Optimal propulsive flapping in Stokes flows
TL;DR: The kinematics of optimal flapping are observed to depend weakly on the flapper shape and are very similar to the figure-eight motion observed in the motion of insect wings.
Abstract: Swimming fish and flying insects use the flapping of fins and wings to generate thrust. In contrast, microscopic organisms typically deform their appendages in a wavelike fashion. Since a flapping motion with two degrees of freedom is able, in theory, to produce net forces from a time-periodic actuation at all Reynolds number, we compute in this paper the optimal flapping kinematics of a rigid spheroid in a Stokes flow. The hydrodynamics for the force generation and energetics of the flapping motion is solved exactly. We then compute analytically the gradient of a flapping efficiency in the space of all flapping gaits and employ it to derive numerically the optimal flapping kinematics as a function of the shape of the flapper and the amplitude of the motion. The kinematics of optimal flapping are observed to depend weakly on the flapper shape and are very similar to the figure-eight motion observed in the motion of insect wings. Our results suggest that flapping could be a exploited experimentally as a propulsion mechanism valid across the whole range of Reynolds numbers.
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Journal Article•
TL;DR: The demonstration involved a tall rectangular transparent vessel of corn syrup, projected by an overhead projector turned on its side, and the figures reproduce transparencies used in the talk.
211 citations
TL;DR: In this article, the authors 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.
Abstract: 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.
122 citations
05 Nov 2020
TL;DR: In this article, the fluid dynamics of cell motility is discussed, covering phenomena ranging from single-cell motion to instabilities in cell populations, using physical intuition to interpret mathematical results, highlighting the history of applied mathematics, physics and biology.
Abstract: Fluid dynamics plays a crucial role in many cellular processes, including the locomotion of cells such as bacteria and spermatozoa. These organisms possess flagella, slender organelles whose time periodic motion in a fluid environment gives rise to motility. Sitting at the intersection of applied mathematics, physics and biology, the fluid dynamics of cell motility is one of the most successful applications of mathematical tools to the understanding of the biological world. Based on courses taught over several years, it details the mathematical modelling necessary to understand cell motility in fluids, covering phenomena ranging from single-cell motion to instabilities in cell populations. Each chapter introduces mathematical models to rationalise experiments, uses physical intuition to interpret mathematical results, highlights the history of the field and discusses notable current research questions. All mathematical derivations are included for students new to the field, and end-of-chapter exercises help consolidate understanding and practise applying the concepts.
113 citations
TL;DR: The paper discusses the swim performance of MPC ABFs fabricated with varying helicity angles and shows that weakly magnetized robots prefer a small helicity angle to achieve corkscrew-type motion.
Abstract: Artificial bacterial flagella (ABFs) are magnetically actuated swimming microrobots inspired by Escherichia coli bacteria, which use a helical tail for propulsion. The ABFs presented are fabricated from a magnetic polymer composite (MPC) containing iron-oxide nanoparticles embedded in an SU-8 polymer that is shaped into a helix by direct laser writing. The paper discusses the swim performance of MPC ABFs fabricated with varying helicity angles. The locomotion model presented contains the fluidic drag of the microrobot, which is calculated based on the resistive force theory. The robot's magnetization is approximated by an analytical model for a soft-magnetic ellipsoid. The helicity angle influences the fluidic and magnetic properties of the robot, and it is shown that weakly magnetized robots prefer a small helicity angle to achieve corkscrew-type motion.
36 citations
TL;DR: In this article, the authors investigated the transport of slightly deformable chiral objects in a uniform shear flow and found up to four different asymptotic states that can be distinguished by a lateral drift velocity of their center of mass, a rotational motion about the center-of-mass and deformations of the object.
Abstract: The transport of slightly deformable chiral objects in a uniform shear flow is investigated. Depending on the equilibrium configuration one finds up to four different asymptotic states that can be distinguished by a lateral drift velocity of their center of mass, a rotational motion about the center of mass and deformations of the object. These deformations influence the magnitudes of the principal axes of the second moment tensor of the considered object and also modify a scalar index characterizing its chirality. Moreover, the deformations induced by the shear flow are essential for the phenomenon of dynamical symmetry breaking: Objects that are achiral under equilibrium conditions may dynamically acquire chirality and consequently experience a drift in the lateral direction.
13 citations
References
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Book•
01 Jan 1965
TL;DR: Low Reynolds number flow theory finds wide application in such diverse fields as sedimentation, fluidization, particle-size classification, dust and mist collection, filtration, centrifugation, polymer and suspension rheology, and a host of other disciplines.
Abstract: Low Reynolds number flow theory finds wide application in such diverse fields as sedimentation, fluidization, particle-size classification, dust and mist collection, filtration, centrifugation, polymer and suspension rheology, flow through porous media, colloid science, aerosol and hydrosal technology, lubrication theory, blood flow, Brownian motion, geophysics, meteorology, and a host of other disciplines. This text provides a comprehensive and detailed account of the physical and mathematical principles underlying such phenomena, heretofore available only in the original literature.
4,648 citations
"Optimal propulsive flapping in Stok..." refers background in this paper
...where A and C are symmetric resistance tensors [45, 46], Ω the rotation rate of the solid body, and U the translation velocity of the spheroid center....
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...In the body frame R1, A and C are diagonal [45, 46], and we write A = λ⊥e ′ xe ′ x + λ‖e ′ ye ′ y + λz′e ′ ze ′ z and C = γ⊥e ′ xe ′ x + γ‖e ′ ye ′ y + γz′e ′ ze ′ z where [λz′ , γz′ ] = [λ⊥, γ⊥] for a prolate spheroid and [λz′ , γz′ ] = [ λ‖, γ‖ ] for an oblate spheroid....
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TL;DR: Weisskopf as mentioned in this paper presented a transparencies of a tall rectangular transparent vessel of corn syrup, projected by an overhead projector turned on its side, which was itself a slightly edited transcript of a tape.
Abstract: Editor’s note: This is a reprint (slightly edited) of a paper of the same title that appeared in the book Physics and Our World: A Symposium in Honor of Victor F. Weisskopf, published by the American Institute of Physics (1976). The personal tone of the original talk has been preserved in the paper, which was itself a slightly edited transcript of a tape. The figures reproduce transparencies used in the talk. The demonstration involved a tall rectangular transparent vessel of corn syrup, projected by an overhead projector turned on its side. Some essential hand waving could not be reproduced.
3,906 citations
TL;DR: The biophysical and mechanical principles of locomotion at the small scales relevant to cell swimming, tens of micrometers and below are reviewed, with emphasis on the simple physical picture and fundamental flow physics phenomena in this regime.
Abstract: Cell motility in viscous fluids is ubiquitous and affects many biological processes, including reproduction, infection and the marine life ecosystem. Here we review the biophysical and mechanical principles of locomotion at the small scales relevant to cell swimming, tens of micrometers and below. At this scale, inertia is unimportant and the Reynolds number is small. Our emphasis is on the simple physical picture and fundamental flow physics phenomena in this regime. We first give a brief overview of the mechanisms for swimming motility, and of the basic properties of flows at low Reynolds number, paying special attention to aspects most relevant for swimming such as resistance matrices for solid bodies, flow singularities and kinematic requirements for net translation. Then we review classical theoretical work on cell motility, in particular early calculations of swimming kinematics with prescribed stroke and the application of resistive force theory and slender-body theory to flagellar locomotion. After examining the physical means by which flagella are actuated, we outline areas of active research, including hydrodynamic interactions, biological locomotion in complex fluids, the design of small-scale artificial swimmers and the optimization of locomotion strategies. (Some figures in this article are in colour only in the electronic version) This article was invited by Christoph Schmidt.
2,274 citations
TL;DR: It is shown that a linear chain of colloidal magnetic particles linked by DNA and attached to a red blood cell can act as a flexible artificial flagellum, which induces a beating pattern that propels the structure, and that the external fields can be adjusted to control the velocity and the direction of motion.
Abstract: Microorganisms such as bacteria and many eukaryotic cells propel themselves with hair-like structures known as flagella, which can exhibit a variety of structures and movement patterns. For example, bacterial flagella are helically shaped and driven at their bases by a reversible rotary engine, which rotates the attached flagellum to give a motion similar to that of a corkscrew. In contrast, eukaryotic cells use flagella that resemble elastic rods and exhibit a beating motion: internally generated stresses give rise to a series of bends that propagate towards the tip. In contrast to this variety of swimming strategies encountered in nature, a controlled swimming motion of artificial micrometre-sized structures has not yet been realized. Here we show that a linear chain of colloidal magnetic particles linked by DNA and attached to a red blood cell can act as a flexible artificial flagellum. The filament aligns with an external uniform magnetic field and is readily actuated by oscillating a transverse field. We find that the actuation induces a beating pattern that propels the structure, and that the external fields can be adjusted to control the velocity and the direction of motion.
1,700 citations
Book•
01 Jan 1991
TL;DR: In this article, the authors focus on determining the motion of particles through a viscous fluid in bounded and unbounded flow, and their central theme is the mobility relation between particle motion and forces.
Abstract: This text focuses on determining the motion of particles through a viscous fluid in bounded and unbounded flow. Its central theme is the mobility relation between particle motion and forces, and Lecture some pages from the more than through time reversibility means then plates arranged. A force distribution of the lamb's general information these properties stokes flow. Advances in late august and singularity, methods vanishing at infinity can be theoretical. Students can be theoretical questions and vanishing at these terms stokeslet. Application of stokes equations lorentz reciprocal theorem can. The are negligible in more general case of chemical. Then the body is to chemical engineering theory in stokes equations. Kim and pressure design methodology of catalysis thermodynamics transport phenomena on. In chemical engineering theory and graduate hours introduction to avoid indexing. Explain the stokeslet which is stokes equations.
1,658 citations
Additional excerpts
...The values for the individual resistance coefficients, λ’s, are known exactly [47] and we always have λ⊥ ≥ λ‖....
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