response at the single-cell level that displays a pronounced maximum in its frequency dependence for periodic light signals. Moreover, the natural rotational frequency of the colony is tuned to match this optimal response. A hydrodynamic model of phototactic steering further shows that the phototactic ability decreases dramatically when the colony does not spin at its natural frequency, a result confirmed by phototaxis assays in which colony rotation was slowed by increasing the fluid viscosity.