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Suga M, Suda S, Ichikawa M, Kimura Y. Self-propelled motion switching in nematic liquid crystal droplets in aqueous surfactant solutions. Phys Rev E 2018; 97:062703. [PMID: 30011466 DOI: 10.1103/physreve.97.062703] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2018] [Indexed: 06/08/2023]
Abstract
The self-propelled motions of micron-sized nematic liquid crystal droplets in an aqueous surfactant solution have been studied by tracking individual droplets over long time periods. Switching between self-propelled modes is observed as the droplet size decreases at a nearly constant dissolution rate: from random to helical and then straight motion. The velocity of the droplet decreases with its size for straight and helical motions but is independent of size for random motion. The switching between helical and straight motions is found to be governed by the self-propelled velocity, and is confirmed by experiments at various surfactant concentrations. The helical motion appears along with a shifting of a point defect from the self-propelled direction of the droplet. The critical velocity for this shift of the defect position is found to be related with the Ericksen number, which is defined by the ratio of the viscous and elastic stresses. In a thin cell whose thickness is smaller than that of the initial droplet size, the droplets show more complex trajectories, including "figure-8s" and zigzags. The appearance of those characteristic motions is attributed to autochemotaxis of the droplet.
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Affiliation(s)
- Mariko Suga
- Department of Physics, School of Science, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan
| | - Saori Suda
- Department of Physics, Graduate School of Science, Kyoto University, Kitashirakawa-Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan
| | - Masatoshi Ichikawa
- Department of Physics, Graduate School of Science, Kyoto University, Kitashirakawa-Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan
| | - Yasuyuki Kimura
- Department of Physics, School of Science, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan
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2
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Tarama M. Swinging motion of active deformable particles in Poiseuille flow. Phys Rev E 2017; 96:022602. [PMID: 28950457 DOI: 10.1103/physreve.96.022602] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2017] [Indexed: 11/07/2022]
Abstract
Dynamics of active deformable particles in an external Poiseuille flow is investigated. To make the analysis general, we employ time-evolution equations derived from symmetry considerations that take into account an elliptical shape deformation. First, we clarify the relation of our model to that of rigid active particles. Then, we study the dynamical modes that active deformable particles exhibit by changing the strength of the external flow. We emphasize the difference between the active particles that tend to self-propel parallel to the elliptical shape deformation and those self-propelling perpendicularly. In particular, a swinging motion around the centerline far from the channel walls is discussed in detail.
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Affiliation(s)
- Mitsusuke Tarama
- Fukui Institute for Fundamental Chemistry, Kyoto University, Kyoto, 606-8103, Japan
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Pande J, Merchant L, Krüger T, Harting J, Smith AS. Effect of body deformability on microswimming. SOFT MATTER 2017; 13:3984-3993. [PMID: 28504290 DOI: 10.1039/c7sm00181a] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
In this work we consider the following question: given a mechanical microswimming mechanism, does increased deformability of the swimmer body hinder or promote the motility of the swimmer? To answer this we run immersed-boundary-lattice-Boltzmann simulations of a microswimmer composed of deformable beads connected with springs. We find that the same deformations in the beads can result in different effects on the swimming velocity, namely an enhancement or a reduction, depending on the other parameters. To understand this we determine analytically the velocity of the swimmer, starting from the forces driving the motion and assuming that the deformations in the beads are known as functions of time and are much smaller than the beads themselves. We find that to the lowest order, only the driving frequency mode of the surface deformations contributes to the swimming velocity, and comparison to the simulations shows that both the velocity-promoting and velocity-hindering effects of bead deformability are reproduced correctly by the theory in the limit of small bead deformations. For the case of active deformations we show that there are critical values of the spring constant - which for a general swimmer corresponds to its main elastic degree of freedom - which decide whether the body deformability is beneficial for motion or not.
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Affiliation(s)
- Jayant Pande
- PULS Group, Department of Physics, Friedrich-Alexander-University Erlangen-Nuremberg, Nägelsbachstraße 49b, 91054 Erlangen, Germany
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Küchler N, Löwen H, Menzel AM. Getting drowned in a swirl: Deformable bead-spring model microswimmers in external flow fields. Phys Rev E 2016; 93:022610. [PMID: 26986380 DOI: 10.1103/physreve.93.022610] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2015] [Indexed: 06/05/2023]
Abstract
Deformability is a central feature of many types of microswimmers, e.g., for artificially generated self-propelled droplets. Here, we analyze deformable bead-spring microswimmers in an externally imposed solvent flow field as simple theoretical model systems. We focus on their behavior in a circular swirl flow in two spatial dimensions. Linear (straight) two-bead swimmers are found to circle around the swirl with a slight drift to the outside with increasing activity. In contrast to that, we observe for triangular three-bead or squarelike four-bead swimmers a tendency of being drawn into the swirl and finally getting drowned, although a radial inward component is absent in the flow field. During one cycle around the swirl, the self-propulsion direction of an active triangular or squarelike swimmer remains almost constant, while their orbits become deformed exhibiting an "egglike" shape. Over time, the swirl flow induces slight net rotations of these swimmer types, which leads to net rotations of the egg-shaped orbits. Interestingly, in certain cases, the orbital rotation changes sense when the swimmer approaches the flow singularity. Our predictions can be verified in real-space experiments on artificial microswimmers.
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Affiliation(s)
- Niklas Küchler
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - Andreas M Menzel
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
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Tarama M, Menzel AM, Löwen H. Deformable microswimmer in a swirl: capturing and scattering dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:032907. [PMID: 25314504 DOI: 10.1103/physreve.90.032907] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/15/2014] [Indexed: 06/04/2023]
Abstract
Inspired by the classical Kepler and Rutherford problem, we investigate an analogous setup in the context of active microswimmers: the behavior of a deformable microswimmer in a swirl flow. First, we identify new steady bound states in the swirl flow and analyze their stability. Second, we study the dynamics of a self-propelled swimmer heading towards the vortex center, and we observe the subsequent capturing and scattering dynamics. We distinguish between two major types of swimmers, those that tend to elongate perpendicularly to the propulsion direction and those that pursue a parallel elongation. While the first ones can get caught by the swirl, the second ones were always observed to be scattered, which proposes a promising escape strategy. This offers a route to design artificial microswimmers that show the desired behavior in complicated flow fields. It should be straightforward to verify our results in a corresponding quasi-two-dimensional experiment using self-propelled droplets on water surfaces.
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Affiliation(s)
- Mitsusuke Tarama
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan and Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany and Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan
| | - Andreas M Menzel
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
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Yoshinaga N. Spontaneous motion and deformation of a self-propelled droplet. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:012913. [PMID: 24580303 DOI: 10.1103/physreve.89.012913] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2013] [Indexed: 06/03/2023]
Abstract
The time evolution equation of motion and shape are derived for a self-propelled droplet driven by a chemical reaction. The coupling between the chemical reaction and motion makes an inhomogeneous concentration distribution as well as a surrounding flow leading to the instability of a stationary state. The instability results in spontaneous motion by which the shape of the droplet deforms from a sphere. We found that the self-propelled droplet is elongated perpendicular to the direction of motion and is characterized as a pusher.
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Affiliation(s)
- Natsuhiko Yoshinaga
- WPI, Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
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Tarama M, Menzel AM, ten Hagen B, Wittkowski R, Ohta T, Löwen H. Dynamics of a deformable active particle under shear flow. J Chem Phys 2013; 139:104906. [DOI: 10.1063/1.4820416] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023] Open
Affiliation(s)
- Mitsusuke Tarama
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
- Institute for Solid State Physics, The University of Tokyo, Kashiwa, Chiba 277-8581, Japan
- Department of Physics, Graduate School of Science, The University of Tokyo, Tokyo 113-0033, Japan
| | - Andreas M. Menzel
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - Borge ten Hagen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - Raphael Wittkowski
- SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
| | - Takao Ohta
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
- Department of Physics, Graduate School of Science, The University of Tokyo, Tokyo 113-0033, Japan
- Soft Matter Center, Ochanomizu University, Tokyo 112-0012, Japan
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
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Blanch-Mercader C, Casademunt J. Spontaneous motility of actin lamellar fragments. PHYSICAL REVIEW LETTERS 2013; 110:078102. [PMID: 25166412 DOI: 10.1103/physrevlett.110.078102] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/29/2012] [Indexed: 06/03/2023]
Abstract
We show that actin lamellar fragments driven solely by polymerization forces at the bounding membrane are generically motile when the circular symmetry is spontaneously broken, with no need of molecular motors or global polarization. We base our study on a nonlinear analysis of a recently introduced minimal model [Callan-Jones et al., Phys. Rev. Lett. 100, 258106 (2008)]. We prove the nonlinear instability of the center of mass and find an exact and simple relation between shape and center-of-mass velocity. A complex subcritical bifurcation scenario into traveling solutions is unfolded, where finite velocities appear through a nonadiabatic mechanism. Examples of traveling solutions and their stability are studied numerically.
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Affiliation(s)
- C Blanch-Mercader
- Departament d'Estructura i Constituents de la Matèria, Universitat de Barcelona, Avinguda Diagonal 647, E-08028 Barcelona, Spain
| | - J Casademunt
- Departament d'Estructura i Constituents de la Matèria, Universitat de Barcelona, Avinguda Diagonal 647, E-08028 Barcelona, Spain
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Wen FL, Leung KT, Chen HY. Trajectories of Listeria-type motility in two dimensions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:061902. [PMID: 23367971 DOI: 10.1103/physreve.86.061902] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2012] [Indexed: 06/01/2023]
Abstract
Force generated by actin polymerization is essential in cell motility and the locomotion of organelles or bacteria such as Listeria monocytogenes. Both in vivo and in vitro experiments on actin-based motility have observed geometrical trajectories including straight lines, circles, S-shaped curves, and translating figure eights. This paper reports a phenomenological model of an actin-propelled disk in two dimensions that generates geometrical trajectories. Our model shows that when the evolutions of actin density and force per filament on the disk are strongly coupled to the disk self-rotation, it is possible for a straight trajectory to lose its stability. When the instability is due to a pitchfork bifurcation, the resulting trajectory is a circle; a straight trajectory can also lose stability through a Hopf bifurcation, and the resulting trajectory is an S-shaped curve. We also show that a half-coated disk, which mimics the distribution of functionalized proteins in Listeria, also undergoes similar symmetry-breaking bifurcations when the straight trajectory loses stability. For both a fully coated disk and a half-coated disk, when the trajectory is an S-shaped curve, the angular frequency of the disk self-rotation is different from that of the disk trajectory. However, for circular trajectories, these angular frequencies are different for a fully coated disk but the same for a half-coated disk.
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Affiliation(s)
- Fu-Lai Wen
- Department of Physics, National Central University, Jhongli, Taiwan 32001, Republic of China
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Tarama M, Ohta T. Spinning motion of a deformable self-propelled particle in two dimensions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:464129. [PMID: 23114593 DOI: 10.1088/0953-8984/24/46/464129] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
We investigate the dynamics of a single deformable self-propelled particle which undergoes a spinning motion in a two-dimensional space. Equations of motion are derived from symmetry arguments for three kinds of variable. One is a vector which represents the velocity of the center of mass. The second is a traceless symmetric tensor representing deformation. The third is an antisymmetric tensor for spinning degree of freedom. By numerical simulations, we have obtained a variety of dynamical states due to interplay between the spinning motion and the deformation. The bifurcations of these dynamical states are analyzed by the simplified equations of motion.
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Yabunaka S, Ohta T, Yoshinaga N. Self-propelled motion of a fluid droplet under chemical reaction. J Chem Phys 2012; 136:074904. [DOI: 10.1063/1.3685805] [Citation(s) in RCA: 53] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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