June 1 - 5, 2010
Keywords: fish swimming, vortices, krill, fins
Abstract: We consider two problems related to the propulsion of
flexible surfaces in vortex wakes.
First, we present a simple model of a trout swimming in a cylinder
wake, which saves energy by slaloming through a vortex
street. We find analytic solutions
and compare with previous experiments and numerics.
Second, we study ``inverted drafting'' in flags, in which the drag force on one flag is increased by excitation from the wake of another. The types of drafting and dynamics (synchronization and erratic flapping) depend on the separation distance between the flags. We may also discuss recent work on krill swimming and an optimal design for fish fins.
The traditional paradigm for the lab-based study of animal behavior has been to place an organism in a restricted environment and to understand it through the lens of a discrete set of allowed behaviors. While these limitations allow for more focused questions and higher data throughput, the particularities of these restrictions almost inevitably have implications for the resulting output. Moreover, the choice of a discretized classification by which the experiment describes the animal’s movements is often fraught with arbitrariness and anthropomorphism -- as well as the fact that a discrete set of behaviors may not even exist in the first place. What we aim to do here is to apply a data-driven approach to parameterize the behavior of a genetic model species, the fruit fly Drosophila melanogaster. Borrowing techniques from computer vision, machine learning, nonlinear dynamics, and statistical physics, our goal is to film long sequences of the insects moving within a relatively unrestricted environment and to translate these sequences into time-series data. From these time-series, we hope to build a descriptive language for fly behavior that can provide insight into how these creatures move, groom, communicate, mate, and otherwise live their lives.
The locomotion of biological microorganisms has been the object of much research over the last half of a century. Although significant progress has been made in the study of motion in Newtonian fluids, many biological cells such as bacteria often encounter viscous environments with suspended microstructures or macromolecules. The physics of micro-propulsion in such a non-Newtonian viscoelastic fluid has only recently started to be addressed. In our work, we present a numerical study of the motility of an axisymmetric spherical squirmer in a polymeric flow.
The microswimmer that we consider here is driven by a purely tangential distortion on the outer surface reproduced as non-homogenous boundary condition on a rigid sphere. We solve the hydrodynamic Stokes equation (zero Reynolds number) with the extra stress term generated by advection and stretching of polymers. As transport equation for the polymeric stress, we use here the nonlinear Giesekus model.
The swimming speed is lower in a visco-elastic fluid and is asymptotically recovering for large Weissenberg numbers approaching values only about 15% smaller than in a Newtonian fluid. Interestingly, the efficiency is seen to significantly increase as the viscosity of the polymeric fluid is increased.
Many biological systems use flexible filaments moving in a viscous fluid to achieve motility or fluid transport. Examples include bacteria that use flagella to swim, paramecium that use cilia for motion and cilia on the wall of the lungs used for particulate removal. In tall of these cases, the filaments are observed to synchronize their motion, and since there is no chemical or physiological coordination, this synchronization is thought to be mediated by hydrodynamic forces. We demonstrate the use of a model system that captures all of the essential features in hydrodynamic synchronization, including multiple filaments interacting through viscous stresses, as well as the presence of structural flexibility in each filament, which is known to be a necessary component for synchronization. We explore the dynamics of hydrodynamic synchronization in this modelsystem using experiments, numerical simluations that employ regularized Stokeslets, and a simple analtyical model. All three approaches give consistent results and point to the relative roles of viscous stresses, structural flexibility in the synchronization dynamics.
Joint work with John O. Kessler (Physics Department, University of Arizona, Tucson, AZ 85721).
Keywords: bacteria, interacting self propelled particles, collective behavior, PIV, bio-fluid-dynamics
Abstract: Spatial order and fast collective coherent dynamics of
populations of swimming bacteria emerges from local
interactions and from flows generated by the organisms’
locomotion. The transition from dilute, to intermediate, to
high concentrations of cells will be demonstrated by movie
clips. Analyses of these data, presented as probability density
functions for swimming velocity, show that the low
concentration phase which exhibits swimming speeds
characteristic of individual bacteria, arrives at the
anomalously high speed phase, ZBN, the ZoomingBioNematic, via
an intermediate phase that exhibits surprisingly low mean
speeds. The origin of this phenomenon relates to scattering and
the known dynamics of velocity flipping. Particle Imaging
Velocimetry (PIV) was used for analysis of mixing, and of
collective velocities, correlated with alignment within
coherent patches.
Supported by the Department of Energy, grant DOE-W-31-109-ENG-38.
Keywords: fish/eddy interaction, vorticity, evolution of
control surfaces and function, turbulence, fish responses.
Abstract: The natural habitats of fishes are characterized by water
movements driven by a
multitude of physical processes of either natural or human
origin. The resultant
unsteadiness is exacerbated when flow interacts with surfaces,
such as the bottom and
banks, and protruding objects, such as corals, boulders, and
woody debris. There is
growing interest in the impacts on performance and behavior of
fishes swimming in
"turbulent flows." The ability of fishes to stabilize body
postures and their swimming
trajectories is thought to be important in determining species
distributions and densities,
and hence resultant assemblages in various habitats.
Furthermore, water flow, structure
and vorticity are related to the shape of the body and fins of
fishes swimming largely in
relatively steady flows. Adaptations to minimize energy losses
would be anticipated. We
suggest such mechanisms may be found in varying the length of
the propulsive wave,
stiffening propulsive surfaces, and shifting to use of the
median and paired fins when
swimming at low speeds. The archetypal streamlined "fish" shape
reduces destabilizing
forces for fishes swimming into eddies. Understanding impacts
of turbulence and
vorticity on fishes is important as human practices modify
water movements, and as
turbulence-generating structures ranging from hardening
shorelines to control erosion,
through designing fish deterrents, to the design of fish
passageways become common.
There has been much recent interest in understanding the
dynamics of low-Reynolds-number swimmers near no-slip boundaries and free capillary
surfaces. This talk will present
theoretical ideas for studying the dynamics of such swimmers
within the framework of
simple two dimensional models. The 2D models are developed
using the methods of complex analysis and afford significant
analytical advantages while
still capturing the essential
mechanisms of (certain) fully three dimensional situations. In
many cases the approach
yields explicit nonlinear dynamical systems that can be
directly studied. The models can
rationalize behaviour observed in numerical and laboratory
experiments and can provide
predictions for the swimmer dynamics in more complicated
situations. We will survey results on swimming near a no-slip wall
[joint work with Y. Or], swimming in other conned
geometries [joint work with O. Samson] and swimming near a free
capillary surface [joint
work with S. Lee, O. Samson, A. Hosoi and E. Lauga].
Using a nonlocal nematic potential, we present a kinetic theory for nonhomogeneous suspensions of micoswimmers. We then study the steady states to an imposed weak shear. Our results show that the activity parameter will result in permeative or oscillatory flow behaviors at the leading order depending the Leslie tumbling parameter. The linear viscoelasticity is also calculated, which is similar to chiral liquid crystals.
Keywords: vortices, locomotion, swimming, flying
Abstract: The formation and shedding of fluid vortices is an inevitable consequence
of movement for all but the smallest of swimming and flying organisms. Can
animals use these vortices to enhance locomotion? If so, can their methods
of vortex-enhanced propulsion be translated to engineered systems? This
talk will describe experimental studies of jellyfish and numerical
simulations of eels that suggest candidate mechanisms to enhance the
efficiency and speed of locomotion by using vortices. A bio-inspired
underwater vehicle is created to test the ideas in an engineering context.
It appears that swimming and flying animals have significant opportunities
to optimize their locomotion by making use of vortices.
Keywords: squid, scallop, jet propulsion, hydrodynamic efficiency, Antarctica, ontogeny, scaling
Abstract: Among multicellular animals, jet propulsion is nature’s simplest (and arguably its oldest) form of aquatic locomotion. Any flexible, hollow body girdled by circumferential muscle fibers, can, by expelling fluid through an orifice, produce thrust and thereby swim. Despite the fundamental simplicity of this locomotory mechanism, aspects of its realization in nature continue to provide insight into the physiology, ecology, and evolution of a wide variety of animals. In this talk, I report on two mollusks that use jet propulsion. The Antarctic scallop is one of only a few bivalves that can swim. Like its temperate and tropical cousins, it claps its shells together to expel a jet of water sufficiently powerful to lift both its internal organs and its dense calcium-carbonate shell off the seafloor. But the Antarctic scallop must perform this feat in water at -1.86 degrees C, a temperature at which muscle power is reduced and water’s viscosity is 1.43 times that of tropical water. Shell mass in the Antarctic scallop is much reduced relative to tropical scallops, but muscle mass is reduced even more. The only net advantage evident in Antarctic scallops is the increased resilience of the “spring” that opens the shell, suggesting that even slight increases in hydrodynamic efficiency can be selected during evolution. Increases in hydrodynamic efficiency may also play an important role in squid locomotion. Unlike most jet propulsors (e.g., jellyfish, salps, clams), squids can actively control the size of the orifice through which water is expelled. Appropriate narrowing of the jet orifice during mantle contraction can boost the efficiency of both the hydrodynamics of propulsion and the contraction of muscle. This potential increase in efficiency may be most important in small juvenile squid, for whom jet propulsion is otherwise very inefficient.
We present a formulation for coupled solutions of fluid and body dynamics in problems of biolocomotion. This formulation unifies the treatment
at moderate to high Reynolds number with the corresponding inviscid problem. By a viscous splitting of the Navier–Stokes equations, inertial forces from the fluid are distinguished from the viscous forces, and the former are further decomposed into contributions from body motion in irrotational fluid and ambient fluid vorticity about an equivalent stationary body. In particular, the added mass of the fluid is combined with the intrinsic inertia of the body to allow for simulations of bodies of arbitrary mass, including massless or neutrally buoyant bodies. The resulting dynamical equations can potentially illuminate the role of vorticity in locomotion, and provide new pathways toward reduced-order modeling. Examples of articulated or continuously deforming bodies undergoing swimming or flying kinematics are presented and discussed.
In this new implementation of the Immersed Interface Method, we solve for the coupled dynamics of free moving objects in a fluid. We test the code by comparing our results with experimental data on falling plates and cylinders. We further present the dynamics of an array of falling cylinders and contrast the results of the even and odd configuration.
The ulcer-causing gastric pathogen Helicobacter pylori is able to swim through the viscoelastic mucus gel that coats the stomach wall, but its mechanism of locomotion through an acidic gel environment is poorly understood. This experimental study indicates that the helicoidal-shaped H. pylori achieves motility by altering the rheological properties of its environment. H. pylori locally raises the pH of its environment in order to survive in the acidic conditions of the stomach. This local change of pH affects the rheology of the surrounding mucus material. We show that gastric mucus is pH dependent, changing from a gel at acidic conditions (low pH) into a viscous solution at more neutral conditions (higher pH). Microscopy studies of the motility of H. pylori in gastric mucin show that the bacteria swim freely at high pH, and are strongly constrained at low pH.
Joint work with J. P. Celli, B. S. Turner, N. H. Afdahl, S. Keates, I. Ghiran, C. Kelly, G. H. McKinley, P. So, S. Erramilli, and R. Bansil.
http://dx.doi.org/10.1073/pnas.0903438106
In an effort towards an understanding of the generation and control of vertebrate locomotion, including the role of the CPG and its interactions with reflexive feedback, muscle mechanics,
and external fluid dynamics, we study a simple vertebrate, the lamprey.
Lamprey body undulations are a result of a wave of neural activation that passes from head to tail, causing a wave of muscle
activation. These active forces are mediated by passive structural forces.
We present a model that includes the complete fluid-structure interaction problem, in which the body is elastic and deforms according to both internal muscular forces and
external fluid forces. The model uses an immersed-boundary framework for solving the Navier-Stokes equations of fluid motion, and includes a nonlinear muscle model, an elastic body, and an adaptive solver that is accurate at length and velocity scales that are appropriate for swimming lampreys.
The effects of various body and environmental properties, including tapered and uniform body shapes, different body stiffness, varying muscle parameters, and a range of viscosities are examined as they relate
to swimming dynamics and energy requirements. (This is joint work with Chia-yu Hsu, Eric Tytell, Thelma Williams, Tyler McMillen and Avis Cohen.)
Keywords: hydrodynamics, lift-based propulsion, leading edge tubercles, dolphin, whale, manta, vorticity control
Abstract: Optimization of energy by large aquatic animals (e.g., dolphins, whales, manta) requires adaptations that control hydrodynamic flow to reduce drag, and improve thrust production and efficiency. Although streamlining of the body and appendages minimizes drag, highly derived aquatic animals utilize mechanisms of propulsion and control based on lift generation, which maximizes thrust production and minimizing drag. Oscillations of the wing-like fins and flukes, which are hydrofoils, generate thrust throughout the stroke cycle and maintain a propulsive efficiency over 80%. This high efficiency is dependent on spanwise and chordwise bending and management of swimming kinematics to control vorticity. Control of vorticity to improve locomotor performance for maneuverability is enhanced by modification to the leading edge of control surfaces. The humpback whale (Megaptera novaeangliae) flippers are unique because of the presence of large tubercles along the leading edge, which gives this surface a scalloped appearance. The tubercles function to produce vortical flows over the surface of the flipper and control lift characteristics at high angles of attack, where stall would occur. The potential benefits from mimicking these biological innovations as applied to engineered systems operating in fluids are high speeds, vorticity control, reduced detection, energy economy, and enhanced maneuverability.
Throughout the natural world, cells and organisms use flagella and cilia to propel fluid, achieve cell motility and a range of other functions. The mechanism regulating their waveform, however, is a long-standing biological problem. Indeed, the emergence of such flagellar undulatory waves is a consequence of an intricate balance of fluid dynamic viscous forces, flagellar elastic resistance, and the active bending generated by internal motor proteins. By using theoretical modelling and numerical computations accounting for high curvatures observed physiologically, we show that flagellar compression due to viscous friction and the internal forces may initiates an effective buckling behaviour that leads to an asymmetric flagellar beating and, consequently, switching sperm swimming from a straight migratory trajectory to a circling path. These results demonstrate that observed asymmetric flagellar beating may arise due to a dynamic instability, and not necessarily require some intrinsic asymmetric in the beating mechanism. This behaviour may be important in understanding mammalian sperm trapping, potentially a crucial step in natural fertilisation.
Studying human spermotozoa motility is a subject of growing
importance due to human male subfertility and the fact that the
in-vitro fertilisation interventions that bypass normal sperm
motility are invasive and entail significant risk for the
healthy female partner, as well as being economically
prohibitive for many. We present examples of how fluid and
continuum dynamics can provide novel insights concerning the
mechanics of human spermatozoon behaviour, focussing on the
interpretation of recent high resolution imaging.
In this talk I will summarize our recent progress in experiments and models of the locomotion of a sand-swimming lizard, the sandfish ({em Scincus scincus}). We use high speed x-ray imaging to study how the 10 cm-long sandfish swims at 2 body-lengths/sec within sand, a granular material that displays solid and fluid-like behavior. Below the surface the lizard no longer uses limbs for propulsion but generates thrust to overcome drag by propagating an undulatory traveling wave down the body. While viscous hydrodynamics can predict swimming speed in fluids like water, an equivalent theory for granular drag is not available. To predict sandfish swimming speed, we develop an empirical resistive force model by measuring drag force on a small cylinder oriented at different angles relative to the displacement direction and summing these forces over the animal movement profile. The model correctly predicts the animal's wave efficiency (ratio of forward speed to wave speed) as approximately 0.5. The empirical model agrees with a more detailed (and more accurate) numerical simulation: a multi-segment model of the sandfish coupled to a multi-particle Molecular Dynamics simulation of the granular media. The agreement between models and the prediction of biological wave efficiency demonstrate that the non-inertial swimming occurs in a frictional fluid and the Molecular Dynamics simulation allows us to visualize the self-generated fluid surrounding the sandfish as it swims. We use the principles discovered to construct a sand-swimming physical model (a robot) which, like in our empirical and multi-particle numerical model, swims fastest using the preferred sandfish wave pattern.
Legged locomotion on flowing ground ({em e.g.}~granular media) is unlike locomotion on hard ground because feet experience both solid- and fluid-like forces during surface penetration. Recent bio-inspired legged robots display speed relative to body size on hard ground comparable to high performing organisms like cockroaches but suffer significant performance loss on flowing materials like sand. In laboratory experiments we study the performance (speed) of a small (2.3~kg) six-legged robot, SandBot, as it runs on a bed of granular media (1~mm poppy seeds). For an alternating tripod gait on the granular bed, standard gait control parameters achieve speeds at best two orders of magnitude smaller than the 2~body lengths/s ($approx 60$~cm/s) for motion on hard ground. However, empirical adjustment of these control parameters away from the hard ground settings, restores good performance, yielding top speeds of 30~cm/s. Robot speed depends sensitively on the packing fraction $phi$ and the limb frequency $omega$, and a dramatic transition from rotary walking to slow swimming occurs when $phi$ becomes small enough and/or $omega$ large enough. We propose a kinematic model of the rotary walking mode based on generic features of penetration and slip of a curved limb in granular media. The model captures the dependence of robot speed on limb frequency and the transition between walking and swimming modes but highlights the need for a deeper understanding of the physics of granular media. Journal paper: Li et al, PNAS, 2009.
Experiments and simulations indicate that suspensions of swimming microorganisms can exhibit complex phenomena, including pattern-forming instabilities, large scale fluid motions and enhanced passive scalar transport. This talk is an overview of theoretical and computational work describing some of these phenomena. Emphasis will be placed on analysis of various correlation functions associated with the dynamics. The talk concludes with a brief presentation of new directions in this area, including the coordinated motion of collections of bacterial flagella.
This is joint work with Patrick T. Underhill and Pieter J. A. Jansssen.
A nonlinear unsteady Darcy's equation to include inertial effects of a
Hele-Shaw flow and the conditions under which it reduces to the
classical Darcy's law are discussed. In the absence of surface tension,
we derive a generalized Polubarinova-Galin equation for flows in a
circular Hele-Shaw cell using the method of conformal mapping. The
linear stability of the base-flow state is examined by perturbing the
conformal mapping in form of polynomial modes. We find that small
inertia always has the tendency to stabilize the interface.
Keywords: active suspensions, kinetic theory
Abstract: One of the challenges in modeling the transport properties of complex
fluids (e.g. many biofluids, polymer solutions, particle suspensions) is
describing the interaction between the suspended micro-structure with the
fluid itself. Here I will focus on understanding the dynamics of active
suspensions, like swimming bacteria or artificial micro-swimmers. Using a
recently derived kinetic model, I have investigated the linearized
structure of such an active system near a state of uniformity and
isotropy. I will show that system instability can arise only from the
dynamics of the first azimuthal mode in swimmer orientation, that the
growth of fluctuations for a suspension of anterior actuated swimmers is
associated with a proliferation of oscillations in swimmer orientation,
that diffusion acts as a smoothing parameter, and that at small-scales the
system is controlled independently of the nature of the suspension.
Finally a prediction about the onset of the instability as a function of
the volume
concentration of anterior actuated swimmers and a comparison with
numerical simulations is made.
Plasma membrane blebs are dynamic cytoskeleton-regulated cell protrusions that have been implicated in apoptosis, cytokinesis, and cell movement. A variety of theoretical and experimental results support the hypothesis that nonapoptotic membrane blebbing plays a central role for cell migration and cancer cell invasion. For cancer cells crawling through a 3D matrix, there are two morphologically distinguished modes of invasion: one that appears as a mesenchymal cell movement that relies on proteolytic degradation of the surrounding matrix and another that adopts a rounded, more amoeboid mode of motility that frequently is accompanied by cell blebbing. Here we will focus on the latter mode--cell migration through a 3D matrix by cell blebbing.
To date, because of the limitation of experimental systems, most mechanisms governing plasma membrane blebbing are derived from 2D standard cell cultures that display blebbing under certain conditions. For example, much has been done for blebbing cells crawling on a substrate by adhesion. When lifted to 3D environment, the mechanisms may be totally different, and in the absence of interaction between the cell and the extracellular matrix, we now come to the classic physical problem: swimming in low Reynolds number fluid. One possible propulsive mechanism in a low Reynolds number environment is cyclic deformation of the cell membrane. Two of the most important biological phenomena related to this cyclic cell shape deformation are the observed shape oscillations and cell blebbing. The former one may be well generalized to a single swimming sphere at low Reynolds number that exerts self-propulsion by means of small amplitude, high-frequency waves over the surface. However, for the cell blebbing problem, one sphere model may not be adequate. Instead, a minimal model may comprise several connecting spheres that can exchange mass among them.
In the poster, we will first present a brief review of fundamental theories of swimming at low Reynolds number, together with some previous models. Next we will advance several of my models and discuss their properties.
Joint work with Andrew K. Dickerson, Zachary G. Mills, Paul C. Foster (School of Mechanical Engineering, Georgia Institute of Technology).
While much attention has been devoted to the ability of animals to propel themselves through fluids, less work has been done on how they exploit fluids in their grooming habits. The problem of how animals clean and dry themselves involves complex flexible surfaces (hair, skin), unsteady speeds, and wetting/de-wetting of drops and fluid ligaments. In this experimental investigation, we investigate the ability of dogs, rats, mice and other hirsute mammals to rapidly oscillate their bodies in order to shed water droplets, nature's analogy to the spin cycle on a washing machine. High-speed videography and fur-particle tracking is employed to determine the angular position of the animal's shoulder skin as a function of time. We formulate the conditions for de-wetting and propulsion of water drops based on the balance of the forces of surface tension, centripetal forces (which tend to pull drops normally from the skin) and angular-acceleration forces (which tend to slide drops). We find that smaller animals shake fastest: specifically, shaking frequency scales as the shoulder radius to the -1/2 power, as is required for centripetal forces on drops to remain constant as animals grow. An important consideration in this process is the looseness of the skin with respect to the body, whose presence increases the peak speed and acceleration of their fur. The energy expenditure and remaining water moisture content of self-drying mammals is estimated.
We numerically investigate the bundling between flagella. For this, we
consider two flexible helices next to each other. Each helix is
modeled as several prolate spheroids connected at the tips by springs.
On the first spheroid, a constant torque is applied. Torsion springs
at the connections provide bending and twisting resistance.
Hydrodynamic interactions are incorporated via a modified non-singular
Stokeslet. Additionally, there is a repulsive force and torque, based
on the Gay-Berne potential to prevent crossing of the flagella.
Our results provide some insights in the details of the bundling
process. In the initial stage, rotlet interactions between the
rotating helices ensures that both deflect each other. Due to the end
point fixation, this deflection combined with the rotlet interaction
leads to the flagella rotating around each other. Longer simulations
show that the tips of a flagella pair only rotate about once around
each other, in contrast with a more complicated entwinement suggested
before. Flagella closer together bundle faster.
Most micro-organisms often swim in a variety of complex environments as their natural habitat. For instance, Paramecium tend to congregate and swim near the boundaries. We investigate the locomotion of Paramecium in confined geometries while comparing its motion in the un-bounded fluid. A modified theoretical model based on Taylor’s sheet is developed to study the boundary effect on its motion. During experiments, we introduce Paramecium in capillary tubes of different sizes and measure the influence of the tube diameter on the swimming velocity. The data from the experiments is compared with the theoretical model to test its validity and understand the ciliary locomotion of organisms in a confined channel.
The passive locomotion of a body placed in the flow of periodically-generated vortices is studied. This work is motivated by recent experimental evidence that live and dead trout exploit the vortices in the wake of an oscillating cylinder to swim upstream. We consider a simple model of a rigid body interacting dynamically with point vortices introduced periodically into the flow to emulate the shedding of vortices from an external source. We show the existence of periodic solutions where the body `swims' passively against the flow by extracting energy from the ambient vortices. We also find solutions where the body holds station in the incoming wake. However, for bodies of elongated geometries, rotational instabilities may hinder their motion. We propose active feedback control strategies to overcome these instabilities. (This is joint work with my graduate student Babak G. Oskouei)
Models for aquatic locomotion generally seek to balance fidelity and scope with analytical or computational tractability. When the goal in model development is a platform for model-based feedback control design, analytical structure is essential to provide a point of access for most current design techniques, but some fidelity may be sacrificed as long as the scope of the model encompasses the range of situations under which control will be applied. This talk will describe a model for simplified fishlike swimming based on the Hamiltonian equations governing the interaction of a free deformable body with a system of point vortices in a planar ideal fluid. The use of this model in designing motion-control strategies for a biologically inspired robotic vehicle will be discussed, with a particular focus on the realization of energy-efficient gaits for solitary swimming and energy-harvesting methods for controlled schooling.
Keyword: waves, turbulence, walking, swimming, larvae, crabs
Abstract: Turbulent ambient currents and waves in marine habitats impose forces on organisms. The locomotory performance of organisms swimming in the water column and moving across the substratum is affected by environmental fluid dynamic forces. Therefore, the functional significance of morphological features and kinematics of locomoting organisms can best be understood if studied under the range of flow conditions they experience in their natural habitats. Three examples will be discussed: 1) Many bottom-dwelling marine animals produce microscopic larvae that are dispersed to new sites by ambient water currents. How do these weakly-swimming larvae carried in wavy, turbulent water flow manage to land on the sea floor in suitable habitats? 2) Horseshoe "crabs", Limulus polyphemus, gather in the surf zone to mate. How can they crawl in the waves without being pushed in the wrong direction or overturned by the back-and-forth flow of the waves? 3) Shore crabs, Grapsus tenuicrustatus, also live on wave-swept shores, where they spend part of their time in air and part underwater. How do they run in air (where gravity predominates) versus underwater (where hydrodynamic forces are important), and what happens when a wave hits?
We perform physical experiments with self-propelled rods which
undergo
directed random motion on a substrate motivated by collective
behavior
in various active living systems such as bacterial colonies and
hoofed
animal herds. In particular, we examine the persistent random
motion
of rods as a function of the area fraction ϕ and study the
effect of
steric interactions on their diffusion properties.
Self-propelled rods
of length l and width w are fabricated with a spherocylindrical
head
attached to a beaded chain tail, and show directed motion on a
vibrated substrate. The mean square displacement on the
substrate grows linearly with time t for ϕ<w/l,
before displaying caging as ϕ is
increased, and stops well below the close packing limit. Direction
autocorrelations decay progressively slower with ϕ. We describe the
observed decrease of SPR propagation speed c(ϕ) with a tube model [1].
Further, we discuss the observed collective behavior such as
aggregation at the boundaries and swirling motion which arise because
of physical interactions between individuals [2].
[1]: "Concentration Dependent Diffusion of Self-Propelled
Rods," A.
Kudrolli, Phys. Rev. Lett. 104, 088001 (2010).
[2]: "Swarming and swirling in self-propelled granular rods,"
A.
Kudrolli, G. Lumay, D. Volfson, and L. Tsimring, Phys. Rev.
Lett. 100,
058001 (2008).
Same abstract as the contributed talk.
This experimental work is investigating a new and unique passive boundary-layer separation control methodology derived from shark skin, functioning at the micro-scale level. The skin and denticles (scales) of sharks represent over 400 million years of natural selection for swimming efficiency. Evolutionary adaptations in the morphological structure of the shark skin, to develop unique boundary layer control (BLC) mechanisms, stem from the ensuing decrease in drag, probable increase in fin performance (e.g. thrust production) and enhanced turning agility for fast-swimming sharks. Shark denticles have been documented to be capable of bristling. A bristled microgeometry mimicking shark skin results in the formation of a system of interlocking embedded cavity vortices. Three mechanisms have been hypothesized which lead to boundary layer control via deterrence of separation over the shark skin. The first mechanism is the formation of embedded micro-vortices that increase momentum in the very near-wall region due to the resulting partial slip condition. The second mechanism is that the preferential flow direction inherent in the surface geometry inhibits global flow reversal and leads to passive actuation via denticle bristling. The third mechanism involves turbulence augmentation, or an additional energizing of flow, in the near-wall region and cavities, leading to higher partial slip velocities. The study involves engineers, working together with biologists Dr. Phil Motta (University of South Florida) and Dr. Robert Hueter (Mote Marine Laboratory), to fully comprehend the morphological bristling mechanism of shark denticles. Initial results for scale angles and morphology on hammerhead and shortfin mako sharks along with flow measurements over shark skin models embedded in a turbulent boundary layer will be presented.
To study the hydrodynamics of swimming of multi-flagellated
bacteria, such as Escherichia coli, we develop a simulation
method using a bead-spring model to account for the
hydrodynamic and the mechanical interactions between multiple
flagella and the cell body, the reversal of the rotation of a
flagellum in a tumble and associated polymorphic
transformations of the flagellum. This simulation reproduces
the experimentally observed behaviors of E. coli, namely, a
three-dimensional random-walk trajectory in run-and-tumble
motion and steady clockwise swimming near a wall. Here we show
using a modeled cell that the polymorphic transformation of
flagellum in a tumble facilitates the reorientation of the
cell, and that the time-averaged flow field near a cell in a
run has double-layered helical streamlines. Moreover, the
instantaneous flow field, which is strongly time-dependent, is
more than 10-fold larger in magnitude than the time-averaged
flow, large enough to affect the migration behavior of
surrounding chemoattractants, with the Péclet number for these
molecules being larger than one near a swimming cell.
Keywords: Low Reynolds number; locomotion; symmetry-breaking; synchronization; cilia; optimization
Abstract: Fluid mechanics plays a crucial role in many cellular processes. One example is the external fluid mechanics of motile cells such as bacteria, spermatozoa, algae, and essentially half of the microorganisms on earth. The most commonly-studied organisms exploit the bending or rotation of a small number of flagella (short whip-like organelles, length scale from a few to tens of microns) to create fluid-based propulsion. As a difference, Ciliated microorganisms swim by exploiting the coordinated surface beating of many cilia (which are short flagella) distributed along their surface. In this talk, we consider two instances of symmetry-breaking arising in small-scale locomotion. First, we address the observed flagellar synchronization between eukaryotic cells swimming in close proximity. By using a two-dimensional model, we show analytically and computationally that synchronization between co-swimming cells can be driven by hydrodynamic interactions alone if there is a geometrical symmetry-breaking displayed by the their flagellar waveforms. In a second part, we pose the problem of ciliary propulsion as an optimization problem. Specifically, for a spherical body, we compute numerically and theoretically the time-periodic tangential deformations of the body surface which leads to swimming of the body with optimal hydrodynamic efficiency. We show that this calculation leads to symmetry-breaking in the surface actuation, and the emergence of waves, reminiscent of the metachronal waves displayed by real biological cilia.
Joint work with W. B. Dickson
^{2}, J. L. van
Leeuwen
^{1}, and M. H. Dickinson
^{2}.
As they descend, the autorotating seeds of maples and some
other trees generate unexpectedly high lift, but how they
attain this elevated
performance is unknown. To elucidate the mechanisms
responsible, we measured the three-dimensional flow around
dynamically scaled models of maple and hornbeam seeds. Our
results indicate that these seeds attain high lift by
generating a stable leading-edge vortex (LEV) as they descend.
The compact LEV, which we verified on real specimens, allows
maple seeds to remain in the air more effectively than do a
variety of nonautorotating seeds. LEVs also explain the high
lift generated by hovering insects, bats, and possibly birds,
suggesting that the use of LEVs represents a convergent
aerodynamic solution in the evolution of flight performance in
both animals and plants.
^{1} Experimental Zoology Group, Wageningen University, 6709 PG
Wageningen, Netherlands.
^{2} Bioengineering and Biology, California Institute of
Technology, Pasadena, CA 91125, USA.
Science 12 June 2009:
Vol. 324. no. 5933, pp. 1438 - 1440
DOI: 10.1126/science.1174196
http://www.sciencemag.org/cgi/content/abstract/324/5933/1438
We consider the stirring of an inviscid or Stoksian fluid caused by the locomotion of bodies through it. The swimmers are approximated by non-interacting cylinders or spheres moving steadily along straight lines. We find the displacement of fluid particles caused by the nearby passage of a swimmer as a function of an impact parameter. We use this to compute the effective diffusion coefficient from the random walk of a fluid particle under the influence of a distribution of swimming bodies. We find good agreement between theoretical results with simulations and identifies regions of dominant contribution to mixing. Also It is shown that Stokesian squirmers yields a great boost in effective diffusivity.
Joint work with Jean-Luc Thiffeault and Stephen Childress.
Suspensions of micro-swimmers display complex dynamics in response to
chemical substances. They preferentially move and orient toward gradients
of such a chemo-attractant in a process called chemotaxis. We present a
new chemotaxis model based on the kinetic theory of swimmer suspensions in
low Reynolds number fluid that is coupled to the chemo-attractant
dynamics. The chemotactic response is included as a phenomenon due to
fluxes in the individual swimmer. Entropy and linear stability analysis
indicates a chemotaxis-induced instability at finite wavelengths for
pusher and puller bacteria alike and regardless of their shape ratio.
Nonlinear dynamics are investigated using numerical simulations of the
full system in two dimensions. We observe aggregation in suspensions of
pullers and mixing in suspensions of pushers.
Using three-dimensional computer simulations, we examine
hovering aerodynamics of flexible planar wings oscillating at
resonance. We model flexible wings as tilted elastic plates
whose sinusoidal plunging motion is imposed at the plate root.
Our simulations reveal that large-amplitude, resonance
oscillations of elastic wings drastically enhance aerodynamic
lift and efficiency of low-Reynolds-number plunging. Driven by
a simple sinusoidal stroke, flexible wings at resonance
generate a hovering force comparable to that of small insects
that employ a very efficient, but much more complicated stroke
kinematics. Our results indicate the feasibility of using
flexible wings driven by a simple harmonic stroke for designing
efficient microscale flying machines.
When studying the mechanics of swimming and flying, engineers and
scientists often pose questions in the form of optimization strategies. This
approach has been quite useful when trying to understand the kinematics of
insect flight or the frequency that fish beat their tails. Understanding the
kinematics and the morphology of animals that multitask is not as
straightforward. For example, the elaborate tails of male guppy fish are
likely not optimized for swimming efficiency or speed, but they do increase
the likelihood of attracting a mate. In this presentation, the fluid
dynamics of the currents generated by the upside down jellyfish *Cassiopea
sp. *will be presented in the context of swimming and feeding. Medusae of
this genus are unusual in that they typically rest upside down on the ocean
floor and pulse their bells to generate feeding currents, only swimming when
significantly disturbed. The pulsing kinematics and fluid flow around these
upside-down jellyfish is investigated using a combination of videography,
digital particle image velocimetry, and numerical simulation. There is no
evidence of the formation of a train of vortex rings as observed in oblate
medusae exhibiting rowing propulsion. Instead, significant mixing occurs
around and directly above the oral arms and secondary mouths. Numerical
simulations using the immersed boundary method agree with experimental
measurements and suggest that the presence of porous oral arms induce net
horizontal flow towards the bell and the absence of coherent vortex
structures. The implications of these results on feeding and swimming
efficiency will be discussed.
Spines and other thin projections from cell surfaces literally expand the volume of fluid with which a cell interacts and may provide effective levers on which the flow can act. We use an immersed boundary formulation to solve the coupled phytoplankton-fluid system to predict the 3D trajectories of the cells within a background flow. We examine the effect of spines on the period of rotation of phytoplankton in linear shear flow.
Joint work with John O. Dabiri.
We study the dynamics and stability of the vortex wakes of
swimming
fish, with the aim of quantifying the role of vortex dynamics
in
determining the
performance and limitations of fish-like swimmers (cf the work
on
vortex rings and their relation to the performance of jetting
swimmers
by Gharib et al 1998, Krueger and Gharib 2003, Linden and
Turner 2004,
Dabiri et al 2010). In order to enable studies of the dynamics
and
stability of these vortex flows, we analyze wake kinematics
using
Lagrangian coherent structures (LCS) (Haller 2000, 2001). We
computed
FTLE field in both two and three dimensions to extract the 2D
and 3D
LCS in the wake of a numerically-simulated, self-propelled
anguilliform swimmer (Kern and Koumoutsakos 2006). The
attracting and
repelling LCS in the flow were found to clearly bound the
vortices
shed by the swimmer (Green et al 2010, Shadden et al 2006), and
the
shedding of two vortex ring per cycle and formation of a double
row of
vortex rings in the wake was observed. Fluid transport in the
wake was
studied using passive drifters seeded into the flow, and we
observed
the formation of slender lobes along the length of the swimmer,
which
"pull" fluid into the wake such that fluid particles inside
each of
these lobes are entrained into separate vortices in the
swimmer's
wake. Changes in the LCS in a flow are known to correspond to
changes
in the structure and dynamics of the underlying vortices (Green
et al
2010, O'Farrell and Dabiri 2010), thus future work will focus
on
analysis of changes in LCS structure as indicators of changes
in the
dynamics and stability of the underlying vortex flow.
References:
1) M. Gharib. E. Rambod, and K. Shariff. A universal time scale
for
vortex ring formation. J. Fluid Mech., 360:121-140, 1998.
2) P. S. Krueger and M. Gharib. The significance of vortex ring
formation to the impulse and thrust of a starting jet. Phys.
Fluids. 15:1271-81, 2003.
3) P. F. Linden and J. S. Turner. 'Optimal' vortex rings
and aquatic propulsion mechanisms. Proc. R. Soc. B, 271:647-53, 2004.
4) J. O. Dabiri, S. P. Colin, K. Katija, and J. H.
Costello. A wake-based correlate of swimming performance and foraging
behavior in seven co-occurring jelly fish species. J. Exp. Biol., 13 (8):
1217-25,
2010.
5) G. Haller. Finding finite-time invariant manifolds in
two-dimensional velocity fields. Chaos, 10:99, 2000.
6) G. Haller. Distinguished material surfaces and coherent
structures
in three-dimensional ﬂows. Physica D, 149:1851–61, 2001.
7) S. Kern and P. Komoutsakos. Simulations of optimized
anguilliform
swimming. J. Exp. Biol., 209:4841–57, 2006.
8) M. A Green, C. W. Rowley, and A. J. Smits. Using
hyperbolic
Lagrangian Coherent Structures to investigate vortices in
bio-inspired
fluid flows. Chaos, 20:017509, 2010.
9) S. .C. Shadden, J. O. Dabiri, and J. E. Marsden.
Lagrangian
analysis of fluid transport in empirical vortex ring flows. Phys.
Fluids., 18:047105, 2006.
10) C. O’Farrell and J. O. Dabiri. A Lagrangian approach to
identifying vortex pinch-off. Chaos, 20:017513, 2010.
The dynamics of a simple micro-swimmer model near a no-slip wall is formulated and analyzed. The model consists of an assemblage of spheres where propulsion is generated by rotation of the spheres. The geometric structure of the dynamics is analyzed, and stability properties of translation parallel to the wall are derived. The results are demonstrated through simulations and motion experiments on a macro-scale robotic swimmer in viscous fluid.
I will also present results of a recent joint work with Darren Crowdy on utilizing complex analysis to formulate an explicit two-dimensional dynamic model of a treadmilling swimmer near a wall, and discuss ongoing work on extension to shape-changing controlled swimmers such as Purcell’s three-link swimmer model near a wall.
The underlying basis of how swimming organisms propel
themselves forward against resistance from the surrounding
fluid has been studied for almost a century. Many traditional
analyses have centered on decomposing the total force on a
swimming body into drag and thrust. The validity of this
decomposition has been controversial since it is not expected
to hold for finite Reynolds number swimming. Yet, we report an
approximate drag-thrust decomposition for one class of
undulatory propulsors - the ribbon fins of gymnotiform and
balistiform swimmers. The conclusion is based on
high-resolution numerical simulations to calculate the force
acting on an undulatory ribbon fin of the black ghost knifefish
(Apteronotus albifrons). We show that drag-thrust decomposition
is possible because there is very little spatial overlap
between the drag-associated flow field and the
thrust-associated flow field. This decomposition is different
from the decomposition due to Lighthill that has been widely
discussed in literature over the past four decades.
The results above are used to interrogate balistiform and
gymnotiform swimmers that move by undulating elongated ribbon
fins attached to a body that is held nearly rigid. The question
of whether this evolutionary adaptation may have a hydrodynamic
basis was considered by Lighthill and Blake. They proposed,
based on Lighthill's elongated body theory, that the ability of
the ribbon fin to generate thrust is enhanced by the presence
of a rigid body. This mechanism, commonly referred to as
“momentum enhancement”, has been widely discussed in literature
over the past two decades. Our results show that there is no
momentum enhancement. This is explained by noting that the
dominant mechanism of thrust generation by ribbon fins is
different from that assumed in the theoretical approach of
Lighthill. Nevertheless, many features of the morphology of
gymnotiform and balistiform swimmers do appear to have a
hydrodynamic basis. Specifically, it is found that the observed
height of the ribbon fin, for a given body size, is such that
the mechanical energy spent per unit distance, i.e., the
mechanical cost of transport (COT) is optimized.
Many open issues remain. First, it remains to be explored
whether the drag-thrust decomposition can be extended to
anguilliform and carangiform swimming. Second, while we have
found optimal fin height for gymnotiform and balistiform
swimmers for a given body size, it is still unclear whether
keeping part of the body rigid is hydrodynamically better
compared to a mode of swimming where the entire body is
undulated (like in anguilliform swimming). Preliminary results
interrogating these aspects will be discussed.
A set of linearized equations of motion, using a spring-link model, is derived for undulatory swimming. The transverse translational and rotational equations of motion give natural deformation modes of the body which feeds energy to the axial translational motion. It is found, consistent with prior work, that anisotropy in drag is required to enable swimming. The first three deformation modes are excited the most and consequently contribute most to the forward swimming velocity. Typical imposed frequencies, for the case of eel considered here, are found to be lower than the lowest natural frequency of the deformation modes of the body. Thus, lower modes are found to be more easily triggered by the muscle forcing.
A novel constraint-based formulation to simulate self-propulsion has been developed. The numerical approach is used to obtain the following results. A drag-thrust decomposition is found in the propulsion by undulatory ribbon fins of gymnotiform and balistiform swimmers. The height of the ribbon fin of a gymnotiform swimmer seems optimized with respect to the mechanical Cost of Transport (COT). This can be explained based on the drag-thrust decomposition. Optimization based on COT is also found to work in case of pectoral fin movements of larval zebrafish.
Jellyfish represents a group of animals that have an axisymmetric body and swim by periodically contracting the body and generating axisymmetric jets and vortices. In this study, jellyfish is modeled as an axisymmetric swimmer with a thin, flexible body. The wake vortex generated by the swimmer is approximated by a circular vortex sheet. Using this approach, the fluid dynamics and characteristics of the fluid wake are investigated. Swimming performance is also evaluated to quantify the effects of body shape and swimming modes. The study provides insights on fluid dynamical basis of jellyfish swimming and how certain body kinematics of jellyfish enhance the swimming performance.
Flying insects execute aerial maneuvers through subtle
manipulations of their wing motions. Here, we measure the free-flight
kinematics of fruit flies and determine how they modulate their wing
pitching to induce sharp turns. By analyzing the torques these insects
exert to pitch their wings, we infer that the wing hinge acts as a
torsional spring that passively resists the wing’s tendency to flip in
response to aerodynamic and inertial forces. To turn, the insects
asymmetrically change the spring rest angles to generate asymmetric rowing
motions of their wings. Thus, insects can generate these maneuvers using
only a slight active actuation that biases their wing motion.
For animals and machines alike, maintaining balance during flight is a
crucial and demanding task. The need for airplane flight stability led to
a schism between aviators who sought built-in, or passive, stability and
those who emphasized the need for active controls. How has this tension
played out for the first flyers, the insects? Our group combines table-top
experiments on fruit flies and lap-top physically-based simulations to
study insect flight stability and control. First, we show how directly
perturbing the flight of insects unlocks the physics of flapping-wing
flight and also reveals some remarkable properties of these critters’
sensory-neural systems. Second, we argue that these sophisticated fight
control systems are largely sculpted by the physical requirement of
stability. This idea leads to a general theory that links the body plans
of insects with the controllers that must suppress the growth of
instabilities, and we apply this theory to a variety of modern insects,
flapping-wing robots, and even the prehistoric insects that were the first
to take to the air.
Joint work with Amir Alizadeh Pahlavan.
The effects of an external shear flow on the dynamics and pattern formation in a dilute suspension of swimming micro-organisms are investigated using a linear stability analysis and three-dimensional numerical simulations, based on the kinetic model previously developed by Saintillan and Shelley [``Instabilities, pattern formation, and mixing in active suspensions,'' Phys.~Fluids textbf{20}, 123304 (2008)]. The external shear flow is found to damp the instabilities that occur in these suspensions by controlling the orientation of the particles. We demonstrate that the rate of damping is direction-dependent: it is fastest in the flow direction, but slowest the direction perpendicular to the shear plane. As a result, transitions from three- to two- to one-dimensional instabilities are observed to occur as shear rate increases, and above a certain shear rate the instabilities altogether disappear. The density patterns and flow structures that arise at long times in the suspensions are also analyzed from the numerical simulations using standard techniques from the literature on turbulent flows. The imposed shear flow is found to have an effect on both density patterns and flow structures, which typically align with the extensional axis of the external flow. The disturbance flows in the simulations are shown to exhibit similarities with turbulent flows. However, the flows described herein are also significantly different owing to the strong predominance of large scales, as exemplified by the very rapid decay of the kinetic energy spectrum, an effect further enhanced after the transitions to two- and one-dimensional instabilities.
Active particle suspensions, of which a bath of swimming bacteria is a paradigmatic example, are characterized by complex dynamics involving strong fluctuations and large-scale correlated motions. These motions, which result from the many-body interactions between particles, are biologically relevant as they impact mean particle transport, mixing and diffusion, with possible consequences for nutrient uptake and the spreading of bacterial infections. To analyze these effects, a kinetic theory is presented and applied to elucidate the dynamics and pattern formation arising from mean-field interactions. Based on this model, the stability of both aligned and isotropic suspensions is investigated. In aligned suspensions, an instability is shown to always occur at finite wavelengths, in agreement with previous predictions and simulations. In isotropic suspensions, a new instability for the active particle stress is also found to exist, in which shear stresses are eigenmodes and grow exponentially at low wavenumbers, resulting in large-scale fluctuations in suspensions of pusher particles above a threshold concentration. Numerical simulations of the kinetic equations are also performed, and applied to study the long-time nonlinear dynamics, which are characterized by transient particles clusters that form and break up in time, as well as complex chaotic flows correlated on the system size. The predictions from the kinetic model are then tested using direct particle simulations accounting for multi-body hydrodynamic interactions between model microswimmers: these simulations confirm the existence of a transition to correlated motions and large-scale flows above a certain volume fraction, as demonstrated by a sharp increase in density fluctuations, velocity correlation lengths, and mean particle velocities. The effect of this transition on fluid mixing is also investigated, and the emergence of large-scale flows is shown to significantly enhance convective mixing. To conclude, consequences of particle activity on the effective rheology of the suspensions are briefly discussed. We demonstrate that the rheology is characterized by much stronger normal stress differences than in passive suspensions, and that tail-actuated swimmers result in a strong decrease in the effective shear viscosity of the fluid.
Many creatures navigate their world through undulation – the
unidirectional propagation of bending waves along the body.
Undulatory
locomotion in a fluid is well studied, at least at low Reynolds
number.
There, undulation breaks time-reversal symmetry and an organism
can
locomote by using the anisotropy of fluid drag with respect to
body shape.
On land, limbless creatures such as snakes also use undulation
to traverse
"featureless" surfaces with relative ease. I will discuss
theoretical
models and experimental observations that illustrate how snakes
accomplish
this by using the frictional anisotropy provided their scales,
as well as
selective body lifting. To provide another example of an
undulator in
action, I will discuss some recent modeling and experiments
that show how
swimming nematodes interact with microfluidic environments
filled with
immovable obstacles.
Joint work with Ahammed Anwar Chengala.
The effects of flow shear on the swimming behavior of halophilic microalga Dunaliella primolecta is examined by an in-house developed digital holographic microscopy and microfluidic channel. To investigate the shear-induced response, the algal culture is injected into a channel with a cross section of 3.5 x 0.4 mm at several fluid flow rates, generating shear rates that are consistent with the energy dissipation levels in estuaries, coastal waters, and lakes. We quantified the kinematics of D. primolecta by the estimates of 3D swimming velocities, auto-correlation swimming velocities, kinetic spectral densities and swimming-induced dispersion. Preliminary analysis indicate that swimming velocities and dispersion were strongly mediated by local fluid shear rates. On-going analysis is aimed to reveal scaling parameters and functional relationships among small-scale fluid motion and microorganism motility characteristics.
Joint work with Harsh Agarwal.
There is growing interest in understanding microscale biophysical processes such as the kinematics and dynamics of swimming microorganisms, and their interactions with surrounding fluids. Statistically robust experimental observations on swimming characteristics of bacteria in a wall bounded shear flow are crucial for understanding cell attachment and detachment during the initial formation of a biofilm. In this paper, we integrate microfluidics and holography to measure 3-D trajectories of a model bacteria, Escherichia coli (AW405), subjecting to a carefully controlled shear flow. Experiments are conducted in a straight mchannel of 40x3x0.2 mm with shear rates up to 200 (1/s). Holographic microscopic movies recorded at 40X magnification and 15 fps are streamed real-time to a data acquisition computer for an extended period of time (>5 min) that allows us to examine long term responses of bacteria in the presence of flow shear. Three-dimensional locations and orientations of bacteria are extracted with a resolution of 0.185 μm in lateral directions and 0.5 μm in the wall normal direction. The 3-D trajectories are tracked by an in-house developed particle tracking algorithm. Over three thousand of 3D trajectories over a sample volume of 380×380×200 μm have been obtained for our control (quiescent flow). Swimming characteristics, i.e. swimming velocities, Lagrangian spectra, dispersion coefficients, is extracted to quantify the cell-flow and cell-wall interactions. Preliminary results have revealed that near wall hydrodynamic interactions, i.e. swimming in circles and reducing lateral migration, cause the reduction in wall-normal dispersion, subsequently are responsible for wall trapping and prompting attachment. On-going analysis is to understand the effects of shear flow on such a mechanism.
Interest is growing
rapidly in understanding the swimming behaviour of micro-organisms near
solid surfaces. This is an important aspect of biofilm initiation and has
significant implications for the shipping, water and medical industries.
Through boundary element methods, we can accurately simulate hydrodynamic
interactions between a single bacterium and solid surfaces even when the
separation distance is small. Past experiments and analytical arguments
have shown that bacteria propelled by a flagellum tend to follow curved
trajectories rather than straight when swimming near a surface. Our
simulations verify this and we find that there can also be a stable
separation from the wall, leading to circular orbits. We show that
parameters controlling the shape of the swimmer can significantly influence
this equilibrium distance. Hence, this model suggests that certain
"designs" of bacteria accumulate at boundaries while others do not.
A number of findings from recent works are presented. At intermediate Reynolds number, where both inertia and viscous dissipation are important, we have observed through experiment and numerical simulation a number of counter-intuitive behaviors in a flapping wing system with passive pitching [joint work with L. Moret, M. Shelley, and J. Zhang]. The behavior of shape-changing bodies are also considered, along with consequences on vortex shedding and vortex-interaction dynamics, driven either by a recoil force from internal oscillations (recoil) or by an external background flow (hovering) [joint work with M. Shelley, S. Childress, and T. Tokieda]. Other problems are investigated at low Reynolds number, where viscous dissipation dominates inertial effects. These include the effects of elastic bending costs on the optimal swimming shape of slender bodies, the locomotion of bilayer vesicles, and the swimming behavior and efficiency of a fluid-extruding body ("jet propulsion") at zero Reynolds number [joint work with E. Lauga and A. Evans].
A body immersed in a highly viscous fluid can locomote by drawing in and expelling fluid through pores at its surface. We consider this mechanism of jet propulsion without inertia in the case of spheroidal bodies, and derive both the swimming velocity and the hydrodynamic efficiency. Elementary examples are presented, and exact axisymmetric solutions for spherical, prolate spheroidal, and oblate spheroidal body shapes are provided. In each case, entirely and partially porous (i.e. jetting) surfaces are considered, and the optimal jetting flow profiles at the surface for maximizing the hydrodynamic efficiency are determined computationally. The maximal efficiency which may be achieved by a sphere using such jet propulsion is 12.5%, a significant improvement upon traditional flagella-based means of locomotion at zero Reynolds number. Unlike other swimming mechanisms which rely on the presentation of a small cross section in the direction of motion, the efficiency of a jetting body at low Reynolds number increases as the body becomes more oblate, and limits to approximately 162% in the case of a flat plate swimming along its axis of symmetry. Our results are discussed in the light of slime extrusion mechanisms occurring in many cyanobacteria.
(Joint work with E. Lauga)
Blebbing occurs when the cytoskeleton detaches from the cell membrane, resulting in the pressure-driven flow of cytosol towards the area of detachment and the local expansion of the cell membrane. Recent interest has focused metastatic cancer cells that use blebs for cell motility. We present a dynamic computational model of the cell that includes mechanics of and the interactions between the intracellular fluid, the actin cortex, and the cell membrane. The cortex is an active, elastic, permeable material, which moves with a velocity distinct from that of the background fluid. The Immersed Boundary Method is modified to account for the relative motion between the cortex and the fluid. The computational model is used to explore several hypotheses for bleb formation, and these simulations are compared to experimental results. Additionally, a pressure threshold for bleb initiation, which depends crucially on the constitutive law for the membrane, is predicted based on reduced analytic models. These predictions are further explored in the full computational model and identified with underlying cellular processes.
In order to develop better methods for diagnosis and treatment
of infertility, as well as safer contraceptives, more must be
learned about how mammalian sperm move through the female
reproductive tract. Crucial phases of mammalian sperm transport
include passage through the cervix and uterotubal junction,
storage of sperm in the oviductal storage reservoir, release
from the reservoir, and location of the egg. There is some
evidence for the existence of special passageways for sperm in
the cervix, but this needs to be demonstrated and the mechanism
of guiding sperm through the cervix needs to be elucidated.
Passage of sperm through the uterotubal junction requires sperm
to have certain proteins, but how these proteins function is
not known. There is evidence that sperm must undergo motility
hyperactivation in order to be released from the oviductal
storage reservoir; however, the process is not understood.
Finally, it is not clear whether there are chemotactic agents
that emanate from the vicinity of the egg to modulate sperm
flagellar beating patterns in order to guide them toward the
egg. There are three main areas in which bioengineers can
provide crucial help for elucidating these mysteries: (1) by
developing a method for measuring and comparing sperm flagellar
bending patterns, (2) by improving optical equipment for
viewing the movement of sperm within the female reproductive
tract, and (3) by developing chambers that mimic the physical
environment of the tract so that molecular mechanisms that
regulate sperm movement can be elucidated. USDA CSREES NRICGP
2008-35203-19031 and NIH 1RO3HD062471-01.
Joint work with Haixin Chang (Cornell University) .
Hyperactivation, a swimming pattern used by mammalian sperm in
the oviduct, is essential for fertilization. It is
characterized by highly asymmetrical flagellar beating and an
increase of cytoplasmic Ca^{2+}. We observed that some mouse sperm
swimming in the oviduct produce high-amplitude pro-hook bends
(bends in the direction of the hook on the head) while others
produce high-amplitude anti-hook bends. Switching direction of
the high-amplitude bends could serve to re-direct sperm toward
oocytes. Our objective was to test the hypothesis that
different Ca^{2+} cell signaling pathways produce pro-hook and
anti-hook patterns. In vitro, sperm that hyperactivated during
capacitation (a process that prepares sperm for fertilization)
swam using large pro-hook bends, which resulted from influx of
Ca^{2+} through plasma membrane CatSper channels. The anesthetic
procaine and the K^{+}-channel blocker 4-Aminopyridine (4-AP) also
each induced large pro-hook bends. In contrast, thimerosal,
which triggers Ca^{2+} release from an intracellular
Ca^{2+} storage
site, induced large anti-hook bends. When capacitated sperm
were treated with thimerosal, 90% switched from pro-hook to
anti-hook bending. Sperm loaded with the fluorescent
Ca^{2+}
indicator Fluo-4 AM revealed that thimerosal initiated a
Ca^{2+}
increase at the base of the flagellum, while 4-AP initiated an
increase in the principal piece of the flagellum. Proteins were
extracted from sperm for examination of phosphorylation
patterns induced by Ca^{2+} signaling. Procaine and 4-AP
treatments phosphorylated threonine and serine residues of some
proteins, whereas thimerosal treatment dephosphorylated some
proteins. Tyrosine phosphorylation was unaffected. We concluded
that pro-hook hyperactivation, associated with sperm
capacitation, can be modulated by a distinct Ca^{2+} signaling
system to re-direct sperm toward oocytes. NIH 1R03HD062471-01.
Seed dispersal is the means by which plants expand and colonize new areas. To
maximize their range, some plants have developed elaborate gliding, spinning or
tumbling winged seedpods, whose aerodynamics enable them to extend their flight
time and range. Such winged seedpods are often light and thin, which generally
decreases their surface loading and hence their rate of descent. As a
consequence, they can be flexible. We are broadly interested in elucidating the
role of flexibility in passive flight. The influence of flexibility on the
flight of autorotating winged seedpods is examined through an experimental
investigation of tumbling rectangular paper strips freely falling in air. Our
results suggest the existence of a critical length above which the wing bends.
We develop a theoretical model that demonstrates that this buckling is prompted
by inertial forces associated with the tumbling motion, and yields a buckling
criterion consistent with that observed. We further develop a reduced model for
the flight dynamics of flexible tumbling wings that illustrates the effect of
aeroelastic coupling on flight characteristics and rationalizes experimentally
observed variations in the wing's falling speed and range.
Keywords: locomotion, motion planning, verification, control, robotic birds,
perching
Abstract: Locomotion in fluids (and on terrain) often involves complex nonlinear
dynamics and non-trivial notions of stability including limit cycles
and dynamically stable maneuvers. In this talk I will describe some
new algorithms for automatically verifying stability (via a Lyapunov
function) and estimating regions of attraction for dynamic nonlinear
locomotion. These tools have important implications for motion
planning and feedback design, which I will demonstrate by describing
our attempts to build robots that fly like a bird and execute post-
stall maneuvers to land on a perch.
I will first give an brief overview of the immersed interface method for fluid-solid interaction. I will then focus on
the application of the method to numerical simulation of insect flight. In particular, I will present (1) a boundary
condition capturing approach for the prescribed kinematics of an insect wing, (2) a matrix formulation of the
Newton dynamics for insect flight, and (3) a coupling approach to couple the aerodynamics and Newton dynamics
of insect flight.
Joint work with D. W. Murphy^{1}, D.R. Webster^{1}, S.
Kawaguchi^{2}, R. King^{2}, and F.
Sotiropoulos^{3}.
The locomotion of Antarctic krill (Euphausia superba) is known
to depend on the metachronal paddling of the animal’s five
pairs of pleopods. A wave passing along these swimming
appendages from posterior to anterior transfers momentum to the
surrounding fluid, thus producing thrust. The kinematics of
these pleopods, however, have not been fully characterized.
Determining the kinematics of krill in various swimming modes
will shed light on the fluid mechanics of krill locomotion and
thereby deepen our understanding of krill sensing and
schooling. High speed footage (250 fps) of freely swimming
juvenile and adult Antarctic krill was acquired at the
Australian Antarctic Division in Hobart, Tasmania. Various
swimming modes were identified based on swimming angle and
behavior, and two-dimensional kinematic parameters such as
pleopod stroke frequency, amplitude, stroke overlap, and animal
velocity were investigated as a function of these swimming
modes. The variability of these parameters over time provides
insight into the high sensitivity and responsiveness of krill
to their hydrodynamic environment. Useful comparisons can also
be made to previously gathered kinematics data for pacific
krill (Euphausia pacifica), which live in a much lower
viscosity environment. These parameters will prove necessary in
future computational fluid dynamics (CFD) simulations of krill
locomotion.
^{1} School of Civil and Environmental Engineering, Georgia
Institute of Technology, Atlanta, GA 30332-0355 USA
^{2} Australian Antarctic Division, Kingston, Tasmania, Australia
7050
^{3} Saint Anthony Falls Laboratory, University of Minnesota,
Minneapolis, MN 55414
Joint work with Kourosh Shoele, Dept of Structural Engr, UCSD.
Fins of bony fishes are characterized by a skeleton-reinforced membrane structure consisting of a soft collagen membrane strengthened by embedded flexible rays. Morphologically, each ray is connected to a group of muscles so that the fish can control the rotational motion of each ray individually, enabling multi-degree of freedom control over the fin motion and deformation. We have developed a fluid-structure interaction model to simulate the kinematics and dynamic performance of a structurally idealized fin. This method includes a boundary-element model of the fluid motion and a fully-nonlinear Euler-Bernoulli beam model of the embedded rays. Using this model we studied thrust generation and propulsion efficiency of the fin at different combinations of parameters. Effects of kinematic as well as structural properties are examined. It has been illustrated that the fish’s capacity to control the motion of each individual ray, as well as the anisotropic deformability of the fin determined by distribution of the rays (especially the detailed distribution of ray stiffness), are essential to high propulsion performance. Finally, we note that this structural design is a recurring motif in nature. Several similar biostructures will be discussed.