1
|
Mousavi SM, Gompper G, Winkler RG. Active bath-induced localization and collapse of passive semiflexible polymers. J Chem Phys 2021; 155:044902. [PMID: 34340385 DOI: 10.1063/5.0058150] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
The conformational and dynamical properties of a passive polymer embedded in a bath of active Brownian particles (ABPs) are studied by Langevin dynamics simulations. Various activities and ABP concentrations below and above the critical values for motility-induced phase separation (MIPS) are considered. In a homogeneous ABP fluid, the embedded polymer swells with increasing bath activity, with stronger swelling for larger densities. The polymer dynamics is enhanced, with the diffusion coefficient increasing by a power-law with increasing activity, where the exponent depends on the ABP concentration. For ABP concentrations in the MIPS regime, we observe a localization of the polymer in the low-density ABP phase associated with polymer collapse for moderate activities and a reswelling for high activities accompanied by a preferred localization in the high-density ABP phase. Localization and reswelling are independent of the polymer stiffness, with stiff polymers behaving similarly to flexible polymers. The polymer collapse is associated with a slowdown of its dynamics and a significantly smaller center-of-mass diffusion coefficient. In general, the polymer dynamics can only partially be described by an effective (bath) temperature. Moreover, the properties of a polymer embedded in a homogeneous active bath deviate quantitatively from those of a polymer composed of active monomers, i.e., linear chains of ABPs; however, such a polymer exhibits qualitatively similar activity-dependent features.
Collapse
Affiliation(s)
- S Mahdiyeh Mousavi
- Theoretical Physics of Living Matter, Institute for Advanced Simulation and Institute of Biological Information Processing, Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - Gerhard Gompper
- Theoretical Physics of Living Matter, Institute for Advanced Simulation and Institute of Biological Information Processing, Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - Roland G Winkler
- Theoretical Physics of Living Matter, Institute for Advanced Simulation and Institute of Biological Information Processing, Forschungszentrum Jülich, D-52425 Jülich, Germany
| |
Collapse
|
2
|
Yamamoto R, Molina JJ, Nakayama Y. Smoothed profile method for direct numerical simulations of hydrodynamically interacting particles. SOFT MATTER 2021; 17:4226-4253. [PMID: 33908448 DOI: 10.1039/d0sm02210a] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
A general method is presented for computing the motions of hydrodynamically interacting particles in various kinds of host fluids for arbitrary Reynolds numbers. The method follows the standard procedure for performing direct numerical simulations (DNS) of particulate systems, where the Navier-Stokes equation must be solved consistently with the motion of the rigid particles, which defines the temporal boundary conditions to be satisfied by the Navier-Stokes equation. The smoothed profile (SP) method provides an efficient numerical scheme for coupling the continuum fluid mechanics with the dispersed moving particles, which are allowed to have arbitrary shapes. In this method, the sharp boundaries between solid particles and the host fluid are replaced with a smeared out thin shell (interfacial) region, which can be accurately resolved on a fixed Cartesian grid utilizing a SP function with a finite thickness. The accuracy of the SP method is illustrated by comparison with known exact results. In the present paper, the high degree of versatility of the SP method is demonstrated by considering several types of active and passive particle suspensions.
Collapse
Affiliation(s)
- Ryoichi Yamamoto
- Department of Chemical Engineering, Kyoto University, Kyoto 615-8510, Japan.
| | - John J Molina
- Department of Chemical Engineering, Kyoto University, Kyoto 615-8510, Japan.
| | - Yasuya Nakayama
- Department of Chemical Engineering, Kyushu University, Fukuoka 819-0395, Japan
| |
Collapse
|
3
|
Xu RK, Jiang HJ, Hou ZH. Simulation study of passive rod diffusion in active bath: Nonmonotonic length dependence and abnormal translation-rotation coupling. CHINESE J CHEM PHYS 2021. [DOI: 10.1063/1674-0068/cjcp2006091] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Affiliation(s)
- Rui-kai Xu
- Department of Chemical Physics & Hefei National Laboratory for Physical Sciences at the Microscale, iChEM, University of Science and Technology of China, Hefei 230026, China
| | - Hui-jun Jiang
- Department of Chemical Physics & Hefei National Laboratory for Physical Sciences at the Microscale, iChEM, University of Science and Technology of China, Hefei 230026, China
| | - Zhong-huai Hou
- Department of Chemical Physics & Hefei National Laboratory for Physical Sciences at the Microscale, iChEM, University of Science and Technology of China, Hefei 230026, China
| |
Collapse
|
4
|
Deng J, Molaei M, Chisholm NG, Stebe KJ. Motile Bacteria at Oil-Water Interfaces: Pseudomonas aeruginosa. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2020; 36:6888-6902. [PMID: 32097012 DOI: 10.1021/acs.langmuir.9b03578] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Bacteria are important examples of active or self-propelled colloids. Because of their directed motion, they accumulate near interfaces. There, they can become trapped and swim adjacent to the interface via hydrodynamic interactions, or they can adsorb directly and swim in an adhered state with complex trajectories that differ from those in bulk in both form and spatiotemporal implications. We have adopted the monotrichous bacterium Pseudomonas aeruginosa PA01 as a model species and have studied its motion at oil-aqueous interfaces. We have identified conditions in which bacteria swim persistently without restructuring the interface, allowing detailed and prolonged study of their motion. In addition to characterizing the ensemble behavior of the bacteria, we have observed a gallery of distinct trajectories of individual swimmers on and near fluid interfaces. We attribute these diverse swimming behaviors to differing trapped states for the bacteria in the fluid interface. These trajectory types include Brownian diffusive paths for passive adsorbed bacteria, curvilinear trajectories including curly paths with radii of curvature larger than the cell body length, and rapid pirouette motions with radii of curvature comparable to the cell body length. Finally, we see interfacial visitors that come and go from the interfacial plane. We characterize these individual swimmer motions. This work may impact nutrient cycles for bacteria on or near interfaces in nature. This work will also have implications in microrobotics, as active colloids in general and bacteria in particular are used to carry cargo in this burgeoning field. Finally, these results have implications in engineering of active surfaces that exploit interfacially trapped self-propelled colloids.
Collapse
Affiliation(s)
- Jiayi Deng
- Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, United States
| | - Mehdi Molaei
- Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, United States
| | - Nicholas G Chisholm
- Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, United States
| | - Kathleen J Stebe
- Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, United States
| |
Collapse
|
5
|
Wang C, Jiang H. The inhibition of concentrated active baths. J Chem Phys 2020; 152:184907. [PMID: 32414266 DOI: 10.1063/5.0005313] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Passive tracers in the active bath express fascinating behaviors. However, most studies are restricted to dilute active baths. Here, we use 2D simulation of suspensions consisting of active Brownian particles and a passive disk-shaped tracer to investigate tracers' diffusive behaviors in a wide range of volume fractions. Due to the competition between the thermal noise and collisions with active particles, tracers express a first transition from the normal diffusion to the superdiffusion at a short time scale and recur to normal diffusion at a long time scale. At a low volume fraction, infrequent active collisions retard the first transition of smaller tracers. At a high volume fraction, active particles with high activity aggregating around tracers induce a bimodal probability distribution function of tracer displacements during superdiffusion. Considering the enhancement of diffusion, the non-dimensional enhanced diffusivity increases asymptotically with the Peclet number. The asymptotic line gives an upper limit of non-dimensional enhanced diffusivity of tracers. Cases with lower enhanced diffusion have a high volume fraction and a low active velocity that indicates the inhibition of concentrated active baths. With the high negentropic work of these cases, the inhibition is explained as the change of the configuration of active baths for introducing tracers.
Collapse
Affiliation(s)
- Chen Wang
- CAS Key Laboratory of Mechanical Behavior and Design of Materials, Hefei National Laboratory for Physical Science at the Microscale, CAS Center for Excellence in Complex System Mechanics, Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Hongyuan Jiang
- CAS Key Laboratory of Mechanical Behavior and Design of Materials, Hefei National Laboratory for Physical Science at the Microscale, CAS Center for Excellence in Complex System Mechanics, Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China
| |
Collapse
|
6
|
Dey KK. Dynamic Coupling at Low Reynolds Number. Angew Chem Int Ed Engl 2019; 58:2208-2228. [DOI: 10.1002/anie.201804599] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2018] [Indexed: 01/10/2023]
Affiliation(s)
- Krishna Kanti Dey
- Discipline of PhysicsIndian Institute of Technology Gandhinagar Gandhinagar Gujarat 382355 India
| |
Collapse
|
7
|
Affiliation(s)
- Krishna Kanti Dey
- Discipline of Physics; Indian Institute of Technology Gandhinagar; Gandhinagar Gujarat 382355 Indien
| |
Collapse
|
8
|
Schwarzendahl FJ, Mazza MG. Maximum in density heterogeneities of active swimmers. SOFT MATTER 2018; 14:4666-4678. [PMID: 29717736 DOI: 10.1039/c7sm02301d] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Suspensions of unicellular microswimmers such as flagellated bacteria or motile algae can exhibit spontaneous density heterogeneities at large enough concentrations. We introduce a novel model for biological microswimmers that creates the flow field of the corresponding microswimmers, and takes into account the shape anisotropy of the swimmer's body and stroke-averaged flagella. By employing multiparticle collision dynamics, we directly couple the swimmer's dynamics to the fluid's. We characterize the nonequilibrium phase diagram, as the filling fraction and Péclet number are varied, and find density heterogeneities in the distribution of both pullers and pushers, due to hydrodynamic instabilities. We find a maximum degree of clustering at intermediate filling fractions and at large Péclet numbers resulting from a competition of hydrodynamic and steric interactions between the swimmers. We develop an analytical theory that supports these results. This maximum might represent an optimum for the microorganisms' colonization of their environment.
Collapse
Affiliation(s)
- Fabian Jan Schwarzendahl
- Max-Planck-Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany.
| | | |
Collapse
|
9
|
Zöttl A, Stark H. Simulating squirmers with multiparticle collision dynamics. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2018; 41:61. [PMID: 29766348 DOI: 10.1140/epje/i2018-11670-3] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/27/2018] [Accepted: 04/23/2018] [Indexed: 06/08/2023]
Abstract
Multiparticle collision dynamics is a modern coarse-grained simulation technique to treat the hydrodynamics of Newtonian fluids by solving the Navier-Stokes equations. Naturally, it also includes thermal noise. Initially it has been applied extensively to spherical colloids or bead-spring polymers immersed in a fluid. Here, we review and discuss the use of multiparticle collision dynamics for studying the motion of spherical model microswimmers called squirmers moving in viscous fluids.
Collapse
Affiliation(s)
- Andreas Zöttl
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, OX1 3NP, Oxford, UK.
- Institute for Theoretical Physics, Technische Universität Berlin, Hardenbergstr. 36, 10623, Berlin, Germany.
| | - Holger Stark
- Institute for Theoretical Physics, Technische Universität Berlin, Hardenbergstr. 36, 10623, Berlin, Germany
| |
Collapse
|
10
|
Wang Q, Othmer HG. Analysis of a model microswimmer with applications to blebbing cells and mini-robots. J Math Biol 2018; 76:1699-1763. [PMID: 29497820 DOI: 10.1007/s00285-018-1225-y] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2016] [Revised: 01/05/2018] [Indexed: 11/25/2022]
Abstract
Recent research has shown that motile cells can adapt their mode of propulsion depending on the environment in which they find themselves. One mode is swimming by blebbing or other shape changes, and in this paper we analyze a class of models for movement of cells by blebbing and of nano-robots in a viscous fluid at low Reynolds number. At the level of individuals, the shape changes comprise volume exchanges between connected spheres that can control their separation, which are simple enough that significant analytical results can be obtained. Our goal is to understand how the efficiency of movement depends on the amplitude and period of the volume exchanges when the spheres approach closely during a cycle. Previous analyses were predicated on wide separation, and we show that the speed increases significantly as the separation decreases due to the strong hydrodynamic interactions between spheres in close proximity. The scallop theorem asserts that at least two degrees of freedom are needed to produce net motion in a cyclic sequence of shape changes, and we show that these degrees can reside in different swimmers whose collective motion is studied. We also show that different combinations of mode sharing can lead to significant differences in the translation and performance of pairs of swimmers.
Collapse
Affiliation(s)
- Qixuan Wang
- 540R Rowland Hall, University of California, Irvine, Irvine, USA.
| | - Hans G Othmer
- School of Mathematics, 270A Vincent Hall, University of Minnesota, Minneapolis, USA
| |
Collapse
|
11
|
Oyama N, Molina JJ, Yamamoto R. Do hydrodynamically assisted binary collisions lead to orientational ordering of microswimmers? THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2017; 40:95. [PMID: 29110098 DOI: 10.1140/epje/i2017-11586-4] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2017] [Accepted: 10/23/2017] [Indexed: 06/07/2023]
Abstract
We have investigated the onset of collective motion in systems of model microswimmers, by performing a comprehensive analysis of the binary collision dynamics using three-dimensional direct numerical simulations (DNS) with hydrodynamic interactions. From this data, we have constructed a simplified binary collision model (BCM) which accurately reproduces the collective behavior obtained from the DNS for most cases. Thus, we show that global alignment can mostly arise solely from binary collisions. Although the agreement between both models (DNS and BCM) is not perfect, the parameter range in which notable differences appear is also that for which strong density fluctuations are present in the system (where pseudo-sound mound can be observed (N. Oyama et al., Phys. Rev. E 93, 043114 (2016))).
Collapse
Affiliation(s)
- Norihiro Oyama
- Mathematics for Advanced Materials-OIL, AIST-Tohoku University, 980-8577, Sendai, Japan.
| | - John Jairo Molina
- Department of Chemical Engineering, Kyoto University, 615-8510, Kyoto, Japan
| | - Ryoichi Yamamoto
- Department of Chemical Engineering, Kyoto University, 615-8510, Kyoto, Japan
- Institute of Industrial Science, The University of Tokyo, 153-8505, Tokyo, Japan
| |
Collapse
|
12
|
Stenhammar J, Nardini C, Nash RW, Marenduzzo D, Morozov A. Role of Correlations in the Collective Behavior of Microswimmer Suspensions. PHYSICAL REVIEW LETTERS 2017; 119:028005. [PMID: 28753351 DOI: 10.1103/physrevlett.119.028005] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2017] [Indexed: 06/07/2023]
Abstract
In this Letter, we study the collective behavior of a large number of self-propelled microswimmers immersed in a fluid. Using unprecedentedly large-scale lattice Boltzmann simulations, we reproduce the transition to bacterial turbulence. We show that, even well below the transition, swimmers move in a correlated fashion that cannot be described by a mean-field approach. We develop a novel kinetic theory that captures these correlations and is nonperturbative in the swimmer density. To provide an experimentally accessible measure of correlations, we calculate the diffusivity of passive tracers and reveal its nontrivial density dependence. The theory is in quantitative agreement with the lattice Boltzmann simulations and captures the asymmetry between pusher and puller swimmers below the transition to turbulence.
Collapse
Affiliation(s)
- Joakim Stenhammar
- Division of Physical Chemistry, Lund University, P.O. Box 124, S-221 00 Lund, Sweden
| | - Cesare Nardini
- DAMTP, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
- SUPA, School of Physics and Astronomy, The University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
- Service de Physique de l'État Condensé, CNRS UMR 3680, CEA-Saclay, 91191 Gif-sur-Yvette, France
| | - Rupert W Nash
- EPCC, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Davide Marenduzzo
- SUPA, School of Physics and Astronomy, The University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Alexander Morozov
- SUPA, School of Physics and Astronomy, The University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| |
Collapse
|
13
|
Abstract
We study the diffusion of a Brownian probe particle of size R in a dilute dispersion of active Brownian particles of size a, characteristic swim speed U_{0}, reorientation time τ_{R}, and mechanical energy k_{s}T_{s}=ζ_{a}U_{0}^{2}τ_{R}/6, where ζ_{a} is the Stokes drag coefficient of a swimmer. The probe has a thermal diffusivity D_{P}=k_{B}T/ζ_{P}, where k_{B}T is the thermal energy of the solvent and ζ_{P} is the Stokes drag coefficient for the probe. When the swimmers are inactive, collisions between the probe and the swimmers sterically hinder the probe's diffusive motion. In competition with this steric hindrance is an enhancement driven by the activity of the swimmers. The strength of swimming relative to thermal diffusion is set by Pe_{s}=U_{0}a/D_{P}. The active contribution to the diffusivity scales as Pe_{s}^{2} for weak swimming and Pe_{s} for strong swimming, but the transition between these two regimes is nonmonotonic. When fluctuations in the probe motion decay on the time scale τ_{R}, the active diffusivity scales as k_{s}T_{s}/ζ_{P}: the probe moves as if it were immersed in a solvent with energy k_{s}T_{s} rather than k_{B}T.
Collapse
Affiliation(s)
- Eric W Burkholder
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - John F Brady
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| |
Collapse
|
14
|
de Graaf J, Stenhammar J. Lattice-Boltzmann simulations of microswimmer-tracer interactions. Phys Rev E 2017; 95:023302. [PMID: 28297968 DOI: 10.1103/physreve.95.023302] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2016] [Indexed: 06/06/2023]
Abstract
Hydrodynamic interactions in systems composed of self-propelled particles, such as swimming microorganisms and passive tracers, have a significant impact on the tracer dynamics compared to the equivalent "dry" sample. However, such interactions are often difficult to take into account in simulations due to their computational cost. Here, we perform a systematic investigation of swimmer-tracer interaction using an efficient force-counterforce-based lattice-Boltzmann (LB) algorithm [De Graaf et al., J. Chem. Phys. 144, 134106 (2016)JCPSA60021-960610.1063/1.4944962] in order to validate its ability to capture the relevant low-Reynolds-number physics. We show that the LB algorithm reproduces far-field theoretical results well, both in a system with periodic boundary conditions and in a spherical cavity with no-slip walls, for which we derive expressions here. The force-lattice coupling of the LB algorithm leads to a "smearing out" of the flow field, which strongly perturbs the tracer trajectories at close swimmer-tracer separations, and we analyze how this effect can be accurately captured using a simple renormalized hydrodynamic theory. Finally, we show that care must be taken when using LB algorithms to simulate systems of self-propelled particles, since its finite momentum transport time can lead to significant deviations from theoretical predictions based on Stokes flow. These insights should prove relevant to the future study of large-scale microswimmer suspensions using these methods.
Collapse
Affiliation(s)
- Joost de Graaf
- SUPA, School of Physics and Astronomy, University of Edinburgh, King's Buildings, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, United Kingdom
| | - Joakim Stenhammar
- Division of Physical Chemistry, Lund University, Box 124, S-221 00 Lund, Sweden
| |
Collapse
|
15
|
Yang O, Peng Y, Liu Z, Tang C, Xu X, Cheng X. Dynamics of ellipsoidal tracers in swimming algal suspensions. Phys Rev E 2016; 94:042601. [PMID: 27841492 DOI: 10.1103/physreve.94.042601] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2016] [Indexed: 11/07/2022]
Abstract
Enhanced diffusion of passive tracers immersed in active fluids is a universal feature of active fluids and has been extensively studied in recent years. Similar to microrheology for equilibrium complex fluids, the unusual enhanced particle dynamics reveal intrinsic properties of active fluids. Nevertheless, previous studies have shown that the translational dynamics of spherical tracers are qualitatively similar, independent of whether active particles are pushers or pullers-the two fundamental classes of active fluids. Is it possible to distinguish pushers from pullers by simply imaging the dynamics of passive tracers? Here, we investigated the diffusion of isolated ellipsoids in algal C. reinhardtii suspensions-a model for puller-type active fluids. In combination with our previous results on pusher-type E. coli suspensions [Peng et al., Phys. Rev. Lett. 116, 068303 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.068303], we showed that the dynamics of asymmetric tracers show a profound difference in pushers and pullers due to their rotational degree of freedom. Although the laboratory-frame translation and rotation of ellipsoids are enhanced in both pushers and pullers, similar to spherical tracers, the anisotropic diffusion in the body frame of ellipsoids shows opposite trends in the two classes of active fluids. An ellipsoid diffuses fastest along its major axis when immersed in pullers, whereas it diffuses slowest along the major axis in pushers. This striking difference can be qualitatively explained using a simple hydrodynamic model. In addition, our study on algal suspensions reveals that the influence of the near-field advection of algal swimming flows on the translation and rotation of ellipsoids shows different ranges and strengths. Our work provides not only new insights into universal organizing principles of active fluids, but also a convenient tool for detecting the class of active particles.
Collapse
Affiliation(s)
- Ou Yang
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Yi Peng
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Zhengyang Liu
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Chao Tang
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Xinliang Xu
- Beijing Computational Science Research Center, Beijing 100193, China
| | - Xiang Cheng
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA
| |
Collapse
|
16
|
Park JD, Myung JS, Ahn KH. A review on particle dynamics simulation techniques for colloidal dispersions: Methods and applications. KOREAN J CHEM ENG 2016. [DOI: 10.1007/s11814-016-0229-9] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
|
17
|
Jeanneret R, Pushkin DO, Kantsler V, Polin M. Entrainment dominates the interaction of microalgae with micron-sized objects. Nat Commun 2016; 7:12518. [PMID: 27535609 PMCID: PMC4992151 DOI: 10.1038/ncomms12518] [Citation(s) in RCA: 44] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/02/2016] [Accepted: 07/08/2016] [Indexed: 12/31/2022] Open
Abstract
The incessant activity of swimming microorganisms has a direct physical effect on surrounding microscopic objects, leading to enhanced diffusion far beyond the level of Brownian motion with possible influences on the spatial distribution of non-motile planktonic species and particulate drifters. Here we study in detail the effect of eukaryotic flagellates, represented by the green microalga Chlamydomonas reinhardtii, on microparticles. Macro- and microscopic experiments reveal that microorganism-colloid interactions are dominated by rare close encounters leading to large displacements through direct entrainment. Simulations and theoretical modelling show that the ensuing particle dynamics can be understood in terms of a simple jump-diffusion process, combining standard diffusion with Poisson-distributed jumps. This heterogeneous dynamics is likely to depend on generic features of the near-field of swimming microorganisms with front-mounted flagella.
Collapse
Affiliation(s)
- Raphaël Jeanneret
- Physics Department, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK
| | - Dmitri O Pushkin
- Department of Mathematics, University of York, Heslington, York YO10 5DD, UK
| | - Vasily Kantsler
- Physics Department, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK
| | - Marco Polin
- Physics Department, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK
| |
Collapse
|
18
|
Peng Y, Lai L, Tai YS, Zhang K, Xu X, Cheng X. Diffusion of Ellipsoids in Bacterial Suspensions. PHYSICAL REVIEW LETTERS 2016; 116:068303. [PMID: 26919019 DOI: 10.1103/physrevlett.116.068303] [Citation(s) in RCA: 56] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2015] [Indexed: 05/25/2023]
Abstract
Active fluids such as swarming bacteria and motile colloids exhibit exotic properties different from conventional equilibrium materials. As a peculiar example, a spherical tracer immersed inside active fluids shows an enhanced translational diffusion, orders of magnitude stronger than its intrinsic Brownian motion. Here, rather than spherical tracers, we investigate the diffusion of isolated ellipsoids in a quasi-two-dimensional bacterial bath. Our study shows a nonlinear enhancement of both translational and rotational diffusions of ellipsoids. More importantly, we uncover an anomalous coupling between particles' translation and rotation that is strictly prohibited in Brownian diffusion. The coupling reveals a counterintuitive anisotropic particle diffusion, where an ellipsoid diffuses fastest along its minor axis in its body frame. Combining experiments with theoretical modeling, we show that such an anomalous diffusive behavior arises from the generic straining flow of swimming bacteria. Our work illustrates an unexpected feature of active fluids and deepens our understanding of transport processes in microbiological systems.
Collapse
Affiliation(s)
- Yi Peng
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Lipeng Lai
- Beijing Computational Science Research Center, Beijing 100193, China
| | - Yi-Shu Tai
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Kechun Zhang
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Xinliang Xu
- Beijing Computational Science Research Center, Beijing 100193, China
| | - Xiang Cheng
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA
| |
Collapse
|
19
|
Thiffeault JL. Distribution of particle displacements due to swimming microorganisms. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:023023. [PMID: 26382519 DOI: 10.1103/physreve.92.023023] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/18/2015] [Indexed: 06/05/2023]
Abstract
The experiments of Leptos et al. [Phys. Rev. Lett. 103, 198103 (2009)] show that the displacements of small particles affected by swimming microorganisms achieve a non-Gaussian distribution, which nevertheless scales diffusively--the "diffusive scaling." We use a simple model where the particles undergo repeated "kicks" due to the swimmers to explain the shape of the distribution as a function of the volume fraction of swimmers. The net displacement is determined by the inverse Fourier transform of a single-swimmer characteristic function. The only adjustable parameter is the strength of the stresslet term in our spherical squirmer model. We give a criterion for convergence to a Gaussian distribution in terms of moments of the drift function and show that the experimentally observed diffusive scaling is a transient related to the slow crossover of the fourth moment from a ballistic to a linear regime with path length. We also present a simple model, with logarithmic drift function, that can be solved analytically.
Collapse
Affiliation(s)
- Jean-Luc Thiffeault
- Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, Wisconsin 53706, USA
| |
Collapse
|
20
|
Saintillan D, Shelley MJ. Theory of Active Suspensions. COMPLEX FLUIDS IN BIOLOGICAL SYSTEMS 2015. [DOI: 10.1007/978-1-4939-2065-5_9] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
|
21
|
Morozov A, Marenduzzo D. Enhanced diffusion of tracer particles in dilute bacterial suspensions. SOFT MATTER 2014; 10:2748-2758. [PMID: 24668266 DOI: 10.1039/c3sm52201f] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Swimming bacteria create long-range velocity fields that stir a large volume of fluid and move around passive particles dispersed in the fluid. Recent experiments and simulations have shown that long-time mean-squared displacement of passive particles in a bath of swimming bacteria exhibits diffusive behaviour with an effective diffusion coefficient significantly larger than its thermal counterpart. A comprehensive theoretical prediction of this effective diffusion coefficient and the understanding of the enhancement mechanism remain a challenge. Here, we adapt the kinetic theory by Lin et al., J. Fluid Mech., 2011, 669, 167 developed for 'squirmers' to the bacterial case to quantitatively predict enhanced diffusivity of tracer particles in dilute two- and three-dimensional suspensions of swimming bacteria. We demonstrate that the effective diffusion coefficient is a product of the bacterial number density, their swimming speed, a geometric factor characterising the velocity field created by a single bacterium, and a numerical factor. We show that the numerical factor is, in fact, a rather strong function of the system parameters, most notably the run length of the bacteria, and that these dependencies have to be taken into account to quantitatively predict the enhanced diffusivity. We perform molecular-dynamics-type simulations to confirm the conclusions of the kinetic theory. Our results are in good agreement with the values of enhanced diffusivity measured in recent two- and three-dimensional experiments.
Collapse
Affiliation(s)
- Alexander Morozov
- SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh, UK.
| | | |
Collapse
|
22
|
|
23
|
Pushkin DO, Yeomans JM. Fluid mixing by curved trajectories of microswimmers. PHYSICAL REVIEW LETTERS 2013; 111:188101. [PMID: 24237566 DOI: 10.1103/physrevlett.111.188101] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/23/2013] [Indexed: 06/02/2023]
Abstract
We consider the tracer diffusion D(rr) that arises from the run-and-tumble motion of low Reynolds number swimmers, such as bacteria. Assuming a dilute suspension, where the bacteria move in uncorrelated runs of length λ, we obtain an exact expression for D(rr) for dipolar swimmers in three dimensions, hence explaining the surprising result that this is independent of λ. We compare D(rr) to the contribution to tracer diffusion from entrainment.
Collapse
Affiliation(s)
- Dmitri O Pushkin
- The Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford OX1 3NP, United Kingdom
| | | |
Collapse
|
24
|
Saintillan D, Shelley MJ. Emergence of coherent structures and large-scale flows in motile suspensions. J R Soc Interface 2011; 9:571-85. [PMID: 21865254 DOI: 10.1098/rsif.2011.0355] [Citation(s) in RCA: 66] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
The emergence of coherent structures, large-scale flows and correlated dynamics in suspensions of motile particles such as swimming micro-organisms or artificial microswimmers is studied using direct particle simulations. A detailed model is proposed for a slender rod-like particle that propels itself in a viscous fluid by exerting a prescribed tangential stress on its surface, and a method is devised for the efficient calculation of hydrodynamic interactions in large-scale suspensions of such particles using slender-body theory and a smooth particle-mesh Ewald algorithm. Simulations are performed with periodic boundary conditions for various system sizes and suspension volume fractions, and demonstrate a transition to large-scale correlated motions in suspensions of rear-actuated swimmers, or Pushers, above a critical volume fraction or system size. This transition, which is not observed in suspensions of head-actuated swimmers, or Pullers, is seen most clearly in particle velocity and passive tracer statistics. These observations are consistent with predictions from our previous mean-field kinetic theory, one of which states that instabilities will arise in uniform isotropic suspensions of Pushers when the product of the linear system size with the suspension volume fraction exceeds a given threshold. We also find that the collective dynamics of Pushers result in giant number fluctuations, local alignment of swimmers and strongly mixing flows. Suspensions of Pullers, which evince no large-scale dynamics, nonetheless display interesting deviations from the random isotropic state.
Collapse
Affiliation(s)
- David Saintillan
- Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA.
| | | |
Collapse
|
25
|
Enhancement of biomixing by swimming algal cells in two-dimensional films. Proc Natl Acad Sci U S A 2011; 108:10391-5. [PMID: 21659630 DOI: 10.1073/pnas.1107046108] [Citation(s) in RCA: 92] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
Abstract
Fluid mixing in active suspensions of microorganisms is important to ecological phenomena and presents a fascinating stochastic process. We investigate the mixing produced by swimming unicellular algal cells (Chlamydomonas) in quasi-two-dimensional liquid films by simultaneously tracking the motion of the cells and that of microscopic passive tracer particles advected by the fluid. The reduced spatial dimension of the system leads to long-range flows and a surprisingly strong dependence of tracer transport on the concentration of swimmers, which is explored over a wide range. The mean square displacements are well described by a stochastic Langevin model, which is used to parameterize the mixing. The effective diffusion coefficient D grows rapidly with the swimmer concentration Φ as D ∼ Φ(3/2), as a result of the increasing frequency of tracer-swimmer interactions and the long-range hydrodynamic disturbances created by the swimmers. Conditional sampling of the tracer data based on the instantaneous swimmer position shows that the rapid growth of the diffusivity enhancement with concentration must be due to particle interactions with multiple swimmers simultaneously. Finally, the anomalous probability distributions of tracer displacements become Gaussian at high concentration, but manifest strong power-law tails at low concentration, while the tracer displacements always grow diffusively in time.
Collapse
|
26
|
|