Hydrodynamic synchronization and clustering in ratcheting colloidal matter
Fluid-mediated hydrodynamic interactions help synchronize and assemble microscopic particles driven with a ratchet effect.
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Hydrodynamic synchronization and clustering in ratcheting colloidal matter
Abstract
Ratchet transport systems are widespread in physics and biology; however, the effect of the dispersing medium in the collective dynamics of these out-of-equilibrium systems has been often overlooked. We show that, in a traveling wave magnetic ratchet, long-range hydrodynamic interactions (HIs) produce a series of remarkable phenomena on the transport and assembly of interacting Brownian particles. We demonstrate that HIs induce the resynchronization with the traveling wave that emerges as a “speed-up” effect, characterized by a net raise of the translational speed, which doubles that of single particles. When competing with dipolar forces and the underlying substrate symmetry, HIs promote the formation of clusters that grow perpendicular to the driving direction. We support our findings both with Langevin dynamics and with a theoretical model that accounts for the fluid-mediated interactions. Our work illustrates the role of the dispersing medium on the dynamics of driven colloidal matter and unveils the growing process and cluster morphologies above a periodic substrate.
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REFERENCES AND NOTES
1
S. Matthias, F. Müller, Asymmetric pores in a silicon membrane acting as massively parallel Brownian ratchets.
Nature
424
, 53–57 (2003).
2
M. J. Skaug, C. Schwemmer, S. Fringes, C. D. Rawlings, A. W. Knoll, Nanofluidic rocking Brownian motors.
Science
359
, 1505–1508 (2018).
3
I. U. Vakarelski, N. A. Patankar, J. O. Marston, D. Y. C. Chan, S. T. Thoroddsen, Stabilization of Leidenfrost vapour layer by textured superhydrophobic surfaces.
Nature
489
, 274–277 (2012).
4
S. Feng, P. Zhu, H. Zheng, H. Zhan, C. Chen, J. Li, L. Wang, X. Yao, Y. Liu, Z. Wang, Three-dimensional capillary ratchet-induced liquid directional steering.
Science
373
, 1344–1348 (2021).
5
H. Mazal, M. Iljina, I. Riven, G. Haran, Ultrafast pore-loop dynamics in a AAA+ machine point to a Brownian-ratchet mechanism for protein translocation.
Sci. Adv.
7
, eabg4674 (2021).
6
R. D. Astumian, Thermodynamics and kinetics of a Brownian motor.
Science
276
, 917–922 (1997).
7
D. Keller, C. Bustamante, The mechanochemistry of molecular motors.
Biophys. J.
78
, 541–556 (2000).
8
J. W. McCausland, X. Yang, G. R. Squyres, Z. Lyu, K. E. Bruce, M. M. Lamanna, B. Söderström, E. C. Garner, M. E. Winkler, J. Xiao, J. Liu, Treadmilling FtsZ polymers drive the directional movement of sPG-synthesis enzymes via a Brownian ratchet mechanism.
Nat. Commun.
12
, 609 (2021).
9
P. Reimann, Brownian motors: Noisy transport far from equilibrium.
Phys. Rep.
361
, 57–265 (2002).
10
P. Hänggi, F. Marchesoni, Artificial Brownian motors: Controlling transport on the nanoscale.
Rev. Mod. Phys.
81
, 387–442 (2009).
11
J. Rousselet, L. Salome, A. Ajdari, J. Prost, Directional motion of Brownian particles induced by a periodic asymmetric potential.
Nature
370
, 446–447 (1994).
12
L. P. Faucheux, L. S. Bourdieu, P. D. Kaplan, A. J. Libchaber, Optical thermal ratchet.
Phys. Rev. Lett.
74
, 1504–1507 (1995).
13
K. Gunnarsson, P. E. Roy, S. Felton, J. Pihl, P. Svedlindh, S. Berner, H. Lidbaum, S. Oscarsson, Programmable motion and separation of single magnetic particles on patterned magnetic surfaces.
Adv. Mater.
17
, 1730–1734 (2005).
14
B. Yellen, O. Hovorka, G. Friedman, Arranging matter by magnetic nanoparticle assemblers.
Proc. Natl. Acad. Sci. U.S.A.
102
, 8860–8864 (2005).
15
A. Ros, R. Eichhorn, J. Regtmeier, T. T. Duong, P. Reimann, D. Anselmetti, Absolute negative particle mobility.
Nature
436
, 928 (2005).
16
S.-H. Lee, K. Ladavac, M. Polin, D. G. Grier, Observation of flux reversal in a symmetric optical thermal ratchet.
Phys. Rev. Lett.
94
, 110601 (2005).
17
J. Frank, R. K. Agrawal, A ratchet-like inter-subunit reorganization of the ribosome during translocation.
Nature
406
, 318–322 (2000).
18
C. C. de Souza Silva, J. V. de Vondel, M. Morelle, V. V. Moshchalkov, Controlled multiple reversals of a ratchet effect.
Nature
440
, 651–654 (2006).
19
C. J. O. Reichhardt, C. Reichhardt, Ratchet effects in active matter systems.
Annu. Rev. Condens. Matter. Phys.
8
, 51–75 (2017).
20
S. Park, J. Song, J. S. Kim, In silico construction of a flexibility-based DNA Brownian ratchet for directional nanoparticle delivery.
Science
5
, eaav4943 (2019).
21
I. H. Riedel, K. Kruse, J. Howard, A self-organized vortex array of hydrodynamically entrained sperm cells.
Science
309
, 300–303 (2005).
22
A. Vilfan, F. Jülicher, Hydrodynamic flow patterns and synchronization of beating cilia.
Phys. Rev. Lett.
96
, 058102 (2006).
23
M. Baron, J. Bławzdziewicz, E. Wajnryb, Hydrodynamic crystals: Collective dynamics of regular arrays of spherical particles in a parallel-wall channel.
Phys. Rev. Lett.
100
, 174502 (2008).
24
Y. Goto, H. Tanaka, Purely hydrodynamic ordering of rotating disks at a finite Reynolds number.
Nat. Commun.
6
, 5994 (2015).
25
K. Yeo, E. Lushi, P. M. Vlahovska, Collective dynamics in a binary mixture of hydrodynamically coupled microrotors.
Phys. Rev. Lett.
114
, 188301 (2015).
26
T. M. Squires, M. P. Brenner, Like-charge attraction and hydrodynamic interaction.
Phys. Rev. Lett.
85
, 4976–4979 (2000).
27
J. Santana-Solano, J. L. Arauz-Lara, Hydrodynamic interactions in quasi-two-dimensional colloidal suspensions.
Phys. Rev. Lett.
87
, 038302 (2001).
28
A. Grimm, H. Stark, Hydrodynamic interactions enhance the performance of Brownian ratchets.
Soft Matter
7
, 3219–3227 (2011).
29
P. K. Ghosh, V. R. Misko, F. Marchesoni, F. Nori, Self-propelled janus particles in a ratchet: Numerical simulations.
Phys. Rev. Lett.
110
, 268301 (2013).
30
A. V. Arzola, M. Villasante-Barahona, K. Volke-Sepúlveda, P. Jákl, P. Zemánek, Omnidirectional transport in fully reconfigurable two dimensional optical ratchets.
Phys. Rev. Lett.
118
, 138002 (2017).
31
C. Marquet, A. Buguin, L. Talini, P. Silberzan, Rectified motion of colloids in asymmetrically structured channels.
Phys. Rev. Lett.
88
, 168301 (2002).
32
B. H. Wunsch, J. T. Smith, S. M. Gifford, C. Wang, M. Brink, R. L. Bruce, R. H. Austin, G. Stolovitzky, Y. Astier, Nanoscale lateral displacement arrays for the separation of exosomes and colloids down to 20 nm.
Nat. Nanotechnol.
11
, 936–940 (2016).
33
A. V. Straube, P. Tierno, Tunable interactions between paramagnetic colloidal particles driven in a modulated ratchet potential.
Soft Matter
10
, 3915–3925 (2014).
34
F. Martinez-Pedrero, H. Massana-Cid, T. Ziegler, T. H. Johansen, A. V. Straube, P. Tierno, Bidirectional particle transport and size selective sorting of Brownian particles in a flashing spatially periodic energy landscape.
Phys. Chem. Chem. Phys.
18
, 26353–26357 (2016).
35
J. R. Blake, A note on the image system for a stokeslet in a no-slip boundary.
Proc. Camb. Philos. Soc.
70
, 303–310 (1971).
36
A. V. Straube, P. Tierno, Synchronous vs. asynchronous transport of a paramagnetic particle in a modulated ratchet potential.
Europhys. Lett.
103
, 28001 (2013).
37
C. Lutz, M. Reichert, H. Stark, C. Bechinger, Surmounting barriers: The benefit of hydrodynamic interactions.
Europhys. Lett.
74
, 719–725 (2006).
38
T. Neuhaus, M. Marechal, M. Schmiedeberg, H. Löwen, Rhombic preordering on a square substrate.
Phys. Rev. Lett.
110
, 118301 (2013).
39
H. Kawamoto, K. Seki, N. Kuromiya, Mechanism of travelling-wave transport of particles.
J. Phys. D Appl. Phys.
39
, 1249–1256 (2006).
40
B. B. Yellen, R. M. Erb, H. S. Son, R. Hewlin, H. Shang, G. U. Lee, Traveling wave magnetophoresis for high resolution chip based separations.
Lab Chip
7
, 1681–1688 (2007).
41
C. Sándor, A. Libál, C. Reichhardt, C. J. O. Reichhardt, Collective transport for active matter run-and-tumble disk systems on a traveling-wave substrate.
Phys. Rev. E
95
, 012607 (2017).
42
R. E. Goldstein, Traveling-wave chemotaxis.
Phys. Rev. Lett.
77
, 775–778 (1996).
43
M. Hirano, K. Shinjo, Atomistic locking and friction.
Phys. Rev. B Condens. Matter
41
, 11837–11851 (1990).
44
D. Cole, S. Bending, S. Savel’ev, A. Grigorenko, T. Tamegai, F. Nori, Ratchet without spatial asymmetry for controlling the motion of magnetic flux quanta using time-asymmetric drives.
Nat. Mater.
5
, 305–311 (2006).
45
M. Belovs, R. Livanovics, A. Cebers, Hydrodynamic synchronization of pairs of puller type magnetotactic bacteria in a high frequency rotating magnetic field.
Soft Matter
15
, 1627–1632 (2019).
46
J. Kotar, M. Leoni, B. Bassetti, M. Lagomarsino, P. Cicuta, Hydrodynamic synchronization of colloidal oscillators.
Proc. Natl. Acad. Sci. U.S.A.
107
, 7669–7673 (2010).
47
N. Uchida, R. Golestanian, Generic conditions for hydrodynamic synchronization.
Phys. Rev. Lett.
106
, 058104 (2011).
48
B. Lau, O. Kedem, J. Schwabacher, D. Kwasnieski, E. A. Weiss, An introduction to ratchets in chemistry and biology.
Mater. Horiz.
4
, 310–318 (2017).
49
R. D. Astumian, M. Bier, Fluctuation driven ratchets: Molecular motors.
Phys. Rev. Lett.
72
, 1766–1769 (1994).
50
F. Jülicher, A. Ajdari, J. Prost, Modeling molecular motors.
Rev. Mod. Phys.
69
, 1269–1282 (1997).
51
P. Malgaretti, I. Pagonabarraga, D. Frenkel, Running faster together: Huge speed up of thermal ratchets due to hydrodynamic coupling.
Phys. Rev. Lett.
109
, 168101 (2012).
52
S. Kassem, T. van Leeuwen, A. S. Lubbe, M. R. Wilson, B. L. Feringa, D. A. Leigh, Artificial molecular motors.
Chem. Soc. Rev.
46
, 2592–2621 (2017).
53
C. Appert-Rolland, M. Ebbinghaus, L. Santen, Intracellular transport driven by cytoskeletal motors: General mechanisms and defects.
Phys. Rep.
593
, 1–59 (2015).
54
C. Hepp, B. Maier, Kinetics of DNA uptake during transformation provide evidence for a translocation ratchet mechanism.
Proc. Natl. Acad. Sci. U.S.A.
113
, 12467–12472 (2016).
55
P. Galajda, J. Keymer, P. Chaikin, R. Austin, A wall of funnels concentrates swimming bacteria.
J. Bacteriol.
189
, 8704–8707 (2007).
56
M. B. Wan, C. J. Olson Reichhardt, Z. Nussinov, C. Reichhardt, Rectification of swimming bacteria and self-driven particle systems by arrays of asymmetric barriers.
Phys. Rev. Lett.
101
, 018102 (2008).
57
L. Angelani, R. Di Leonardo, G. Ruocco, Self-starting micromotors in a bacterial bath.
Phys. Rev. Lett.
102
, 048104 (2009).
58
R. D. Leonardo, L. Angelani, D. Dell’Arciprete, G. Ruocco, V. Iebba, S. Schippa, M. P. Conte, F. Mecarini, F. De Angelis, E. Di Fabrizio, Bacterial ratchet motors.
Proc. Natl. Acad. Sci. U.S.A.
107
, 9541–9545 (2010).
59
P. Tierno, F. Sagués, T. H. Johansen, T. M. Fischer, Colloidal transport on magnetic garnet films.
Phys. Chem. Chem. Phys.
11
, 9615–9625 (2009).
60
P. Tierno, Magnetically reconfigurable colloidal patterns arranged from arrays of selfassembled microscopic dimers.
Soft Matter
8
, 11443 (2012).
Information & Authors
Information
Published In
Science Advances
Volume
8
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Issue
23
June 2022
June 2022
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Copyright © 2022 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC).
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Submission history
Received
: 4 February 2022
Accepted
: 19 April 2022
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Acknowledgments
We thank T. H. Johansen for providing us the FGF film.
Funding:
This work has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 Research and Innovation Programme (grant agreement no. 811234). S.G.L. and I.P. acknowledge support from Horizon 2020 program through 766972-FET-OPEN-NANOPHLOW. R.L.S. acknowledges support from the Swiss National Science Foundation (grant 180729). I.P. acknowledges support from Ministerio de Ciencia, Innovación y Universidades (grant no. PGC2018-098373-B-100 AEI/FEDER-EU) and from Generalitat de Catalunya under project 2017SGR-884 and Swiss National Science Foundation project no. 200021-175719. P.T. acknowledges support from Ministerio de Ciencia, Innovación y Universidades (PID2019-108842GB-C21) and the Generalitat de Catalunya (ICREA Acadèmia).
Author contributions:
S.G.L. performed numerical simulations and theory. R.L.S. carried out the experiments. I.P. and P.T. supervised the work. All authors discussed and interpreted the result of the manuscript.
Competing interests:
The authors declare that they have no competing interests.
Data and materials availability:
All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials.
Authors
Affiliations
Departament de Física de la Matèria Condensada, Universitat de Barcelona, Barcelona, Spain.
Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, Barcelona 08028, Spain.
Departament de Física de la Matèria Condensada, Universitat de Barcelona, Barcelona, Spain.
Departament de Física de la Matèria Condensada, Universitat de Barcelona, Barcelona, Spain.
Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, Barcelona 08028, Spain.
CECAM, Centre Européen de Calcul Atomique et Moléculaire, École Polytechnique Fédérale de Lausanne, Batochime, Avenue Forel 2, 1015 Lausanne, Switzerland.
Departament de Física de la Matèria Condensada, Universitat de Barcelona, Barcelona, Spain.
Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, Barcelona 08028, Spain.
Institut de Nanociència i Nanotecnologia, IN
2
UB, Universitat de Barcelona, Barcelona, Spain.
Funding Information
Swiss National Science Foundation
: 180729
H2020: 766972-FET-OPEN-NANOPHLOW
Ministerio de Ciencia Innovacio Universidades: PGC2018-098373- B-100 AEI/FEDER-EU
Ministerio de Ciencia Innovacio Universidades: PID2019- 108842GB-C21
Notes
*Corresponding author. Email:
[email protected]
†
These authors contributed equally to this work.
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