1
|
Tang ZS, Li JJ, Zhu WJ, Ai BQ. Collective self-optimization of binary mixed heterogeneous populations. Phys Rev E 2024; 109:024405. [PMID: 38491669 DOI: 10.1103/physreve.109.024405] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2023] [Accepted: 01/16/2024] [Indexed: 03/18/2024]
Abstract
To maximize the survival chances of society members, collective self-organization must balance individual interests with promoting the collective welfare. Although situations where group members have equal optimal values are clear, how varying optimal values impacts group dynamics remains unclear. To address this gap, we conducted a self-optimization study of a binary system incorporating communication-enabled active particles with distinct optimal values. We demonstrate that similar particles will spontaneously aggregate and separate from each other to maximize their individual benefits during the process of self-optimization. Our research shows that both types of particles can produce the optimal field values at low density. However, only one type of particle can achieve the optimal field values at medium density. At high densities, neither type of particle is effective in reaching the optimal field values. Interestingly, we observed that during the self-optimization process, the mixture demixed spontaneously under certain circumstances of mixed particles. Particles with higher optimal values developed into larger clusters, while particles with lower optimal values migrated outside of these clusters, resulting in the separation of the mixture. To achieve this separation, suitable noise intensity, particle density, and the significant difference in optimal values were necessary. Our results provide a more profound comprehension of the self-optimization of synthetic or biological agents' communication and provide valuable insight into separating binary species and mixtures.
Collapse
Affiliation(s)
- Zhao-Sha Tang
- Key Laboratory of Atomic and Subatomic Structure and Quantum Control (Ministry of Education), Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, School of Physics, South China Normal University, Guangzhou 510006, China
| | - Jia-Jian Li
- Key Laboratory of Atomic and Subatomic Structure and Quantum Control (Ministry of Education), Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, School of Physics, South China Normal University, Guangzhou 510006, China
| | - Wei-Jing Zhu
- School of Photoelectric Engineering, Guangdong Polytechnic Normal University, Guangzhou 510665, China
| | - Bao-Quan Ai
- Key Laboratory of Atomic and Subatomic Structure and Quantum Control (Ministry of Education), Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, School of Physics, South China Normal University, Guangzhou 510006, China
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, and Guangdong-Hong Kong Joint Laboratory of Quantum Matter, South China Normal University, Guangzhou 510006, China
| |
Collapse
|
2
|
Ai BQ. Brownian motors powered by nonreciprocal interactions. Phys Rev E 2023; 108:064409. [PMID: 38243494 DOI: 10.1103/physreve.108.064409] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2023] [Accepted: 11/28/2023] [Indexed: 01/21/2024]
Abstract
Traditional models for molecular (Brownian) motors predominantly depend on nonequilibrium driving, while particle interactions rigorously adhere to Newton's third law. However, numerous living and natural systems at various scales seem to defy this well-established law. In this study, we investigated the transport of mixed Brownian particles in a two-dimensional ratchet potential with nonreciprocal interactions. Our findings reveal that these nonreciprocal interactions can introduce a zero-mean nonequilibrium driving force. This force is capable of disrupting the thermodynamic equilibrium and inducing directed motion. The direction of this motion is determined by the asymmetry of the potential. Interestingly, the average velocity is a peaked function of the degree of nonreciprocity, while the effective diffusion consistently increases with the increase of nonreciprocity. There exists an optimal temperature or packing fraction at which the average velocity reaches its maximum value. We share a mechanism for particle rectification, devoid of particle-autonomous nonequilibrium drive, with potential usage in systems characterized by nonreciprocal interactions.
Collapse
Affiliation(s)
- Bao-Quan Ai
- Key Laboratory of Atomic and Subatomic Structure and Quantum Control (Ministry of Education), Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, School of Physics, South China Normal University, Guangzhou 510006, People's Republic of China
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, and Guangdong-Hong Kong Joint Laboratory of Quantum Matter, South China Normal University, Guangzhou 510006, People's Republic of China
| |
Collapse
|
3
|
Kalinay P, Slanina F. Ratchet effect in an asymmetric two-dimensional system of Janus particles. Phys Rev E 2023; 108:014606. [PMID: 37583160 DOI: 10.1103/physreve.108.014606] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2023] [Accepted: 06/28/2023] [Indexed: 08/17/2023]
Abstract
We consider a disk-like Janus particle self-driven by a force of constant magnitude f, but an arbitrary direction depending on the stochastic rotation of the disk. The particle diffuses in a two-dimensional channel of varying width 2h(x). We applied the procedure mapping the 2+1-dimensional Fokker-Planck equation onto the longitudinal coordinate x; the result is the Fick-Jacobs equation extended by the spatially dependent effective diffusion constant D(x) and an additional effective potential -γ(x), derived recursively within the mapping procedure. Unlike the entropic potential ∼lnh(x), γ(x) becomes an increasing or decreasing function also in periodic channels, depending on the asymmetry of h(x) and thus it visualizes the net force driving the ratchet current. We demonstrate the appearance of the ratchet effect on a trial asymmetric channel; our theory is verified by a numerical solution of the corresponding Fokker-Planck equation. Isotropic driving force f results in the monotonic decrease of the ratchet current with a growing ratio α=D_{R}/D_{T} of the rotation and the translation diffusion constants; asymptotically going ∼1/α^{2}. If we allow anisotropy of the force, we can observe the current reversal depending on α.
Collapse
Affiliation(s)
- Pavol Kalinay
- Institute of Physics, Slovak Academy of Sciences, Dúbravska cesta 9, 84511, Bratislava, Slovakia
| | - František Slanina
- Institute of Physics, Czech Academy of Sciences, Na Slovance 2, CZ-18200, Praha, Czech Republic
| |
Collapse
|
4
|
Kalinay P. Transverse dichotomic ratchet in a two-dimensional corrugated channel. Phys Rev E 2022; 106:044126. [PMID: 36397573 DOI: 10.1103/physreve.106.044126] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2022] [Accepted: 09/23/2022] [Indexed: 06/16/2023]
Abstract
A particle diffusing in a two-dimensional channel of varying width h(x) is considered. It is driven by a force of constant magnitude f, but random orientation across the channel. We suggest the projection technique to study the ratchet effect appearing in this system. Reducing the transverse coordinate, as well as the orientation of the force in the full-dimensional Fokker-Planck equation, we arrive at the generalized Fick-Jacobs equation, describing dynamics of the system in the longitudinal coordinate x only. The additional effective potential -γ(x), calculated within the mapping procedure, exhibits an increasing or decreasing part in the channel shaped by an asymmetric periodic h(x), which determines the appearing ratchet current. As shown on a specific example, random driving in the transverse direction is much more effective than that in the longitudinal direction, at least for quickly flipping orientation of the force. Also, the transverse and the longitudinal driving push the rectified current in opposite directions along the same channel.
Collapse
Affiliation(s)
- Pavol Kalinay
- Institute of Physics, Slovak Academy of Sciences, Dúbravska cesta 9, 84511, Bratislava, Slovakia
| |
Collapse
|
5
|
Codutti A, Charsooghi MA, Cerdá-Doñate E, Taïeb HM, Robinson T, Faivre D, Klumpp S. Interplay of surface interaction and magnetic torque in single-cell motion of magnetotactic bacteria in microfluidic confinement. eLife 2022; 11:71527. [PMID: 35852850 PMCID: PMC9365388 DOI: 10.7554/elife.71527] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2021] [Accepted: 07/18/2022] [Indexed: 11/21/2022] Open
Abstract
Swimming microorganisms often experience complex environments in their natural habitat. The same is true for microswimmers in envisioned biomedical applications. The simple aqueous conditions typically studied in the lab differ strongly from those found in these environments and often exclude the effects of small volume confinement or the influence that external fields have on their motion. In this work, we investigate magnetically steerable microswimmers, specifically magnetotactic bacteria, in strong spatial confinement and under the influence of an external magnetic field. We trap single cells in micrometer-sized microfluidic chambers and track and analyze their motion, which shows a variety of different trajectories, depending on the chamber size and the strength of the magnetic field. Combining these experimental observations with simulations using a variant of an active Brownian particle model, we explain the variety of trajectories by the interplay between the wall interactions and the magnetic torque. We also analyze the pronounced cell-to-cell heterogeneity, which makes single-cell tracking essential for an understanding of the motility patterns. In this way, our work establishes a basis for the analysis and prediction of microswimmer motility in more complex environments.
Collapse
Affiliation(s)
- Agnese Codutti
- Biomaterials Department, Max Planck Institute of Colloids and Interfaces
| | | | - Elisa Cerdá-Doñate
- Biomaterials Department, Max Planck Institute of Colloids and Interfaces
| | - Hubert M Taïeb
- Biomaterials Department, Max Planck Institute of Colloids and Interfaces
| | - Tom Robinson
- Theory and Bio‐systems Department, Max Planck Institute of Colloids and Interfaces
| | | | - Stefan Klumpp
- Institute for the Dynamics of Complex Systems, University of Göttingen
| |
Collapse
|
6
|
Heeremans T, Deblais A, Bonn D, Woutersen S. Chromatographic separation of active polymer-like worm mixtures by contour length and activity. SCIENCE ADVANCES 2022; 8:eabj7918. [PMID: 35675403 PMCID: PMC9177071 DOI: 10.1126/sciadv.abj7918] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/13/2023]
Abstract
The convective transport rate of polymers through confined geometries depends on their size, allowing for size-based separation of polymer mixtures (chromatography). Here, we investigate whether mixtures of active polymers can be separated in a similar manner based on their activity. We use thin, living Tubifex tubifex worms as a model system for active polymers and study the transport of these worms by an imposed flow through a channel filled with a hexagonal pillar array. The transport rate through the channel depends strongly on the degree of activity, an effect that we assign to the different distribution of conformations sampled by the worms depending on their activity. Our results demonstrate a unique way to sort mixtures of active polymers based on their activity and provide a versatile and convenient experimental system to investigate the hydrodynamics of active polymers.
Collapse
Affiliation(s)
- Tess Heeremans
- Van der Waals-Zeeman Institute, IoP, University of Amsterdam, Science Park 904, 1098 XH, Amsterdam, Netherlands
| | - Antoine Deblais
- Van der Waals-Zeeman Institute, IoP, University of Amsterdam, Science Park 904, 1098 XH, Amsterdam, Netherlands
- Corresponding author. (A.D.); (D.B.); (S.W.)
| | - Daniel Bonn
- Van der Waals-Zeeman Institute, IoP, University of Amsterdam, Science Park 904, 1098 XH, Amsterdam, Netherlands
- Corresponding author. (A.D.); (D.B.); (S.W.)
| | - Sander Woutersen
- Van ’t Hoff Institute for Molecular Sciences, University of Amsterdam, Science Park 904, 1098 XH, Amsterdam, Netherlands
- Corresponding author. (A.D.); (D.B.); (S.W.)
| |
Collapse
|
7
|
Kalinay P, Slanina F. Dichotomic ratchet in a two-dimensional corrugated channel. Phys Rev E 2021; 104:064115. [PMID: 35030943 DOI: 10.1103/physreve.104.064115] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2021] [Accepted: 11/29/2021] [Indexed: 06/14/2023]
Abstract
We consider a particle diffusing in a two-dimensional (2D) channel of varying width h(x). It is driven by a force of constant magnitude f but random orientation there or back along the channel. We derive the effective generalized Fick-Jacobs equation for this system, which describes the dynamics of such a particle in the longitudinal coordinate x. Aside from the effective diffusion coefficient D(x), our mapping also generates an additional effective potential -γ(x) added to the entropic potential -log[h(x)]. It acquires an increasing or decreasing component in asymmetric periodic channels, and thus it explains appearance of the ratchet current. We study this effect on a trial example and compare the results of our true 2D theory with a commonly used effective one-dimensional description; the data are verified by the numerical solution of the full 2D problem.
Collapse
Affiliation(s)
- Pavol Kalinay
- Institute of Physics, Slovak Academy of Sciences, Dúbravska cesta 9, 84511, Bratislava, Slovakia
| | - František Slanina
- Institute of Physics, Czech Academy of Sciences, Na Slovance 2, CZ-18221, Prague, Czech Republic
| |
Collapse
|
8
|
Ai BQ, Guo RX. Large-scale demixing in a binary mixture of cells with rigidity disparity in biological tissues. Phys Rev E 2021; 104:064411. [PMID: 35030891 DOI: 10.1103/physreve.104.064411] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2021] [Accepted: 12/15/2021] [Indexed: 06/14/2023]
Abstract
Physical demixing on large scales of embryonic cell populations is fundamental to metazoan development, but whether a rigidity disparity alone is sufficient to driving large-scale demixing in a binary mixture of cell tissues is still an open question. To answer this question, we study mixing and demixing in a binary mixture of rigidity disparity cell tissues without heterotypic interactions using the Voronoi-based cellular model. Under suitable system parameters, the solid-like cells in the mixture can aggregate into a large cluster and the large-scale demixing occurs, which addresses that a rigidity disparity alone is sufficient to drive large-scale demixing. Remarkably, there exists an optimal temperature or rigidity disparity at which the binary mixture can be separated to the maximum extent. The necessary condition for the separation of mixtures is that the two types of cells are solid-like and liquid-like, respectively. The observation of robust demixing on large scales suggests that the sorting of progenitor cells may occur very early in the development process before robust heterotypic interfacial tensions are established. Our findings are relevant to understanding the mechanisms that drive cell sorting in confluent tissues.
Collapse
Affiliation(s)
- Bao-Quan Ai
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China and Guangdong-Hong Kong Joint Laboratory of Quantum Matter, South China Normal University, Guangzhou 510006, China
| | - Rui-Xue Guo
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China and Guangdong-Hong Kong Joint Laboratory of Quantum Matter, South China Normal University, Guangzhou 510006, China
| |
Collapse
|
9
|
Coppola S, Kantsler V. Curved ratchets improve bacteria rectification in microfluidic devices. Phys Rev E 2021; 104:014602. [PMID: 34412208 DOI: 10.1103/physreve.104.014602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2021] [Accepted: 06/16/2021] [Indexed: 11/07/2022]
Abstract
We study how bacteria rectification in microfluidics devices can be optimized by performing experiments with eight ratchets of different shape and size. Results show that curved ratchets perform best and that their radius of curvature influences how well they perform, as it affects the time bacteria spend on the ratchet surface. We find that the optimal bacterial ratchet is a 60μm radius semicircle witch 15μm concavities. We also show that the angle at which bacteria leave the ratchets can play an important role in their efficiency. Lastly, we reproduce our experimental conditions in a simple numerical simulation to confirm our findings.
Collapse
Affiliation(s)
- Simone Coppola
- Physics Department, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Vasily Kantsler
- Physics Department, University of Warwick, Coventry CV4 7AL, United Kingdom
| |
Collapse
|
10
|
Lugo MCL, Bayer KCC, Gonzales SG, Confesor MNP. λ-like transition in the dynamics of ratchet gears in active bath. Phys Rev E 2020; 102:052607. [PMID: 33327070 DOI: 10.1103/physreve.102.052607] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2020] [Accepted: 11/06/2020] [Indexed: 06/12/2023]
Abstract
To what extent the orientational order of self-propelling particles affects the dynamics of active bath-immersed ratchet devices remains unclear. We report experimental results of an inverse λ-like transition of the angular velocity of two ratchet gears in an active bath of self-propelling granular rods (SPRs) at different gear distances. The transition is caused by the phase transition in the orientational order of those SPRs located in the space between the gears. Brownian dynamics simulation of confined SPRs supports these observations. Thus, conditions for the upper bound efficiency of systems of active ratchet gears were obtained.
Collapse
Affiliation(s)
- Maria Christine L Lugo
- Department of Physics and PRISM, MSU-Iligan Institute of Technology, Andres Bonifacio Avenue, Tibanga, Iligan City, Philippines 9200
| | - Khate Cheryl C Bayer
- Department of Physics and PRISM, MSU-Iligan Institute of Technology, Andres Bonifacio Avenue, Tibanga, Iligan City, Philippines 9200
| | - Sheila G Gonzales
- Department of Physics and PRISM, MSU-Iligan Institute of Technology, Andres Bonifacio Avenue, Tibanga, Iligan City, Philippines 9200
| | - Mark Nolan P Confesor
- Department of Physics and PRISM, MSU-Iligan Institute of Technology, Andres Bonifacio Avenue, Tibanga, Iligan City, Philippines 9200
| |
Collapse
|
11
|
Reichhardt C, Reichhardt CJO. Directional locking effects for active matter particles coupled to a periodic substrate. Phys Rev E 2020; 102:042616. [PMID: 33212736 DOI: 10.1103/physreve.102.042616] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2020] [Accepted: 10/12/2020] [Indexed: 06/11/2023]
Abstract
Directional locking occurs when a particle moving over a periodic substrate becomes constrained to travel along certain substrate symmetry directions. Such locking effects arise for colloids and superconducting vortices moving over ordered substrates when the direction of the external drive is varied. Here we study the directional locking of run-and-tumble active matter particles interacting with a periodic array of obstacles. In the absence of an external biasing force, we find that the active particle motion locks to various symmetry directions of the substrate when the run time between tumbles is large. The number of possible locking directions depends on the array density and on the relative sizes of the particles and the obstacles. For a square array of large obstacles, the active particle only locks to the x, y, and 45^{∘} directions, while for smaller obstacles, the number of locking angles increases. Each locking angle satisfies θ=arctan(p/q), where p and q are integers, and the angle of motion can be measured using the ratio of the velocities or the velocity distributions in the x and y directions. When a biasing driving force is applied, the directional locking behavior is affected by the ratio of the self-propulsion force to the biasing force. For large biasing, the behavior resembles that found for directional locking in passive systems. For large obstacles under biased driving, a trapping behavior occurs that is nonmonotonic as a function of increasing run length or increasing self-propulsion force, and the trapping diminishes when the run length is sufficiently large.
Collapse
Affiliation(s)
- C Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - C J O Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| |
Collapse
|
12
|
Ai BQ, Zhou BY, Zhang XM. Binary mixtures of active and passive particles on a sphere. SOFT MATTER 2020; 16:4710-4717. [PMID: 32367106 DOI: 10.1039/d0sm00281j] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
We study the cooperation and segregation dynamics of binary mixtures of active and passive particles on a sphere. According to the competition between rotational diffusion and polar alignment, we find three distinct phases: a mixed phase and two different demixed phases. When rotational diffusion dominates the dynamics, the demixing is due to the aggregation of passive particles, where active and passive particles respectively occupy two hemispheres. When polar alignment is dominated, the demixing is caused by the aggregation of active particles, where active particles occupy the equator of the sphere and passive particles occupy the two poles of the sphere. In this case, there exist a circulating band cluster and two cambered surface clusters, which is a purely curvature-driven effect with no equivalent in the planar model. When rotational diffusion and polar alignment are comparable, particles are completely mixed. Our findings are relevant to the experimental pursuit of segregation dynamics of binary mixtures on curved surfaces.
Collapse
Affiliation(s)
- Bao-Quan Ai
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement, SPTE, South China Normal University, Guangzhou 510006, China.
| | | | | |
Collapse
|
13
|
Martinez R, Alarcon F, Aragones JL, Valeriani C. Trapping flocking particles with asymmetric obstacles. SOFT MATTER 2020; 16:4739-4745. [PMID: 32149319 DOI: 10.1039/c9sm02427a] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Asymmetric obstacles can be exploited to direct the motion and induce sorting of run-and-tumble particles. In this work, we show that flocking particles which follow the Vicsek model aligning rules experience collective trapping in the presence of a wall of funnels made of chevrons, concentrating at the opposite side of the wall of funnels to run-and-tumble particles. Flocking particles can be completely trapped or exhibit a dynamical trapping behaviour; these two regimes open the door to the design of a system with two perpendicular flows of active particles. This systematic study broadens our understanding of the emergence of collective motion of microorganisms in confined environments and directs the design of new microfluidic devices able to control these collective behaviours.
Collapse
Affiliation(s)
- Raul Martinez
- Departamento de Física Teórica de la Materia Condensada, Instituto Nicolás Cabrera and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, E-28049 Madrid, Spain.
| | | | | | | |
Collapse
|
14
|
Zhu WJ, Li TC, Zhong WR, Ai BQ. Rectification and separation of mixtures of active and passive particles driven by temperature difference. J Chem Phys 2020; 152:184903. [PMID: 32414246 DOI: 10.1063/5.0005013] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Transport and separation of binary mixtures of active and passive particles are investigated in the presence of temperature differences. It is found that temperature differences can strongly affect the rectification and separation of the mixtures. For active particles, there exists an optimal temperature difference at which the rectified efficiency is maximal. Passive particles are not propelled and move by collisions with active particles, so the response to temperature differences is more complicated. By changing the system parameters, active particles can change their directions, while passive particles always move in the same direction. The simulation results show that the separation of mixtures is sensitive to the system parameters, such as the angular velocity, the temperature difference, and the polar alignment. The mixed particles can be completely separated under certain conditions.
Collapse
Affiliation(s)
- Wei-Jing Zhu
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
| | - Teng-Chao Li
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
| | - Wei-Rong Zhong
- Siyuan Laboratory, Guangzhou Key Laboratory of Vacuum Coating Technologies and New Energy Materials, Department of Physics, Jinan University, Guangzhou 510632, China
| | - Bao-Quan Ai
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
| |
Collapse
|
15
|
Schakenraad K, Ravazzano L, Sarkar N, Wondergem JAJ, Merks RMH, Giomi L. Topotaxis of active Brownian particles. Phys Rev E 2020; 101:032602. [PMID: 32289917 DOI: 10.1103/physreve.101.032602] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/16/2019] [Accepted: 01/26/2020] [Indexed: 06/11/2023]
Abstract
Recent experimental studies have demonstrated that cellular motion can be directed by topographical gradients, such as those resulting from spatial variations in the features of a micropatterned substrate. This phenomenon, known as topotaxis, has been extensively studied for topographical gradients at the subcellular scale, but can also occur in the presence of a spatially varying density of cell-sized features. Such a large-scale topotaxis has recently been observed in highly motile cells that persistently crawl within an array of obstacles with smoothly varying lattice spacing. We introduce a toy model of large-scale topotaxis, based on active Brownian particles. Using numerical simulations and analytical arguments, we demonstrate that topographical gradients introduce a spatial modulation of the particles' persistence, leading to directed motion toward regions of higher persistence. Our results demonstrate that persistent motion alone is sufficient to drive large-scale topotaxis and could serve as a starting point for more detailed studies on self-propelled particles and cells.
Collapse
Affiliation(s)
- Koen Schakenraad
- Instituut-Lorentz, Leiden University, P.O. Box 9506, 2300 RA Leiden, The Netherlands
- Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands
| | - Linda Ravazzano
- Instituut-Lorentz, Leiden University, P.O. Box 9506, 2300 RA Leiden, The Netherlands
- Center for Complexity and Biosystems, Department of Physics, University of Milan, Via Celoria 16, 20133 Milano, Italy
| | - Niladri Sarkar
- Instituut-Lorentz, Leiden University, P.O. Box 9506, 2300 RA Leiden, The Netherlands
| | - Joeri A J Wondergem
- Kamerlingh Onnes-Huygens Laboratory, Leiden University, P.O. Box 9504, 2300 RA Leiden, The Netherlands
| | - Roeland M H Merks
- Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands
- Institute of Biology, Leiden University, P.O. Box 9505, 2300 RA Leiden, The Netherlands
| | - Luca Giomi
- Instituut-Lorentz, Leiden University, P.O. Box 9506, 2300 RA Leiden, The Netherlands
| |
Collapse
|
16
|
Debnath T, Ghosh PK, Li Y, Marchesoni F, Nori F. Active diffusion limited reactions. J Chem Phys 2019; 150:154902. [DOI: 10.1063/1.5081125] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023] Open
Affiliation(s)
- Tanwi Debnath
- Department of Chemistry, University of Calcutta, Kolkata 700009, India
| | - Pulak K. Ghosh
- Department of Chemistry, Presidency University, Kolkata 700073, India
| | - Yunyun Li
- Center for Phononics and Thermal Energy Science, School of Physics Science and Engineering, Tongji University, Shanghai 200092, People’s Republic of China
| | - Fabio Marchesoni
- Center for Phononics and Thermal Energy Science, School of Physics Science and Engineering, Tongji University, Shanghai 200092, People’s Republic of China
- Dipartimento di Fisica, Università di Camerino, I-62032 Camerino, Italy
| | - Franco Nori
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA
| |
Collapse
|
17
|
Ai BQ, Shao ZG, Zhong WR. Mixing and demixing of binary mixtures of polar chiral active particles. SOFT MATTER 2018; 14:4388-4395. [PMID: 29770829 DOI: 10.1039/c8sm00444g] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We study a binary mixture of polar chiral (counterclockwise or clockwise) active particles in a two-dimensional box with periodic boundary conditions. Besides the excluded volume interactions between particles, the particles are also subjected to the polar velocity alignment. From the extensive Brownian dynamics simulations, it is found that the particle configuration (mixing or demixing) is determined by the competition between the chirality difference and the polar velocity alignment. When the chirality difference competes with the polar velocity alignment, the clockwise particles aggregate in one cluster and the counterclockwise particles aggregate in the other cluster; thus, the particles are demixed and can be separated. However, when the chirality difference or the polar velocity alignment is dominant, the particles are mixed. Our findings could be used for the experimental pursuit of the separation of binary mixtures of chiral active particles.
Collapse
Affiliation(s)
- Bao-Quan Ai
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China.
| | | | | |
Collapse
|
18
|
Sartori P, Chiarello E, Jayaswal G, Pierno M, Mistura G, Brun P, Tiribocchi A, Orlandini E. Wall accumulation of bacteria with different motility patterns. Phys Rev E 2018; 97:022610. [PMID: 29548231 DOI: 10.1103/physreve.97.022610] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2017] [Indexed: 06/08/2023]
Abstract
We systematically investigate the role of different swimming patterns on the concentration distribution of bacterial suspensions confined between two flat walls, by considering wild-type motility Escherichia coli and Pseudomonas aeruginosa, which perform Run and Tumble and Run and Reverse patterns, respectively. The experiments count motile bacteria at different distances from the bottom wall. In agreement with previous studies, an accumulation of motile bacteria close to the walls is observed. Different wall separations, ranging from 100 to 250μm, are tested. The concentration profiles result to be independent on the motility pattern and on the walls' separation. These results are confirmed by numerical simulations, based on a collection of self-propelled dumbbells-like particles interacting only through steric interactions. The good agreement with the simulations suggests that the behavior of the investigated bacterial suspensions is determined mainly by steric collisions and self-propulsion, as well as hydrodynamic interactions.
Collapse
Affiliation(s)
- Paolo Sartori
- Dipartimento di Fisica e Astronomia "Galileo Galilei," Università di Padova, via Marzolo 8, 35131 Padova PD, Italy
| | - Enrico Chiarello
- Dipartimento di Fisica e Astronomia "Galileo Galilei," Università di Padova, via Marzolo 8, 35131 Padova PD, Italy
| | - Gaurav Jayaswal
- Dipartimento di Fisica e Astronomia "Galileo Galilei," Università di Padova, via Marzolo 8, 35131 Padova PD, Italy
| | - Matteo Pierno
- Dipartimento di Fisica e Astronomia "Galileo Galilei," Università di Padova, via Marzolo 8, 35131 Padova PD, Italy
| | - Giampaolo Mistura
- Dipartimento di Fisica e Astronomia "Galileo Galilei," Università di Padova, via Marzolo 8, 35131 Padova PD, Italy
| | - Paola Brun
- Dipartimento di Medicina Molecolare, Università di Padova, via Gabelli 63, 35121 Padova PD, Italy
| | - Adriano Tiribocchi
- Dipartimento di Fisica e Astronomia "Galileo Galilei," Università di Padova and INFN, via Marzolo 8, 35131 Padova PD, Italy
| | - Enzo Orlandini
- Dipartimento di Fisica e Astronomia "Galileo Galilei," Università di Padova and INFN, via Marzolo 8, 35131 Padova PD, Italy
| |
Collapse
|
19
|
Ai BQ, Li FG. Transport of underdamped active particles in ratchet potentials. SOFT MATTER 2017; 13:2536-2542. [PMID: 28318005 DOI: 10.1039/c7sm00405b] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We study the rectified transport of underdamped active noninteracting particles in an asymmetric periodic potential. It is found that the ratchet effect of active noninteracting particles occurs in a single direction (along the easy direction of the substrate asymmetry) in the overdamped limit. However, when the inertia is considered, it is possible to observe reversals of the ratchet effect, where the motion is along the hard direction of the substrate asymmetry. By changing the friction coefficient or the self-propulsion force, the average velocity can change its direction several times. Therefore, by suitably tailoring the parameters, underdamped active particles with different self-propulsion forces can move in different directions and can be separated.
Collapse
Affiliation(s)
- Bao-Quan Ai
- Guangdong Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China.
| | - Feng-Guo Li
- Guangdong Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China.
| |
Collapse
|
20
|
Sosa-Hernández JE, Santillán M, Santana-Solano J. Motility of Escherichia coli in a quasi-two-dimensional porous medium. Phys Rev E 2017; 95:032404. [PMID: 28415239 DOI: 10.1103/physreve.95.032404] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2016] [Indexed: 06/07/2023]
Abstract
Bacterial migration through confined spaces is critical for several phenomena, such as biofilm formation, bacterial transport in soils, and bacterial therapy against cancer. In the present work, E. coli (strain K12-MG1655 WT) motility was characterized by recording and analyzing individual bacterium trajectories in a simulated quasi-two-dimensional porous medium. The porous medium was simulated by enclosing, between slide and cover slip, a bacterial-culture sample mixed with uniform 2.98-μm-diameter spherical latex particles. The porosity of the medium was controlled by changing the latex particle concentration. By statistically analyzing several trajectory parameters (instantaneous velocity, turn angle, mean squared displacement, etc.), and contrasting with the results of a random-walk model developed ad hoc, we were able to quantify the effects that different obstacle concentrations have upon bacterial motility.
Collapse
Affiliation(s)
- Juan Eduardo Sosa-Hernández
- Centro de Investigación y de Estudios Avanzados del IPN, Unidad Monterrey, Vía del Conocimiento 201, Parque PIIT, 66600 Apodaca NL, Mexico
| | - Moisés Santillán
- Centro de Investigación y de Estudios Avanzados del IPN, Unidad Monterrey, Vía del Conocimiento 201, Parque PIIT, 66600 Apodaca NL, Mexico
| | - Jesús Santana-Solano
- Centro de Investigación y de Estudios Avanzados del IPN, Unidad Monterrey, Vía del Conocimiento 201, Parque PIIT, 66600 Apodaca NL, Mexico
| |
Collapse
|
21
|
Ai BQ, He YF, Zhong WR. Effects of hydrodynamic interactions on rectified transport of self-propelled particles. Phys Rev E 2017; 95:012116. [PMID: 28208376 DOI: 10.1103/physreve.95.012116] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2016] [Indexed: 11/07/2022]
Abstract
Directed transport of self-propelled particles is numerically investigated in a three-dimensional asymmetric potential. Beside the steric repulsive forces, hydrodynamic interactions between particles have been taken into account in an approximate way. From numerical simulations, we find that hydrodynamic interactions can strongly affect the rectified transport of self-propelled particles. Hydrodynamic interactions enhance the performance of the rectified transport when particles can easily pass across the barrier of the potential, and reduce the rectified transport when particles are mainly trapped in the potential well.
Collapse
Affiliation(s)
- Bao-Quan Ai
- Guangdong Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
| | - Ya-Feng He
- College of Physics Science and Technology, Hebei University, Baoding 071002, China
| | - Wei-Rong Zhong
- Siyuan Laboratory, Guangzhou Key Laboratory of Vacuum Coating Technologies and New Energy Materials, Department of Physics, Jinan University, Guangzhou 510632, China
| |
Collapse
|
22
|
Chen YF, Chen HY, Sheng YJ, Tsao HK. Directed drift and fluid pumping of nanoswimmers by periodic rectification-diffusion. J Chem Phys 2017; 146:014902. [DOI: 10.1063/1.4973228] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yen-Fu Chen
- Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan 106, Republic of China
| | - Hsuan-Yi Chen
- Department of Physics, National Central University, Jhongli, Taiwan 320, Republic of China
| | - Yu-Jane Sheng
- Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan 106, Republic of China
| | - Heng-Kwong Tsao
- Department of Physics, National Central University, Jhongli, Taiwan 320, Republic of China
- Department of Chemical and Materials Engineering, National Central University, Jhongli, Taiwan 320, Republic of China
| |
Collapse
|
23
|
McDermott D, Olson Reichhardt CJ, Reichhardt C. Collective ratchet effects and reversals for active matter particles on quasi-one-dimensional asymmetric substrates. SOFT MATTER 2016; 12:8606-8615. [PMID: 27714306 DOI: 10.1039/c6sm01394e] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Using computer simulations, we study a two-dimensional system of sterically interacting self-mobile run-and-tumble disk-shaped particles with an underlying periodic quasi-one-dimensional asymmetric substrate, and show that a rich variety of collective active ratchet behaviors arise as a function of particle density, activity, substrate period, and the maximum force exerted by the substrate. The net dc drift, or ratchet transport flux, is nonmonotonic since it increases with increased activity but is diminished by the onset of self-clustering of the active particles. Increasing the particle density decreases the ratchet transport flux for shallow substrates but increases the ratchet transport flux for deep substrates due to collective hopping events. At the highest particle densities, the ratchet motion is destroyed by a self-jamming effect. We show that it is possible to realize reversals of the direction of the net dc drift in the deep substrate limit when multiple rows of active particles can be confined in each substrate minimum, permitting emergent particle-like excitations to appear that experience an inverted effective substrate potential. We map out a phase diagram of the forward and reverse ratchet effects as a function of the particle density, activity, and substrate properties.
Collapse
Affiliation(s)
- Danielle McDermott
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA. and Department of Physics, Wabash College, Crawfordsville, Indiana 47933, USA
| | | | - Charles Reichhardt
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
| |
Collapse
|
24
|
Slanina F. Inertial hydrodynamic ratchet: Rectification of colloidal flow in tubes of variable diameter. Phys Rev E 2016; 94:042610. [PMID: 27841656 DOI: 10.1103/physreve.94.042610] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2016] [Indexed: 06/06/2023]
Abstract
We investigate analytically a microfluidic device consisting of a tube with a nonuniform but spatially periodic diameter, where a fluid driven back and forth by a pump carries colloidal particles. Although the net flow of the fluid is zero, the particles move preferentially in one direction due to the ratchet mechanism, which occurs due to the simultaneous effect of inertial hydrodynamics and Brownian motion. We show that the average current is strongly sensitive to particle size, thus facilitating colloidal particle sorting.
Collapse
Affiliation(s)
- František Slanina
- Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, CZ-18221 Praha, Czech Republic
| |
Collapse
|
25
|
Ai BQ. Ratchet transport powered by chiral active particles. Sci Rep 2016; 6:18740. [PMID: 26795952 PMCID: PMC4726254 DOI: 10.1038/srep18740] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2015] [Accepted: 11/25/2015] [Indexed: 11/17/2022] Open
Abstract
We numerically investigate the ratchet transport of mixtures of active and passive particles in a transversal asymmetric channel. A big passive particle is immersed in a ‘sea’ of active particles. Due to the chirality of active particles, the longitudinal directed transport is induced by the transversal asymmetry. For the active particles, the chirality completely determines the direction of the ratchet transport, the counterclockwise and clockwise particles move to the opposite directions and can be separated. However, for the passive particle, the transport behavior becomes complicated, the direction is determined by competitions among the chirality, the self-propulsion speed, and the packing fraction. Interestingly, within certain parameters, the passive particle moves to the left, while active particles move to the right. In addition, there exist optimal parameters (the chirality, the height of the barrier, the self-propulsion speed and the packing fraction) at which the rectified efficiency takes its maximal value. Our findings could be used for the experimental pursuit of the ratchet transport powered by chiral active particles.
Collapse
Affiliation(s)
- Bao-quan Ai
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
| |
Collapse
|
26
|
Chen YF, Xiao S, Chen HY, Sheng YJ, Tsao HK. Enhancing rectification of a nano-swimmer system by multi-layered asymmetric barriers. NANOSCALE 2015; 7:16451-16459. [PMID: 26394906 DOI: 10.1039/c5nr04124d] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
The rectification of nano-swimmers in two chambers separated by a strip of funnel gates is explored by dissipative particle dynamics simulations. According to the trajectories of active colloids across the funnel zone, two rectification mechanisms are identified: geometry-assisted diffusion and trap-hindered diffusion. In general, geometry-assisted diffusion dominates at a small active force (Fa) and run time (τ) while trap-hindered diffusion governs at a large Fa and τ. The rectification ratio is affected by the funnel shape and various geometries are considered: open/closed triangular, circular and rectangular funnels. The rectification ratio of open funnels is always greater than that of closed funnels. Moreover, the open circular funnel has the best performance while the triangular one has the worst. Rectification can be enhanced as the number of funnel layers is increased. It is found that the rectification ratio of self-propelled colloids can be dramatically augmented by triple-layered funnels to be as high as 30. Our simulation study offers an efficient approach for rectification enhancement.
Collapse
Affiliation(s)
- Yen-Fu Chen
- Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan 106, R.O.C.
| | | | | | | | | |
Collapse
|
27
|
Chen Q, Ai BQ. Sorting of chiral active particles driven by rotary obstacles. J Chem Phys 2015; 143:104113. [DOI: 10.1063/1.4930282] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Qun Chen
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, 510006 Guangzhou, China
| | - Bao-quan Ai
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, 510006 Guangzhou, China
| |
Collapse
|
28
|
Ai BQ, He YF, Zhong WR. Chirality separation of mixed chiral microswimmers in a periodic channel. SOFT MATTER 2015; 11:3852-3859. [PMID: 25864888 DOI: 10.1039/c5sm00651a] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Dynamics and separation of mixed chiral microswimmers are numerically investigated in a channel with regular arrays of rigid half-circle obstacles. For zero shear flow, transport behaviors are the same for different chiral particles: the average velocity decreases with increase of the rotational diffusion coefficient, the direction of the transport can be reversed by tuning the angular velocity, and there exists an optimal value of the packing fraction at which the average velocity takes its maximal value. However, when the shear flow is considered, different chiral particles show different behaviors. By suitably tailoring parameters, particles with different chiralities can move in different directions and can be separated. In addition, we also proposed a space separation method by introducing a constant load, where counterclockwise and clockwise particles stay in different regions of the channel.
Collapse
Affiliation(s)
- Bao-quan Ai
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, 510006 Guangzhou, China.
| | | | | |
Collapse
|
29
|
Spagnolie SE, Moreno-Flores GR, Bartolo D, Lauga E. Geometric capture and escape of a microswimmer colliding with an obstacle. SOFT MATTER 2015; 11:3396-3411. [PMID: 25800455 DOI: 10.1039/c4sm02785j] [Citation(s) in RCA: 66] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Motivated by recent experiments, we consider the hydrodynamic capture of a microswimmer near a stationary spherical obstacle. Simulations of model equations show that a swimmer approaching a small spherical colloid is simply scattered. In contrast, when the colloid is larger than a critical size it acts as a passive trap: the swimmer is hydrodynamically captured along closed trajectories and endlessly orbits around the colloidal sphere. In order to gain physical insight into this hydrodynamic scattering problem, we address it analytically. We provide expressions for the critical trapping radius, the depth of the "basin of attraction," and the scattering angle, which show excellent agreement with our numerical findings. We also demonstrate and rationalize the strong impact of swimming-flow symmetries on the trapping efficiency. Finally, we give the swimmer an opportunity to escape the colloidal traps by considering the effects of Brownian, or active, diffusion. We show that in some cases the trapping time is governed by an Ornstein-Uhlenbeck process, which results in a trapping time distribution that is well-approximated as inverse-Gaussian. The predictions again compare very favorably with the numerical simulations. We envision applications of the theory to bioremediation, microorganism sorting techniques, and the study of bacterial populations in heterogeneous or porous environments.
Collapse
Affiliation(s)
- Saverio E Spagnolie
- Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Dr., Madison, WI 53706, USA.
| | | | | | | |
Collapse
|
30
|
Elgeti J, Winkler RG, Gompper G. Physics of microswimmers--single particle motion and collective behavior: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2015; 78:056601. [PMID: 25919479 DOI: 10.1088/0034-4885/78/5/056601] [Citation(s) in RCA: 624] [Impact Index Per Article: 69.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/13/2023]
Abstract
Locomotion and transport of microorganisms in fluids is an essential aspect of life. Search for food, orientation toward light, spreading of off-spring, and the formation of colonies are only possible due to locomotion. Swimming at the microscale occurs at low Reynolds numbers, where fluid friction and viscosity dominates over inertia. Here, evolution achieved propulsion mechanisms, which overcome and even exploit drag. Prominent propulsion mechanisms are rotating helical flagella, exploited by many bacteria, and snake-like or whip-like motion of eukaryotic flagella, utilized by sperm and algae. For artificial microswimmers, alternative concepts to convert chemical energy or heat into directed motion can be employed, which are potentially more efficient. The dynamics of microswimmers comprises many facets, which are all required to achieve locomotion. In this article, we review the physics of locomotion of biological and synthetic microswimmers, and the collective behavior of their assemblies. Starting from individual microswimmers, we describe the various propulsion mechanism of biological and synthetic systems and address the hydrodynamic aspects of swimming. This comprises synchronization and the concerted beating of flagella and cilia. In addition, the swimming behavior next to surfaces is examined. Finally, collective and cooperate phenomena of various types of isotropic and anisotropic swimmers with and without hydrodynamic interactions are discussed.
Collapse
Affiliation(s)
- J Elgeti
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, D-52425 Jülich, Germany
| | | | | |
Collapse
|
31
|
Kaiser A, Sokolov A, Aranson IS, Lowen H. Mechanisms of Carrier Transport Induced by a Microswimmer Bath. IEEE Trans Nanobioscience 2015; 14:260-6. [DOI: 10.1109/tnb.2014.2361652] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
|
32
|
Guidobaldi HA, Jeyaram Y, Condat CA, Oviedo M, Berdakin I, Moshchalkov VV, Giojalas LC, Silhanek AV, Marconi VI. Disrupting the wall accumulation of human sperm cells by artificial corrugation. BIOMICROFLUIDICS 2015; 9:024122. [PMID: 26015834 PMCID: PMC4409620 DOI: 10.1063/1.4918979] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/06/2015] [Accepted: 04/14/2015] [Indexed: 05/14/2023]
Abstract
Many self-propelled microorganisms are attracted to surfaces. This makes their dynamics in restricted geometries very different from that observed in the bulk. Swimming along walls is beneficial for directing and sorting cells, but may be detrimental if homogeneous populations are desired, such as in counting microchambers. In this work, we characterize the motion of human sperm cells ∼60 μm long, strongly confined to ∼25 μm shallow chambers. We investigate the nature of the cell trajectories between the confining surfaces and their accumulation near the borders. Observed cell trajectories are composed of a succession of quasi-circular and quasi-linear segments. This suggests that the cells follow a path of intermittent trappings near the top and bottom surfaces separated by stretches of quasi-free motion in between the two surfaces, as confirmed by depth resolved confocal microscopy studies. We show that the introduction of artificial petal-shaped corrugation in the lateral boundaries removes the tendency of cells to accumulate near the borders, an effect which we hypothesize may be valuable for microfluidic applications in biomedicine.
Collapse
Affiliation(s)
- H A Guidobaldi
- IIByT-CONICET and FCEFyN, Universidad Nacional de Córdoba , X5016GCA Córdoba, Argentina
| | - Y Jeyaram
- Institute for Nanoscale Physics and Chemistry , KU Leuven, B-3001 Leuven, Belgium
| | - C A Condat
- FaMAF, Universidad Nacional de Córdoba and IFEG-CONICET , X5000HUA Córdoba, Argentina
| | - M Oviedo
- IIByT-CONICET and FCEFyN, Universidad Nacional de Córdoba , X5016GCA Córdoba, Argentina
| | - I Berdakin
- FaMAF, Universidad Nacional de Córdoba and IFEG-CONICET , X5000HUA Córdoba, Argentina
| | - V V Moshchalkov
- Institute for Nanoscale Physics and Chemistry , KU Leuven, B-3001 Leuven, Belgium
| | - L C Giojalas
- IIByT-CONICET and FCEFyN, Universidad Nacional de Córdoba , X5016GCA Córdoba, Argentina
| | - A V Silhanek
- Départment de Physique, Université de Liège , B-4000 Sart Tilman, Belgium
| | - V I Marconi
- FaMAF, Universidad Nacional de Córdoba and IFEG-CONICET , X5000HUA Córdoba, Argentina
| |
Collapse
|
33
|
Sánchez S, Soler L, Katuri J. Chemically powered micro- and nanomotors. Angew Chem Int Ed Engl 2014; 54:1414-44. [PMID: 25504117 DOI: 10.1002/anie.201406096] [Citation(s) in RCA: 586] [Impact Index Per Article: 58.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/10/2014] [Indexed: 11/08/2022]
Abstract
Chemically powered micro- and nanomotors are small devices that are self-propelled by catalytic reactions in fluids. Taking inspiration from biomotors, scientists are aiming to find the best architecture for self-propulsion, understand the mechanisms of motion, and develop accurate control over the motion. Remotely guided nanomotors can transport cargo to desired targets, drill into biomaterials, sense their environment, mix or pump fluids, and clean polluted water. This Review summarizes the major advances in the growing field of catalytic nanomotors, which started ten years ago.
Collapse
Affiliation(s)
- Samuel Sánchez
- Max Planck Institute for Intelligent Systems, Heisenbergstrasse 3, 70569 Stuttgart (Germany) http://www.is.mpg.de/sanchez; Institute for Bioengineering of Catalonia (IBEC), 08028 Barcelona (Spain); Institució Catalana de Recerca i Estudis Avançats (ICREA), 08010 Barcelona (Spain).
| | | | | |
Collapse
|
34
|
|
35
|
Kaiser A, Löwen H. Unusual swelling of a polymer in a bacterial bath. J Chem Phys 2014; 141:044903. [DOI: 10.1063/1.4891095] [Citation(s) in RCA: 74] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
36
|
Ray D, Reichhardt C, Reichhardt CJO. Casimir effect in active matter systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:013019. [PMID: 25122381 DOI: 10.1103/physreve.90.013019] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2014] [Indexed: 06/03/2023]
Abstract
We numerically examine run-and-tumble active matter particles in Casimir geometries composed of two finite parallel walls. We find that there is an attractive force between the two walls of a magnitude that increases with increasing run length. The attraction exhibits an unusual exponential dependence on the wall separation, and it arises due to a depletion of swimmers in the region between the walls by a combination of the motion of the particles along the walls and a geometric shadowing effect. This attraction is robust as long as the wall length is comparable to or smaller than the swimmer run length, and is only slightly reduced by the inclusion of steric interactions between swimmers. We also examine other geometries and find regimes in which there is a crossover from attraction to repulsion between the walls as a function of wall separation and wall length.
Collapse
Affiliation(s)
- D Ray
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA and Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556, USA
| | - C Reichhardt
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - C J Olson Reichhardt
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| |
Collapse
|
37
|
Reichhardt C, Olson Reichhardt CJ. Active matter transport and jamming on disordered landscapes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:012701. [PMID: 25122329 DOI: 10.1103/physreve.90.012701] [Citation(s) in RCA: 70] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2014] [Indexed: 06/03/2023]
Abstract
We numerically examine the transport of active run-and-tumble particles with steric particle-particle interactions driven with a drift force over random disordered landscapes composed of fixed obstacles. For increasing run lengths, the net particle transport initially increases before reaching a maximum and decreasing at larger run lengths. The transport reduction is associated with the formation of cluster or living crystal states that become locally jammed or clogged by the obstacles. We also find that the system dynamically jams at lower particle densities when the run length is increased. Our results indicate that there is an optimal activity level for transport of run-and-tumble type active matter through quenched disorder and could be important for understanding biological transport in complex environments or for applications of active matter particles in random media.
Collapse
Affiliation(s)
- C Reichhardt
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - C J Olson Reichhardt
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| |
Collapse
|
38
|
Guidobaldi A, Jeyaram Y, Berdakin I, Moshchalkov VV, Condat CA, Marconi VI, Giojalas L, Silhanek AV. Geometrical guidance and trapping transition of human sperm cells. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:032720. [PMID: 24730887 DOI: 10.1103/physreve.89.032720] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2013] [Indexed: 05/14/2023]
Abstract
The guidance of human sperm cells under confinement in quasi-2D microchambers is investigated using a purely physical method to control their distribution. Transport property measurements and simulations are performed with diluted sperm populations, for which effects of geometrical guidance and concentration are studied in detail. In particular, a trapping transition at convex angular wall features is identified and analyzed. We also show that highly efficient microratchets can be fabricated by using curved asymmetric obstacles to take advantage of the spermatozoa specific swimming strategy.
Collapse
Affiliation(s)
- A Guidobaldi
- Instituto de Investigaciones Biológicas y Tecnológicas, CONICET and Centro de Biología Celular y Molecular, Universidad Nacional de Córdoba, Ciudad Universitaria, 5000-Córdoba, Argentina
| | - Y Jeyaram
- Institute for Nanoscale Physics and Chemistry, KU Leuven, B-3001 Leuven, Belgium
| | - I Berdakin
- Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba and IFEG-CONICET, X5000HUA Córdoba, Argentina
| | - V V Moshchalkov
- Institute for Nanoscale Physics and Chemistry, KU Leuven, B-3001 Leuven, Belgium
| | - C A Condat
- Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba and IFEG-CONICET, X5000HUA Córdoba, Argentina
| | - V I Marconi
- Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba and IFEG-CONICET, X5000HUA Córdoba, Argentina
| | - L Giojalas
- Instituto de Investigaciones Biológicas y Tecnológicas, CONICET and Centro de Biología Celular y Molecular, Universidad Nacional de Córdoba, Ciudad Universitaria, 5000-Córdoba, Argentina
| | - A V Silhanek
- Département de Physique, Université de Liège, B-4000 Sart Tilman, Belgium
| |
Collapse
|
39
|
Di Salvo ME, Condat CA. Enhancement of microbial motility due to speed-dependent nutrient absorption. Phys Biol 2014; 11:016004. [PMID: 24451235 DOI: 10.1088/1478-3975/11/1/016004] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
Marine microorganisms often reach high swimming speeds, either to take advantage of evanescent nutrient patches or to beat Brownian forces. Since this implies that a sizable part of their energetic budget must be allocated to motion, it is reasonable to assume that some fast-swimming microorganisms may increase their nutrient intake by increasing their speed v. We formulate a model to investigate this hypothesis and its consequences, finding the steady-state solutions and analyzing their stability. Surprisingly, we find that even modest increases in nutrient absorption may lead to a significant increase of the microbial speed. In fact, evaluations obtained using realistic parameter values for bacteria indicate that the speed increase due to the enhanced nutrient absorption may be quite large.
Collapse
Affiliation(s)
- Mario E Di Salvo
- IFEG-CONICET and FaMAF, Universidad Nacional de Córdoba, 5000-Córdoba, Argentina
| | | |
Collapse
|
40
|
Reichhardt C, Olson Reichhardt CJ. Active matter ratchets with an external drift. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:062310. [PMID: 24483447 DOI: 10.1103/physreve.88.062310] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2013] [Indexed: 06/03/2023]
Abstract
When active matter particles such as swimming bacteria are placed in an asymmetric array of funnels, it has been shown that a ratchet effect can occur even in the absence of an external drive. Here we examine active ratchets for two-dimensional arrays of funnels or L shapes where there is also an externally applied dc drive or drift. We show that for certain conditions the ratchet effect can be strongly enhanced and it is possible to have conditions under which run-and-tumble particles with one run length move in the opposite direction from particles with a different run length. For the arrays of L shapes, we find that the application of a drift force can enhance a transverse rectification in the direction perpendicular to the drift. When particle-particle steric interactions are included, we find that the ratchet effects can be either enhanced or suppressed depending on barrier geometry, particle run length, and particle density.
Collapse
Affiliation(s)
- C Reichhardt
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - C J Olson Reichhardt
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| |
Collapse
|
41
|
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
|
42
|
Suárez G, Hoyuelos M, Mártin HO. Transport in a chain of asymmetric cavities: effects of the concentration with hard-core interaction. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:052136. [PMID: 24329243 DOI: 10.1103/physreve.88.052136] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2013] [Revised: 10/17/2013] [Indexed: 06/03/2023]
Abstract
We studied the transport process of overdamped Brownian particles, in a chain of asymmetric cavities, interacting through a hard-core potential. When a force is applied in opposite directions a difference in the drift velocity of the particles inside the cavity can be observed. Previous works on similar systems deal with the low-concentration regime, in which the interaction is irrelevant. In this case it was found that large particles show a stronger asymmetry in the drift velocity when a small force is applied, allowing for the separation of different size particles [Reguera et al., Phys. Rev. Lett. 108, 020604 (2012)]. We found that when the interaction between particles is considered, the behavior of the system is substantially different. For example, as concentration is increased, the small particles are the ones that show a stronger asymmetry. For the case where all the particles in the system are of the same size we took advantage of the particle-vacancy analogy to predict that the left and right currents are almost equal in a region around the concentration 0.5 despite the asymmetry of the cavity.
Collapse
Affiliation(s)
- Gonzalo Suárez
- Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, and Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR-CONICET), Deán Funes 3350, 7600 Mar del Plata, Argentina
| | - Miguel Hoyuelos
- Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, and Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR-CONICET), Deán Funes 3350, 7600 Mar del Plata, Argentina
| | - Héctor O Mártin
- Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, and Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR-CONICET), Deán Funes 3350, 7600 Mar del Plata, Argentina
| |
Collapse
|
43
|
Reichhardt C, Reichhardt CJO. Dynamics and separation of circularly moving particles in asymmetrically patterned arrays. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:042306. [PMID: 24229171 DOI: 10.1103/physreve.88.042306] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2013] [Revised: 09/06/2013] [Indexed: 06/02/2023]
Abstract
There are many examples of driven and active matter systems containing particles that exhibit circular motion with different chiralities, such as swimming bacteria near surfaces or certain types of self-driven colloidal particles. Circular motion of passive particles can also be induced with an external rotating drive. Here we examine particles that move in circles and interact with a periodic array of asymmetric L-shaped obstacles. We find a series of dynamical phases as a function of swimming radius, including regimes where the particle motion is rectified, producing a net dc motion. The direction of the rectification varies with the swimming radius, permitting the separation of particles with different swimming radii. Particles with the same swimming radius but different chirality can also move in different directions over the substrate and be separated. The rectification occurs for specific windows of swimming radii corresponding to periodic orbits in which the particles interact one or more times with the barriers per rotation cycle. The rectification effects are robust against the addition of thermal or diffusive effects, and are in some cases even enhanced by these effects.
Collapse
Affiliation(s)
- C Reichhardt
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 USA
| | | |
Collapse
|