Статті в журналах: "Micro-swimmer"

1

Avron, J. E., O. Kenneth, and D. H. Oaknin. "Pushmepullyou: an efficient micro-swimmer." New Journal of Physics 7 (November 18, 2005): 234. http://dx.doi.org/10.1088/1367-2630/7/1/234.

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2

ALOUGES, FRANÇOIS, ANTONIO DESIMONE, and LUCA HELTAI. "NUMERICAL STRATEGIES FOR STROKE OPTIMIZATION OF AXISYMMETRIC MICROSWIMMERS." Mathematical Models and Methods in Applied Sciences 21, no. 02 (February 2011): 361–87. http://dx.doi.org/10.1142/s0218202511005088.

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We propose a computational method to solve optimal swimming problems, based on the boundary integral formulation of the hydrodynamic interaction between swimmer and surrounding fluid and direct constrained minimization of the energy consumed by the swimmer. We apply our method to axisymmetric model examples. We consider a classical model swimmer (the three-sphere swimmer of Golestanian et al.) as well as a novel axisymmetric swimmer inspired by the observation of biological micro-organisms.

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3

Ishikawa, Takuji. "Stability of a Dumbbell Micro-Swimmer." Micromachines 10, no. 1 (January 7, 2019): 33. http://dx.doi.org/10.3390/mi10010033.

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A squirmer model achieves propulsion by generating surface squirming velocities. This model has been used to analyze the movement of micro-swimmers, such as microorganisms and Janus particles. Although squirmer motion has been widely investigated, motions of two connected squirmers, i.e., a dumbbell squirmer, remain to be clarified. The stable assembly of multiple micro-swimmers could be a key technology for future micromachine applications. Therefore, in this study, we investigated the swimming behavior and stability of a dumbbell squirmer. We first examined far-field stability through linear stability analysis, and found that stable forward swimming could not be achieved by a dumbbell squirmer in the far field without the addition of external torque. We then investigated the swimming speed of a dumbbell squirmer connected by a short rigid rod using a boundary element method. Finally, we investigated the swimming stability of a dumbbell squirmer connected by a spring. Our results demonstrated that stable side-by-side swimming can be achieved by pullers. When the aft squirmer was a strong pusher, fore and aft swimming were stable and swimming speed increased significantly. The findings of this study will be useful for the future design of assembled micro-swimmers.

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4

Ishikawa, Takuji, Tomoyuki Tanaka, Yohsuke Imai, Toshihiro Omori, and Daiki Matsunaga. "Deformation of a micro-torque swimmer." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2185 (January 2016): 20150604. http://dx.doi.org/10.1098/rspa.2015.0604.

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The membrane tension of some kinds of ciliates has been suggested to regulate upward and downward swimming velocities under gravity. Despite its biological importance, deformation and membrane tension of a ciliate have not been clarified fully. In this study, we numerically investigated the deformation of a ciliate swimming freely in a fluid otherwise at rest. The cell body was modelled as a capsule with a hyperelastic membrane enclosing a Newtonian fluid. Thrust forces due to the ciliary beat were modelled as torques distributed above the cell body. The effects of membrane elasticity, the aspect ratio of the cell's reference shape, and the density difference between the cell and the surrounding fluid were investigated. The results showed that the cell deformed like a heart shape, when the capillary number was sufficiently large. Under the influence of gravity, the membrane tension at the anterior end decreased in the upward swimming while it increased in the downward swimming. Moreover, gravity-induced deformation caused the cells to move gravitationally downwards or upwards, which resulted in a positive or negative geotaxis-like behaviour with a physical origin. These results are important in understanding the physiology of a ciliate's biological responses to mechanical stimuli.

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5

Roper, Marcus, Rémi Dreyfus, Jean Baudry, Marc Fermigier, Jérôme Bibette, and Howard A. Stone. "Do magnetic micro-swimmers move like eukaryotic cells?" Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464, no. 2092 (January 15, 2008): 877–904. http://dx.doi.org/10.1098/rspa.2007.0285.

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Recent advances in micro-machining allow very small cargos, such as single red blood cells, to be moved by outfitting them with tails made of micrometre-sized paramagnetic particles yoked together by polymer bridges. When a time-varying magnetic field is applied to such a filament, it bends from side to side and propels itself through the fluid, dragging the load behind it. Here, experimental data and a mathematical model are presented showing the dependence of the swimming speed and direction of the magnetic micro-swimmer upon tunable parameters, such as the field strength and frequency and the filament length. The propulsion of the filament arises from the propagation of bending waves between free and tethered ends: here we show that this gives the micro-swimmer a gait that is intermediate between a eukaryotic cell and a waggled elastic rod. Finally, we extract from the model design principles for constructing the fastest swimming micro-swimmer by tuning experimental parameters.

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6

Pimponi, D., M. Chinappi, P. Gualtieri, and C. M. Casciola. "Hydrodynamics of flagellated microswimmers near free-slip interfaces." Journal of Fluid Mechanics 789 (January 22, 2016): 514–33. http://dx.doi.org/10.1017/jfm.2015.738.

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The hydrodynamics of a flagellated micro-organism is investigated when swimming close to a planar free-slip surface by means of numerical solutions of the Stokes equations obtained via a boundary element method. Depending on the initial conditions, the swimmer can either escape from the free-slip surface or collide with the boundary. Interestingly, the micro-organism does not exhibit a stable orbit. Independently of escape or attraction to the interface, close to a free-slip surface, the swimmer follows a counter-clockwise trajectory, in agreement with experimental findings (Di Leonardo et al., Phys. Rev. Lett., vol. 106 (3), 2011, 038101). The hydrodynamics is indeed modified by the free surface. In fact, when the same swimmer moves close to a no-slip wall, a set of initial conditions exists which result in stable orbits. Moreover, when moving close to a free-slip or a no-slip boundary, the swimmer assumes a different orientation with respect to its trajectory. Taken together, these results contribute to shed light on the hydrodynamical behaviour of micro-organisms close to liquid–air interfaces which are relevant for the formation of interfacial biofilms of aerobic bacteria.

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7

Mathijssen, A. J. T. M., A. Doostmohammadi, J. M. Yeomans, and T. N. Shendruk. "Hydrodynamics of micro-swimmers in films." Journal of Fluid Mechanics 806 (September 29, 2016): 35–70. http://dx.doi.org/10.1017/jfm.2016.479.

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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 a 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 (J. Engng Maths, vol. 10 (4), 1976, pp. 287–303) 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.

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8

Yu, Shimin, Ningze Ma, Hao Yu, Haoran Sun, Xiaocong Chang, Zhiguang Wu, Jiaxuan Deng, et al. "Self-Propelled Janus Microdimer Swimmers under a Rotating Magnetic Field." Nanomaterials 9, no. 12 (November 22, 2019): 1672. http://dx.doi.org/10.3390/nano9121672.

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Recent strides in micro- and nanofabrication technology have enabled researchers to design and develop new micro- and nanorobots for biomedicine and environmental monitoring. Due to its non-invasive remote actuation and convenient navigation abilities, magnetic propulsion has been widely used in micro- and nanoscale robotic systems. In this article, a highly efficient Janus microdimer swimmer propelled by a rotating uniform magnetic field was investigated experimentally and numerically. The velocity of the Janus microdimer swimmer can be modulated by adjusting the magnetic field frequency with a maximum speed of 133 μm·s−1 (≈13.3 body length s−1) at the frequency of 32 Hz. Fast and accurate navigation of these Janus microdimer swimmers in complex environments and near obstacles was also demonstrated. This efficient propulsion behavior of the new Janus microdimer swimmer holds considerable promise for diverse future practical applications ranging from nanoscale manipulation and assembly to nanomedicine.

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9

Iima, M., and A. S. Mikhailov. "Propulsion hydrodynamics of a butterfly micro-swimmer." EPL (Europhysics Letters) 85, no. 4 (February 2009): 44001. http://dx.doi.org/10.1209/0295-5075/85/44001.

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10

KEAVENY, ERIC E., and MARTIN R. MAXEY. "Spiral swimming of an artificial micro-swimmer." Journal of Fluid Mechanics 598 (February 25, 2008): 293–319. http://dx.doi.org/10.1017/s0022112007009949.

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A device constructed from a filament of paramagnetic beads connected to a human red blood cell will swim when subject to an oscillating magnetic field. Bending waves propagate from the tip of the tail toward the red blood cell in a fashion analogous to flagellum beating, making the artificial swimmer a candidate for studying what has been referred to as ‘flexible oar’ micro-swimming. In this study, we demonstrate that under the influence of a rotating field the artificial swimmer will perform ‘corkscrew’-type swimming. We conduct numerical simulations of the swimmer where the paramagnetic tail is represented as a series of rigid spheres connected by flexible but inextensible links. An optimal range of parameters governing the relative strength of viscous, elastic and magnetic forces is identified for swimming speed. A parameterization of the motion is extracted and examined as a function of the driving frequency. With a continuous elastica/resistive force model, we obtain an expression for the swimming speed in the low-frequency limit. Using this expression we explore further the effects of the applied field, the ratio of the transverse field to the constant field, and the ratio of the radius of the sphere to the length of the filament tail on the resulting dynamics.

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11

Gallino, Giacomo, Lailai Zhu, and François Gallaire. "The Hydrodynamics of a Micro-Rocket Propelled by a Deformable Bubble." Fluids 4, no. 1 (March 14, 2019): 48. http://dx.doi.org/10.3390/fluids4010048.

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We perform simulations to study the hydrodynamics of a conical-shaped swimming micro-robot that ejects catalytically produced bubbles from its inside. We underline the nontrivial dependency of the swimming velocity on the bubble deformability and on the geometry of the swimmer. We identify three distinct phases during the bubble evolution: immediately after nucleation the bubble is spherical and its inflation barely affects the swimming speed; then the bubble starts to deform due to the confinement gradient generating a force that propels the swimmer; while in the last phase, the bubble exits the cone, resulting in an increase in the swimmer velocity. Our results shed light on the fundamental hydrodynamics of the propulsion of catalytic conical swimmers and may help to improve the efficiency of these micro-machines.

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12

XU, YUAN-QING, FANG-BAO TIAN, XIAO-YING TANG, and YU-HUA PENG. "A MATHEMATICAL MODEL FOR MICRO- AND NANO-SWIMMERS." Journal of Mechanics in Medicine and Biology 13, no. 06 (December 2013): 1340013. http://dx.doi.org/10.1142/s0219519413400137.

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In order to explore the kinetic characteristics of planktonic microorganisms and nanometer biological motors, a mathematical model is developed to estimate the hydrodynamic force in the migration of micro- and nano-swimmers by using the Laplace transformation and linear superposition. Based on the model, it is found that a micro- and nano-swimmer will enjoy a positive propulsive force by improving frequencies or generating traveling waves along its body if it is not time reversible. The results obtained in this study provide a physical insight into the behaviors of the micro- and nano-swimmer at low Reynolds numbers, and the corresponding quantitative basis can also be potentially used in the design of nanorobot and nanosized biomaterials.

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13

Mathijssen, A. J. T. M., D. O. Pushkin, and J. M. Yeomans. "Tracer trajectories and displacement due to a micro-swimmer near a surface." Journal of Fluid Mechanics 773 (May 27, 2015): 498–519. http://dx.doi.org/10.1017/jfm.2015.269.

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We study tracer particle transport due to flows created by a self-propelled micro-swimmer, such as a swimming bacterium, alga or a microscopic artificial swimmer. Recent theoretical work has shown that as a swimmer moves in the fluid bulk along an infinite straight path, tracer particles far from its path perform closed loops, whereas those close to the swimmer are entrained by its motion. However, in biologically and technologically important cases tracer transport is significantly altered for swimmers that move in a run-and-tumble fashion with a finite persistence length, and/or in the presence of a free surface or a solid boundary. Here we present a systematic analytical and numerical study exploring the resultant regimes and their crossovers. Our focus is on describing qualitative features of the tracer particle transport and developing quantitative tools for its analysis. Our work is a step towards understanding the ecological effects of flows created by swimming organisms, such as enhanced fluid mixing and biofilm formation.

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14

Liu, Fang-Wei, Ye Zhan, and Sung Kwon Cho. "Propulsion reversal in oscillating-bubble powered micro swimmer." Journal of Micromechanics and Microengineering 31, no. 8 (July 7, 2021): 084001. http://dx.doi.org/10.1088/1361-6439/ac0e7f.

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15

Liu, Jinan, and Haihui Ruan. "Modeling of an acoustically actuated artificial micro-swimmer." Bioinspiration & Biomimetics 15, no. 3 (March 3, 2020): 036002. http://dx.doi.org/10.1088/1748-3190/ab6a61.

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16

Ouyang, Zhenyu, Chen Liu, Tingting Qi, Jianzhong Lin, and Xiaoke Ku. "Locomotion of a micro-swimmer towing load through shear-dependent non-Newtonian fluids." Physics of Fluids 35, no. 1 (January 2023): 013334. http://dx.doi.org/10.1063/5.0132452.

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This paper simulates the locomotion of a micro-swimmer towing cargo through a shear-dependent non-Newtonian fluid. We investigate the effect of the shear-dependent rheology (refers to the power-law index n), swimming Reynolds numbers ( Re), and the relative position (refers to the distance ds and the concerning angle θ) between the swimmer and the cargoes on the assemblies' locomotion. For a swimmer towing a cargo, we find that a cargo-puller, cargo-pusher, or pusher-cargo (three typical towing models) swims faster in the shear-thickening fluids than in the shear-thinning fluids at Re ≤ 1. Moreover, the pusher-cargo swims significantly faster than the counterpart puller-cargo at Re ≤ 1. For a swimmer towing two cargoes, we find that the maximum negative swimming speeds can be achieved at θ = 30° and 150°, corresponding to two typical regular-triangle structures assembled by the squirmer and the cargoes. Interestingly, some regular-triangle assemblies (puller with θ = 30° and pusher with θ = 150°) can maintain a swimming opposite to their initial orientation. In addition, we obtain a relation of energy expenditure P ∼ Ren−1; it is also found that the assembly swimming in the shear-thinning fluids is more efficient than in the shear-thickening ones. Our results provide specified guidance in the designing of cargo-carrying micro-swimming devices.

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17

Ishimoto, Kenta, and Darren G. Crowdy. "Dynamics of a treadmilling microswimmer near a no-slip wall in simple shear." Journal of Fluid Mechanics 821 (May 25, 2017): 647–67. http://dx.doi.org/10.1017/jfm.2017.220.

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Induction of flow is commonly used to control the migration of a microswimmer in a confined system such as a microchannel. The motion of a swimmer, in general, is governed by nonlinear equations due to non-trivial hydrodynamic interactions between the flow and the swimmer near a wall. This paper derives analytical expressions for the equations of motion governing a circular treadmilling swimmer in simple shear near a no-slip wall by combining the reciprocal theorem for Stokes flow with an exact solution for the dragging problem of a cylinder near a wall. We demonstrate that the reduced dynamical system possesses a Hamiltonian structure, which we use to show that the swimmer cannot migrate stably at a constant distance from a wall but only exhibit periodic oscillatory motion along the wall, or to escape from it. A treadmilling swimmer with the lowest two treadmilling modes is investigated in detail by means of a bifurcation analysis of the reduced dynamical system. It is found that the swimming direction of oscillatory motion is clarified by the sign of the Hamiltonian in the absence of flow, and that the induction of the flow suppresses upstream migration but aligns swimmer orientations in downstream migration. These results could inform strategies for the transport and control of micro-organisms and micromachines.

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18

Cartwright, Avriel, and Jian Du. "Enhancement of Active Swimming near Fluid Interfaces." Journal of Physics: Conference Series 2224, no. 1 (April 1, 2022): 012034. http://dx.doi.org/10.1088/1742-6596/2224/1/012034.

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Abstract Microorganisms often move through heterogeneous fluid medium composed of multiple materials with very different properties. Biological locomotions are significantly influenced by the physical compositions and rheology of the fluidic environment. Some micro-swimmers are able to exploit nearby deformable interfaces to enhance their speed. Through computational simulations, we investigate the movement of a finite-length undulatory swimmer near interfaces within a viscous two-fluid media. Our results show that significant speed-ups can be obtained only if the active swimmer has a large body elasticity.

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19

Zhang, Z. Y., Y. F. Wang, J. T. Kang, X. H. Qiu, and C. G. Wang. "Helical micro-swimmer: hierarchical tail design and propulsive motility." Soft Matter 18, no. 33 (2022): 6148–56. http://dx.doi.org/10.1039/d2sm00823h.

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20

Ouyang, Zhenyu, and Jianzhong Lin. "Migration of a micro-swimmer in a channel flow." Powder Technology 392 (November 2021): 587–600. http://dx.doi.org/10.1016/j.powtec.2021.07.027.

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21

YAMANAKA, Toshiro, and Fumihito ARAI. "Self-Propelled Micro Swimmer with Red-Blood-Cell Size." Proceedings of JSME annual Conference on Robotics and Mechatronics (Robomec) 2019 (2019): 1P2—A08. http://dx.doi.org/10.1299/jsmermd.2019.1p2-a08.

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22

Paris, Alisier, Dominique Decanini, and Gilgueng Hwang. "On-chip multimodal vortex trap micro-manipulator with multistage bi-helical micro-swimmer." Sensors and Actuators A: Physical 276 (June 2018): 118–24. http://dx.doi.org/10.1016/j.sna.2018.04.019.

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23

Giraldi, Laetitia, and Jean-Baptiste Pomet. "Local Controllability of the Two-Link Magneto-Elastic Micro-Swimmer." IEEE Transactions on Automatic Control 62, no. 5 (May 2017): 2512–18. http://dx.doi.org/10.1109/tac.2016.2600158.

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24

Ishimoto, Kenta. "A spherical squirming swimmer in unsteady Stokes flow." Journal of Fluid Mechanics 723 (April 16, 2013): 163–89. http://dx.doi.org/10.1017/jfm.2013.131.

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AbstractThe motion of a spherical squirmer in unsteady Stokes flow is investigated for a deeper understanding of unsteady inertial effects on swimming micro-organisms and differences of swimming strokes between a wave pattern and a flapping motion. An asymptotic analysis with respect to the small amplitude and the small inertia is performed, and the average swimming velocity after a long period of time under an assumption of a time-periodic stroke is obtained. This analysis shows that the scallop theorem still holds in a long-time asymptotic sense for tangential deformation, but that the time variation of the shape generates a net velocity even for a reciprocal swimmer. It is also found that the inertial effects on the swimming velocity are significant for a flapping swimmer, as contrasted with little influence on that of a swimmer with a wave pattern. The inertial effect is also illustrated with a simple squirmer, so that a reciprocal motion can be almost an optimal stroke under a constraint on energy consumption.

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25

Ye, Chengwei, Jia Liu, Xinyu Wu, Ben Wang, Li Zhang, Yuanyi Zheng, and Tiantian Xu. "Hydrophobicity Influence on Swimming Performance of Magnetically Driven Miniature Helical Swimmers." Micromachines 10, no. 3 (March 6, 2019): 175. http://dx.doi.org/10.3390/mi10030175.

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Helical microswimmers have been involved in a wide variety of applications, ranging from in vivo tasks such as targeted drug delivery to in vitro tasks such as transporting micro objects. Over the past decades, a number of studies have been established on the swimming performance of helical microswimmers and geometrical factors influencing their swimming performance. However, limited studies have focused on the influence of the hydrophobicity of swimmers’ surface on their swimming performance. In this paper, we first demonstrated through theoretical analysis that the hydrophobicity of swimmer’s surface material of the swimmer does affect its swimming performance: the swimmer with more hydrophobic surface is exerted less friction drag torque, and should therefore exhibit a higher step-out frequency, indicating that the swimmer with more hydrophobic surface should have better swimming performance. Then a series of experiments were conducted to verify the theoretical analysis. As a result, the main contribution of this paper is to demonstrate that one potential approach to improve the helical microswimmers’ swimming performance could be making its surface more hydrophobic.

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26

Krishnamurthy, Deepak, and Ganesh Subramanian. "Collective motion in a suspension of micro-swimmers that run-and-tumble and rotary diffuse." Journal of Fluid Mechanics 781 (September 28, 2015): 422–66. http://dx.doi.org/10.1017/jfm.2015.473.

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Recent experiments have shown that suspensions of swimming micro-organisms are characterized by complex dynamics involving enhanced swimming speeds, large-scale correlated motions and enhanced diffusivities of embedded tracer particles. Understanding this dynamics is of fundamental interest and also has relevance to biological systems. The observed collective dynamics has been interpreted as the onset of a hydrodynamic instability, of the quiescent isotropic state of pushers, swimmers with extensile force dipoles, above a critical threshold proportional to the swimmer concentration. In this work, we develop a particle-based model to simulate a suspension of hydrodynamically interacting rod-like swimmers to estimate this threshold. Unlike earlier simulations, the velocity disturbance field due to each swimmer is specified in terms of the intrinsic swimmer stress alone, as per viscous slender-body theory. This allows for a computationally efficient kinematic simulation where the interaction law between swimmers is knowna priori. The neglect of induced stresses is of secondary importance since the aforementioned instability arises solely due to the intrinsic swimmer force dipoles.Our kinematic simulations include, for the first time, intrinsic decorrelation mechanisms found in bacteria, such as tumbling and rotary diffusion. To begin with, we simulate so-called straight swimmers that lack intrinsic orientation decorrelation mechanisms, and a comparison with earlier results serves as a proof of principle. Next, we simulate suspensions of swimmers that tumble and undergo rotary diffusion, as a function of the swimmer number density$(n)$, and the intrinsic decorrelation time (the average duration between tumbles,${\it\tau}$, for tumblers, and the inverse of the rotary diffusivity,$D_{r}^{-1}$, for rotary diffusers). The simulations, as a function of the decorrelation time, are carried out with hydrodynamic interactions (between swimmers) turned off and on, and for both pushers and pullers (swimmers with contractile force dipoles). The ‘interactions-off’ simulations allow for a validation based on analytical expressions for the tracer diffusivity in the stable regime, and reveal a non-trivial box size dependence that arises with varying strength of the hydrodynamic interactions. The ‘interactions-on’ simulations lead us to our main finding: the existence of a box-size-independent parameter that characterizes the onset of instability in a pusher suspension, and is given by$nUL^{2}{\it\tau}$for tumblers and$nUL^{2}/D_{r}$for rotary diffusers; here,$U$and$L$are the swimming speed and swimmer length, respectively. The instability manifests as a bifurcation of the tracer diffusivity curves, in pusher and puller suspensions, for values of the above dimensionless parameters exceeding a critical threshold.

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27

Bae, Albert J., Raheel Ahmad, Eberhard Bodenschatz, Alain Pumir, and Azam Gholami. "Flagellum-driven cargoes: Influence of cargo size and the flagellum-cargo attachment geometry." PLOS ONE 18, no. 3 (March 10, 2023): e0279940. http://dx.doi.org/10.1371/journal.pone.0279940.

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The beating of cilia and flagella, which relies on an efficient conversion of energy from ATP-hydrolysis into mechanical work, offers a promising way to propel synthetic cargoes. Recent experimental realizations of such micro-swimmers, in which micron-sized beads are propelled by isolated and demembranated flagella from the green algae Chlamydomonas reinhardtii (C. reinhardtii), revealed a variety of propulsion modes, depending in particular on the calcium concentration. Here, we investigate theoretically and numerically the propulsion of a bead as a function of the flagellar waveform and the attachment geometries between the bead and the flagellum. To this end, we take advantage of the low Reynolds number of the fluid flows generated by the micro-swimmer, which allows us to neglect fluid inertia. By describing the flagellar waveform as a superposition of a static component and a propagating wave, and using resistive-force theory, we show that the asymmetric sideways attachment of the flagellum to the bead makes a contribution to the rotational velocity of the micro-swimmer that is comparable to the contribution caused by the static component of the flagellar waveform. Remarkably, our analysis reveals the existence of a counter-intuitive propulsion regime in which an increase in the size of the cargo, and hence its drag, leads to an increase in some components of the velocity of the bead. Finally, we discuss the relevance of the uncovered mechanisms for the fabrication of synthetic, bio-actuated medical micro-robots for targeted drug delivery.

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28

Chambrion, Thomas, Laetitia Giraldi, and Alexandre Munnier. "Optimal strokes for driftless swimmers: A general geometric approach." ESAIM: Control, Optimisation and Calculus of Variations 25 (2019): 6. http://dx.doi.org/10.1051/cocv/2017012.

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Swimming consists by definition in propelling through a fluid by means of bodily movements. Thus, from a mathematical point of view, swimming turns into a control problem for which the controls are the deformations of the swimmer. The aim of this paper is to present a unified geometric approach for the optimization of the body deformations of so-called driftless swimmers. The class of driftless swimmers includes, among other, swimmers in a 3D Stokes flow (case of micro-swimmers in viscous fluids) or swimmers in a 2D or 3D potential flow. A general framework is introduced, allowing the complete analysis of five usual nonlinear optimization problems to be carried out. The results are illustrated with examples coming from the literature and with an in-depth study of a swimmer in a 2D potential flow. Numerical tests are also provided.

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29

Berdakin, Ivan, V. I. Marconi, and Adolfo J. Banchio. "Boosting micromachine studies with Stokesian dynamics." Physics of Fluids 34, no. 3 (March 2022): 037102. http://dx.doi.org/10.1063/5.0083528.

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Artificial microswimmers, nano- and microrobots, are essential in many applications from engineering to biology and medicine. We present a Stokesian dynamics study of the dynamical properties and efficiency of one of the simplest artificial swimmers, the three linked spheres swimmer (TLS), extensively shown to be an excellent and model example of a deformable micromachine. Results for two different swimming strokes are compared with an approximate solution based on point force interactions. While this approximation accurately reproduces the solutions for swimmers with long arms and strokes of small amplitude, it fails when the amplitude of the stroke is such that the spheres come close together, a condition where indeed the largest efficiencies are obtained. We find that swimmers with a “square stroke cycle” result more efficient than those with “circular stroke cycle” when the swimmer arms are long compared with the sphere radius, but the differences between the two strokes are smaller when the arms of the swimmers are short. This extended theoretical research of TLS incorporates a much precise description of the swimmer hydrodynamics, demonstrating the relevance of considering the finite size of the constitutive microswimmers spheres. This work expects to trigger future innovative steps contributing to the design of micro- and nanomachines and its applications.

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30

Nematollahisarvestani, Ali, and Amir Shamloo. "Dynamics of a magnetically rotated micro swimmer inspired by paramecium metachronal wave." Progress in Biophysics and Molecular Biology 142 (March 2019): 32–42. http://dx.doi.org/10.1016/j.pbiomolbio.2018.08.002.

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31

Chennaram, S. Sharanya, and T. Sonamani Singh. "Bidirectional Propulsion of Bioinspired Microswimmer in Microchannel at Low Reynolds Number." Journal of Physics: Conference Series 2663, no. 1 (December 1, 2023): 012035. http://dx.doi.org/10.1088/1742-6596/2663/1/012035.

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Abstract Swimming of micro-scale bodies is different from macro-scale counterparts due to low Reynolds number (Re) fluid-swimmer interaction. The Re is defined as the ratio of inertial force to viscous force and it can be expressed as, Re =ρ𝑣𝑙/µ, where ρ and µ are the density and viscosity of the fluid medium, v and l are the velocity and length of the swimmer. For microswimmers, due to the small length scale Re < 1, the inertial forces are negligible compared to viscous forces. Unlike the macroscale swimmers which exploit the inertial force for locomotion, microswimmers must use a different strategy to propel in low Re condition. These strategies are already available and used by microorganisms, which are perfect low Re swimmers, for example, Spermatozoon exploits their tail flexibility and anisotropic drag to swim, and E. coli bacteria use their helical tail to generate a non-reciprocal motion. By mimicking these microswimmers, researchers have developed many bioinspired microswimmers/microrobots having the potential to perform biomedical tasks like drug delivery, cell manipulation, in-situ sensing, and detoxification. Theoretical modeling and simulation of microswimmers are generally done by assuming that the microswimmer is in an infinite fluid medium, but the type of biomedical applications aimed are in confined environments with boundaries. Also, the environments are very complex, and it requires precise control and efficacy. In this paper, we present the modeling of flagellated magnetic microswimmer (inspired by Spermatozoon) in a microchannel using the finite element method. The dynamics were simulated by incorporating the complete hydrodynamic interactions (HI), that is intra-HI between the parts of the swimmer and inter-HI between the swimmer and the boundary walls of the channel. The parametric dependence analysis reveals that swimmer kinematics are dependent on the length and width of the tail, the head radius, width of the channel, and the actuation frequency of the driving magnetic field. These dependencies are explored to find a navigation control mechanism for the propulsion of microswimmer in a channel.

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32

Milster, S., J. Nötel, I. M. Sokolov, and L. Schimansky-Geier. "Eliminating inertia in a stochastic model of a micro-swimmer with constant speed." European Physical Journal Special Topics 226, no. 9 (June 2017): 2039–55. http://dx.doi.org/10.1140/epjst/e2017-70052-8.

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Jeznach, Cole, and Sarah D. Olson. "Dynamics of Swimmers in Fluids with Resistance." Fluids 5, no. 1 (January 19, 2020): 14. http://dx.doi.org/10.3390/fluids5010014.

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Micro-swimmers such as spermatozoa are able to efficiently navigate through viscous fluids that contain a sparse network of fibers or other macromolecules. We utilize the Brinkman equation to capture the fluid dynamics of sparse and stationary obstacles that are represented via a single resistance parameter. The method of regularized Brinkmanlets is utilized to solve for the fluid flow and motion of the swimmer in 2-dimensions when assuming the flagellum (tail) propagates a curvature wave. Extending previous studies, we investigate the dynamics of swimming when varying the resistance parameter, head or cell body radius, and preferred beat form parameters. For a single swimmer, we determine that increased swimming speed occurs for a smaller cell body radius and smaller fluid resistance. Progression of swimmers exhibits complex dynamics when considering hydrodynamic interactions; attraction of two swimmers is a robust phenomenon for smaller beat amplitude of the tail and smaller fluid resistance. Wall attraction is also observed, with a longer time scale of wall attraction with a larger resistance parameter.

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de Graaf, Joost, and Joakim Stenhammar. "Stirring by periodic arrays of microswimmers." Journal of Fluid Mechanics 811 (December 13, 2016): 487–98. http://dx.doi.org/10.1017/jfm.2016.797.

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The interaction between swimming micro-organisms or artificial self-propelled colloids and passive (tracer) particles in a fluid leads to enhanced diffusion of the tracers. This enhancement has attracted strong interest, as it could lead to new strategies to tackle the difficult problem of mixing on a microfluidic scale. Most of the theoretical work on this topic has focused on hydrodynamic interactions between the tracers and swimmers in a bulk fluid. However, in simulations, periodic boundary conditions (PBCs) are often imposed on the sample and the fluid. Here, we theoretically analyse the effect of PBCs on the hydrodynamic interactions between tracer particles and microswimmers. We formulate an Ewald sum for the leading-order stresslet singularity produced by a swimmer to probe the effect of PBCs on tracer trajectories. We find that introducing periodicity into the system has a surprisingly significant effect, even for relatively small swimmer–tracer separations. We also find that the bulk limit is only reached for very large system sizes, which are challenging to simulate with most hydrodynamic solvers.

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35

Thomases, Becca, and Robert D. Guy. "The role of body flexibility in stroke enhancements for finite-length undulatory swimmers in viscoelastic fluids." Journal of Fluid Mechanics 825 (July 19, 2017): 109–32. http://dx.doi.org/10.1017/jfm.2017.383.

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The role of passive body dynamics on the kinematics of swimming micro-organisms in complex fluids is investigated. Asymptotic analysis of small-amplitude motions of a finite-length undulatory swimmer in a Stokes–Oldroyd-B fluid is used to predict shape changes that result as body elasticity and fluid elasticity are varied. Results from the analysis are compared with numerical simulations and the numerically simulated shape changes agree with the analysis at both small and large amplitudes, even for strongly elastic flows. We compute a stroke-induced swimming speed that accounts for the shape changes, but not additional effects of fluid elasticity. Elasticity-induced shape changes lead to larger-amplitude strokes for sufficiently soft swimmers in a viscoelastic fluid, and these stroke boosts can lead to swimming speed-ups. However, for the strokes we examine, we find that additional effects of fluid elasticity generically result in a slow-down. Our high amplitude strokes in strongly elastic flows lead to a qualitatively different regime in which highly concentrated elastic stresses accumulate near swimmer bodies and dramatic slow-downs are seen.

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36

Berti, Luca, Laetitia Giraldi, and Christophe Prud’homme. "Swimming at low Reynolds number." ESAIM: Proceedings and Surveys 67 (2020): 46–60. http://dx.doi.org/10.1051/proc/202067004.

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We address the swimming problem at low Reynolds number. This regime, which is typically used for micro-swimmers, is described by Stokes equations. We couple a PDE solver of Stokes equations, derived from the Feel++ ﬁnite elements library, to a quaternion-based rigid-body solver. We validate our numerical results both on a 2D exact solution and on an exact solution for a rotating rigid body respectively. Finally, we apply them to simulate the motion of a one-hinged swimmer, which obeys to the scallop theorem.

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Esfandbod, Alireza, Hossein Nejat Pishkenari, and Ali Meghdari. "Dynamics and Control of a Novel Microrobot with High Maneuverability." Robotica 39, no. 10 (January 20, 2021): 1729–38. http://dx.doi.org/10.1017/s0263574720001460.

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SUMMARYIn this study, we introduce a novel three-dimensional micro-scale robot capable of swimming in low Reynolds number. The proposed robot consists of three rotating disks linked via three perpendicular adjustable rods, actuated by three rotary and three linear motors, respectively. The robot mechanism has an important property which makes it superior to the previously designed micro swimmers. In fact, our goal is designing a micro swimmer which its controllability matrix has full rank and hence it will be capable to perform any desired maneuver in space. After introducing the mechanism and derivation of the dynamical equations of motion, we propose a control method to steer the robot to the desired position and orientation in the presence of external disturbances in the low Reynolds number flow. Simulation results confirm the successful performance of the proposed mechanism and employed control method demonstrating high maneuverability of microrobot.

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Namdeo, S., S. N. Khaderi, and P. R. Onck. "Numerical modelling of chirality-induced bi-directional swimming of artificial flagella." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2162 (February 8, 2014): 20130547. http://dx.doi.org/10.1098/rspa.2013.0547.

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Biomimetic micro-swimmers can be used for various medical applications, such as targeted drug delivery and micro-object (e.g. biological cells) manipulation, in lab-on-a-chip devices. Bacteria swim using a bundle of flagella (flexible hair-like structures) that form a rotating cork-screw of chiral shape. To mimic bacterial swimming, we employ a computational approach to design a bacterial (chirality-induced) swimmer whose chiral shape and rotational velocity can be controlled by an external magnetic field. In our model, we numerically solve the coupled governing equations that describe the system dynamics (i.e. solid mechanics, fluid dynamics and magnetostatics). We explore the swimming response as a function of the characteristic dimensionless parameters and put special emphasis on controlling the swimming direction. Our results provide fundamental physical insight on the chirality-induced propulsion, and it provides guidelines for the design of magnetic bi-directional micro-swimmers.

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BECKER, L. E., S. A. KOEHLER, and H. A. STONE. "On self-propulsion of micro-machines at low Reynolds number: Purcells three-link swimmer." Journal of Fluid Mechanics 490 (September 10, 2003): 15–35. http://dx.doi.org/10.1017/s0022112003005184.

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40

Zhang, Ce, Shiqi Ma, and Lizhong Xu. "Velocity and Out-Step Frequencies for a Micro-Swimmer Based on Spiral Carbon Nanotubes." Micromachines 14, no. 7 (June 27, 2023): 1320. http://dx.doi.org/10.3390/mi14071320.

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The existing producing processes of micro spiral swimmers are complex. Here, a microswimmer with a magnetic layer on the surface of the spiral carbon nanotubes is proposed, which has a simple producing process. For the microswimmer, its equations of the velocities and out-step frequency are deduced. Using these equations, the velocities and out-step frequency of the microswimmer and their changes with related parameters are investigated. Results show that its velocities are proportional to the radius and helix angle of the spiral carbon nanotubes, and its out-step frequencies are proportional to magnetic field strength, the helix angle and magnetic layer thicknesses of the spiral carbon nanotubes, and inversely proportional to the fluid viscosity. The out-step frequency of the microswimmer is measured, which is in good agreement with the calculative ones.

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41

Wang, Qixuan. "Optimal Strokes of Low Reynolds Number Linked-Sphere Swimmers." Applied Sciences 9, no. 19 (September 26, 2019): 4023. http://dx.doi.org/10.3390/app9194023.

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Optimal gait design is important for micro-organisms and micro-robots that propel themselves in a fluid environment in the absence of external force or torque. The simplest models of shape changes are those that comprise a series of linked-spheres that can change their separation and/or their sizes. We examine the dynamics of three existing linked-sphere types of modeling swimmers in low Reynolds number Newtonian fluids using asymptotic analysis, and obtain their optimal swimming strokes by solving the Euler–Lagrange equation using the shooting method. The numerical results reveal that (1) with the minimal 2 degrees of freedom in shape deformations, the model swimmer adopting the mixed shape deformation modes strategy is more efficient than those with a single-mode of shape deformation modes, and (2) the swimming efficiency mostly decreases as the number of spheres increases, indicating that more degrees of freedom in shape deformations might not be a good strategy in optimal gait design in low Reynolds number locomotion.

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Bregulla, Andreas P., and Frank Cichos. "Size dependent efficiency of photophoretic swimmers." Faraday Discussions 184 (2015): 381–91. http://dx.doi.org/10.1039/c5fd00111k.

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We investigate experimentally the efficiency of self-propelled photophoretic swimmers based on metal-coated polymer particles of different sizes. The metal hemisphere absorbs the incident laser power and converts its energy into heat, which dissipates into the environment. A phoretic surface flow arises from the temperature gradient along the particle surface and drives the particle parallel to its symmetry axis. Scaling the particle size from micro to nanometers, the efficiency of converting optical power into motion is expected to rise with the reciprocal size for ideal swimmers. However, due to the finite size of the metal cap, the efficiency of a real swimmer reveals a maximum depending sensitively on the details of the metal cap shape. We compare the experimental results to numerical simulations.

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Majmudar, Trushant, Eric E. Keaveny, Jun Zhang, and Michael J. Shelley. "Experiments and theory of undulatory locomotion in a simple structured medium." Journal of The Royal Society Interface 9, no. 73 (February 8, 2012): 1809–23. http://dx.doi.org/10.1098/rsif.2011.0856.

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Undulatory locomotion of micro-organisms through geometrically complex, fluidic environments is ubiquitous in nature and requires the organism to negotiate both hydrodynamic effects and geometrical constraints. To understand locomotion through such media, we experimentally investigate swimming of the nematode Caenorhabditis elegans through fluid-filled arrays of micro-pillars and conduct numerical simulations based on a mechanical model of the worm that incorporates hydrodynamic and contact interactions with the lattice. We show that the nematode's path, speed and gait are significantly altered by the presence of the obstacles and depend strongly on lattice spacing. These changes and their dependence on lattice spacing are captured, both qualitatively and quantitatively, by our purely mechanical model. Using the model, we demonstrate that purely mechanical interactions between the swimmer and obstacles can produce complex trajectories, gait changes and velocity fluctuations, yielding some of the life-like dynamics exhibited by the real nematode. Our results show that mechanics, rather than biological sensing and behaviour, can explain some of the observed changes in the worm's locomotory dynamics.

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Elshalakani, Mohamed, and Christoph Brücker. "Simulation of self-coordination in a row of beating flexible flaplets for micro-swimmer applications: Model and experiment study." Journal of Fluids and Structures 94 (April 2020): 102923. http://dx.doi.org/10.1016/j.jfluidstructs.2020.102923.

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45

Zaid, Irwin M., Jörn Dunkel, and Julia M. Yeomans. "Lévy fluctuations and mixing in dilute suspensions of algae and bacteria." Journal of The Royal Society Interface 8, no. 62 (February 23, 2011): 1314–31. http://dx.doi.org/10.1098/rsif.2010.0545.

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Swimming micro-organisms rely on effective mixing strategies to achieve efficient nutrient influx. Recent experiments, probing the mixing capability of unicellular biflagellates, revealed that passive tracer particles exhibit anomalous non-Gaussian diffusion when immersed in a dilute suspension of self-motile Chlamydomonas reinhardtii algae. Qualitatively, this observation can be explained by the fact that the algae induce a fluid flow that may occasionally accelerate the colloidal tracers to relatively large velocities. A satisfactory quantitative theory of enhanced mixing in dilute active suspensions, however, is lacking at present. In particular, it is unclear how non-Gaussian signatures in the tracers' position distribution are linked to the self-propulsion mechanism of a micro-organism. Here, we develop a systematic theoretical description of anomalous tracer diffusion in active suspensions, based on a simplified tracer-swimmer interaction model that captures the typical distance scaling of a microswimmer's flow field. We show that the experimentally observed non-Gaussian tails are generic and arise owing to a combination of truncated Lévy statistics for the velocity field and algebraically decaying time correlations in the fluid. Our analytical considerations are illustrated through extensive simulations, implemented on graphics processing units to achieve the large sample sizes required for analysing the tails of the tracer distributions.

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Das, Asimanshu, Matthew Styslinger, Daniel M. Harris, and Roberto Zenit. "Force and torque-free helical tail robot to study low Reynolds number micro-organism swimming." Review of Scientific Instruments 93, no. 4 (April 1, 2022): 044103. http://dx.doi.org/10.1063/5.0079815.

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Helical propulsion is used by many micro-organisms to swim in viscous-dominated environments. Their swimming dynamics are relatively well understood, but a detailed study of the flow fields is still needed to understand wall effects and hydrodynamic interactions among swimmers. In this letter, we describe the development of an autonomous swimming robot with a helical tail that operates in the Stokes regime. The device uses a battery-based power system with a miniature motor that imposes a rotational speed on a helical tail. The speed, direction, and activation are controlled electronically using an infrared remote control. Since the robot is about 5 cm long, we use highly viscous fluids to match the Reynolds number, Re, to be less than 0.1. Measurements of swimming speeds are conducted for a range of helical wavelengths, λ, head geometries, and rotation rates, ω. We provide comparisons of the experimental measurements with analytical predictions derived from resistive force theory. This force and torque-free neutrally buoyant swimmer mimics the swimming strategy of bacteria more closely than previously used designs and offers a lot of potential for future applications.

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Michelin, Sébastien, and Eric Lauga. "Unsteady feeding and optimal strokes of model ciliates." Journal of Fluid Mechanics 715 (January 9, 2013): 1–31. http://dx.doi.org/10.1017/jfm.2012.484.

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AbstractThe flow field created by swimming micro-organisms not only enables their locomotion but also leads to advective transport of nutrients. In this paper we address analytically and computationally the link between unsteady feeding and unsteady swimming on a model micro-organism, the spherical squirmer, actuating the fluid in a time-periodic manner. We start by performing asymptotic calculations at low Péclet number ($\mathit{Pe}$) on the advection–diffusion problem for the nutrients. We show that the mean rate of feeding as well as its fluctuations in time depend only on the swimming modes of the squirmer up to order ${\mathit{Pe}}^{3/ 2} $, even when no swimming occurs on average, while the influence of non-swimming modes comes in only at order ${\mathit{Pe}}^{2} $. We also show that generically we expect a phase delay between feeding and swimming of $1/ 8\mathrm{th} $ of a period. Numerical computations for illustrative strokes at finite $\mathit{Pe}$ confirm quantitatively our analytical results linking swimming and feeding. We finally derive, and use, an adjoint-based optimization algorithm to determine the optimal unsteady strokes maximizing feeding rate for a fixed energy budget. The overall optimal feeder is always the optimal steady swimmer. Within the set of time-periodic strokes, the optimal feeding strokes are found to be equivalent to those optimizing periodic swimming for all values of the Péclet number, and correspond to a regularization of the overall steady optimal.

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Setter, Eyal, Izhak Bucher, and Shimon Haber. "Propulsion at low Reynolds numbers by multiple traveling waves." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 228, no. 16 (February 12, 2014): 2938–49. http://dx.doi.org/10.1177/0954406214523580.

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Microorganisms or micro-robotic swimmers employ traveling waves as a common swimming mechanism involving time-irreversible deformations of their outer surface. Normally, the deforming surfaces constitute of multiple spatial waves, some standing and others propagating forward or backward. A unique technique is developed here to experimentally decompose a waving surface into its spatial wavelengths in each time instance by processing a sequence of photographs. This information is curve fitted to yield the phase velocity, frequency, and amplitudes of the propagating and receding waves of each component. The significance of the harmonic decomposition is demonstrated using an experimental macro-scale swimmer that utilizes small amplitude circumferential waves. A numerical image processing and curve-fitting procedure is shown and a theoretical model is also developed to account for the hydrodynamic effects of multiple wavelengths. The theoretical results fit well with the experimental data at low speeds, although the contribution of higher harmonics was small in experiment, but the higher harmonics are clearly visible and successfully identified. Still, the importance of the multiharmonics analysis for swimmers, which utilize traveling waves mechanisms, found both in nature and in man-made machines, was formulated and partially verified.

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49

Ren, Zhezheng. "Real model for micro swimmer and the study of the relationship between the swimming speed, pitch angle, and rotation rate for the flagellum." Journal of Physics: Conference Series 2634, no. 1 (November 1, 2023): 012009. http://dx.doi.org/10.1088/1742-6596/2634/1/012009.

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Abstract This study focuses on the fluid mechanics of a microswimmer and explores the relationship between speed, pitch angle, and rotation rate for the flagellar during bacterial swimming. Based on the simulation using MATLAB, it is concluded that when the pitch angle of the flagellar helix is in the range of 0 to 90 degrees, the value of swimming speed increases firstly and decreases. When the angle reaches 46.83 degrees, the speed reaches the maximum point. The radius of the body of the microswimmer is determined by the Buckingham Pi theory. After calculating by using the equations in the related paper and measuring by the real model, we derive that the relationship between swimming speed and the rotation rate for the flagellar filament should be proportional at the low rotation rate so that it can be obtained to optimize the artificial micro swimming device with higher swimming efficiency.

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Park, Yunyoung, Yongsam Kim, and Sookkyung Lim. "Locomotion of a single-flagellated bacterium." Journal of Fluid Mechanics 859 (November 21, 2018): 586–612. http://dx.doi.org/10.1017/jfm.2018.799.

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Single-flagellated bacteria propel themselves by rotating a flagellar motor, translating rotation to the filament through a compliant hook and subsequently driving the rotation of the flagellum. The flagellar motor alternates the direction of rotation between counterclockwise and clockwise, and this leads to the forward and backward directed swimming. Such bacteria can change the course of swimming as the hook experiences its buckling caused by the change of bending rigidity. In this paper, we present a comprehensive model of a monotrichous bacterium as a free swimmer in a viscous fluid. We describe a cell body as a rigid body using the penalty method and a flagellum as an elastic rod using Kirchhoff rod theory. The hydrodynamic interaction of the bacterium is described by the regularized Stokes formulation. Our model of a single-flagellated micro-organism is able to mimic a swimming pattern that is well matched with the experimental observation. Furthermore, we find the critical thresholds of the rotational frequency of the motor and the bending modulus of the hook for the buckling instability, and investigate the dependence of the buckling angle and the reorientation of the swimming cell after buckling on the physical and geometrical parameters of the model.

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