9,340 research outputs found
Dynamics and Stability of Low-Reynolds-Number Swimming Near a Wall
The locomotion of microorganisms and tiny artificial swimmers is governed by low-Reynolds-number
hydrodynamics, where viscous effects dominate and inertial effects are negligible. While the theory
of low-Reynolds-number locomotion is well studied for unbounded fluid domains, the presence of a
boundary has a significant influence on the swimmer’s trajectories and poses problems of dynamic
stability of its motion. In this paper we consider a simple theoretical model of a microswimmer near
a wall, study its dynamics, and analyze the stability of its motion. We highlight the underlying
geometric structure of the dynamics, and establish a relation between the reversing symmetry of
the system and existence and stability of periodic and steady solutions of motion near the wall.
The results are demonstrated by numerical simulations and validated by motion experiments with
macroscale robotic swimmer prototypes
A two-dimensional model of low-Reynolds number swimming beneath a free surface
Biological organisms swimming at low Reynolds number are often influenced by
the presence of rigid boundaries and soft interfaces. In this paper we present
an analysis of locomotion near a free surface with surface tension. Using a
simplified two-dimensional singularity model, and combining a complex variable
approach with conformal mapping techniques, we demonstrate that the deformation
of a free surface can be harnessed to produce steady locomotion parallel to the
interface. The crucial physical ingredient lies in the nonlinear hydrodynamic
coupling between the disturbance flow created by the swimmer and the free
boundary problem at the fluid surface
Physics of Microswimmers - Single Particle Motion and Collective Behavior
Locomotion and transport of microorganisms in fluids is an essential aspect
of life. Search for food, orientation toward light, spreading of off-spring,
and the formation of colonies are only possible due to locomotion. Swimming at
the microscale occurs at low Reynolds numbers, where fluid friction and
viscosity dominates over inertia. Here, evolution achieved propulsion
mechanisms, which overcome and even exploit drag. Prominent propulsion
mechanisms are rotating helical flagella, exploited by many bacteria, and
snake-like or whip-like motion of eukaryotic flagella, utilized by sperm and
algae. For artificial microswimmers, alternative concepts to convert chemical
energy or heat into directed motion can be employed, which are potentially more
efficient. The dynamics of microswimmers comprises many facets, which are all
required to achieve locomotion. In this article, we review the physics of
locomotion of biological and synthetic microswimmers, and the collective
behavior of their assemblies. Starting from individual microswimmers, we
describe the various propulsion mechanism of biological and synthetic systems
and address the hydrodynamic aspects of swimming. This comprises
synchronization and the concerted beating of flagella and cilia. In addition,
the swimming behavior next to surfaces is examined. Finally, collective and
cooperate phenomena of various types of isotropic and anisotropic swimmers with
and without hydrodynamic interactions are discussed.Comment: 54 pages, 59 figures, review article, Reports of Progress in Physics
(to appear
Entropic Lattice Boltzmann Method for Moving and Deforming Geometries in Three Dimensions
Entropic lattice Boltzmann methods have been developed to alleviate intrinsic
stability issues of lattice Boltzmann models for under-resolved simulations.
Its reliability in combination with moving objects was established for various
laminar benchmark flows in two dimensions in our previous work Dorschner et al.
[11] as well as for three dimensional one-way coupled simulations of
engine-type geometries in Dorschner et al. [12] for flat moving walls. The
present contribution aims to fully exploit the advantages of entropic lattice
Boltzmann models in terms of stability and accuracy and extends the methodology
to three-dimensional cases including two-way coupling between fluid and
structure, turbulence and deformable meshes. To cover this wide range of
applications, the classical benchmark of a sedimenting sphere is chosen first
to validate the general two-way coupling algorithm. Increasing the complexity,
we subsequently consider the simulation of a plunging SD7003 airfoil at a
Reynolds number of Re = 40000 and finally, to access the model's performance
for deforming meshes, we conduct a two-way coupled simulation of a
self-propelled anguilliform swimmer. These simulations confirm the viability of
the new fluid-structure interaction lattice Boltzmann algorithm to simulate
flows of engineering relevance.Comment: submitted to Journal of Computational Physic
Towards an analytical description of active microswimmers in clean and in surfactant-covered drops
Geometric confinements are frequently encountered in the biological world and
strongly affect the stability, topology, and transport properties of active
suspensions in viscous flow. Based on a far-field analytical model, the
low-Reynolds-number locomotion of a self-propelled microswimmer moving inside a
clean viscous drop or a drop covered with a homogeneously distributed
surfactant, is theoretically examined. The interfacial viscous stresses induced
by the surfactant are described by the well-established Boussinesq-Scriven
constitutive rheological model. Moreover, the active agent is represented by a
force dipole and the resulting fluid-mediated hydrodynamic couplings between
the swimmer and the confining drop are investigated. We find that the presence
of the surfactant significantly alters the dynamics of the encapsulated swimmer
by enhancing its reorientation. Exact solutions for the velocity images for the
Stokeslet and dipolar flow singularities inside the drop are introduced and
expressed in terms of infinite series of harmonic components. Our results offer
useful insights into guiding principles for the control of confined active
matter systems and support the objective of utilizing synthetic microswimmers
to drive drops for targeted drug delivery applications.Comment: 19 pages, 7 figures. Regular article contributed to the Topical Issue
of the European Physical Journal E entitled "Physics of Motile Active Matter"
edited by Gerhard Gompper, Clemens Bechinger, Holger Stark, and Roland G.
Winkle
Active colloids in complex fluids
We review recent work on active colloids or swimmers, such as self-propelled
microorganisms, phoretic colloidal particles, and artificial micro-robotic
systems, moving in fluid-like environments. These environments can be
water-like and Newtonian but can frequently contain macromolecules, flexible
polymers, soft cells, or hard particles, which impart complex, nonlinear
rheological features to the fluid. While significant progress has been made on
understanding how active colloids move and interact in Newtonian fluids, little
is known on how active colloids behave in complex and non-Newtonian fluids. An
emerging literature is starting to show how fluid rheology can dramatically
change the gaits and speeds of individual swimmers. Simultaneously, a moving
swimmer induces time dependent, three dimensional fluid flows, that can modify
the medium (fluid) rheological properties. This two-way, non-linear coupling at
microscopic scales has profound implications at meso- and macro-scales: steady
state suspension properties, emergent collective behavior, and transport of
passive tracer particles. Recent exciting theoretical results and current
debate on quantifying these complex active fluids highlight the need for
conceptually simple experiments to guide our understanding.Comment: 6 figure
Hydrodynamics of Micro-swimmers in Films
One of the principal mechanisms by which surfaces and interfaces affect
microbial life is by perturbing the hydrodynamic flows generated by swimming.
By summing a recursive series of image systems we derive a numerically
tractable approximation to the three-dimensional flow fields of a Stokeslet
(point force) within a viscous film between a parallel no-slip surface and
no-shear interface and, from this Green's function, we compute the flows
produced by a force- and torque-free micro-swimmer. We also extend the exact
solution of Liron & Mochon (1976) to the film geometry, which demonstrates that
the image series gives a satisfactory approximation to the swimmer flow fields
if the film is sufficiently thick compared to the swimmer size, and we derive
the swimmer flows in the thin-film limit. Concentrating on the thick film case,
we find that the dipole moment induces a bias towards swimmer accumulation at
the no-slip wall rather than the water-air interface, but that higher-order
multipole moments can oppose this. Based on the analytic predictions we propose
an experimental method to find the multipole coefficient that induces circular
swimming trajectories, allowing one to analytically determine the swimmer's
three-dimensional position under a microscope.Comment: 35 pages, 11 figures, 5 table
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