Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Dumbbell dimer dynamics in three-dimensional chiral fluids

Michalis Chatzittofi1,2,* and Yuto Hosaka1,†

  • *Contact author: mike.chatzittofi@ds.mpg.de
  • †Contact author: yuto.hosaka@ds.mpg.de

Phys. Rev. E 112, 055416 – Published 14 November, 2025

DOI: https://doi.org/10.1103/w6pg-4471

Abstract

We study the emergent orientational dynamics of a dumbbell dimer—two asymmetric monomers connected by a linking spring—in a three-dimensional chiral environment with odd viscosity. In classical systems with conserved parity symmetry, reciprocal oscillations of a dimer do not lead to rotational motion. Here, through an analytical calculation, we find that the presence of chirality in the system induces rotational dynamics as a function of the expansion/contraction of the dimer. By incorporating thermal fluctuations, we further find that the rotational diffusivity is affected by the coupling between conformational fluctuations and rotational motion. Our results provide insights into problems where the parity symmetry is broken and can be used as a building block to study similar models at the collective level. These problems include multicomponent molecular machines in odd-viscous fluids and systems with charged polymers where oddity is present through external magnetic fields.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (80)

  1. M. J. Bowick, N. Fakhri, M. C. Marchetti, and S. Ramaswamy, Symmetry, thermodynamics, and topology in active matter, Phys. Rev. X 12, 010501 (2022).
  2. G. Gompper, H. A. Stone, C. Kurzthaler, D. Saintillan, F. Peruani, D. A. Fedosov, T. Auth, C. Cottin-Bizonne, C. Ybert, E. Clément, T. Darnige, A. Lindner, R. E. Goldstein, B. Liebchen, J. Binysh, A. Souslov, L. Isa, R. di Leonardo, G. Frangipane, H. Gu et al., The 2025 motile active matter roadmap, J. Phys.: Condens. Matter 37, 143501 (2025).
  3. C. Battle, C. P. Broedersz, N. Fakhri, V. F. Geyer, J. Howard, C. F. Schmidt, and F. C. MacKintosh, Broken detailed balance at mesoscopic scales in active biological systems, Science 352, 604 (2016).
  4. J. Ignés-Mullol and F. Sagués, Experiments with active and driven synthetic colloids in complex fluids, Curr. Opin. Colloid Interface Sci. 62, 101636 (2022).
  5. R. A. Simha and S. Ramaswamy, Hydrodynamic fluctuations and instabilities in ordered suspensions of self-propelled particles, Phys. Rev. Lett. 89, 058101 (2002).
  6. A. S. Mikhailov and R. Kapral, Hydrodynamic collective effects of active protein machines in solution and lipid bilayers, Proc. Natl. Acad. Sci. USA 112, E3639 (2015).
  7. S. Thampi and J. Yeomans, Active turbulence in active nematics, Eur. Phys. J. Spec. Top. 225, 651 (2016).
  8. M. Guo, A. J. Ehrlicher, M. H. Jensen, M. Renz, J. R. Moore, R. D. Goldman, J. Lippincott-Schwartz, F. C. Mackintosh, and D. A. Weitz, Probing the stochastic, motor-driven properties of the cytoplasm using force spectrum microscopy, Cell 158, 822 (2014).
  9. B. R. Parry, I. V. Surovtsev, M. T. Cabeen, C. S. O'Hem, E. R. Dufresne, and C. Jacobs-Wagner, The bacterial cytoplasm has glass-like properties and is fluidized by metabolic activity, Cell 156, 183 (2014).
  10. P. Illien, T. Adeleke-Larodo, and R. Golestanian, Diffusion of an enzyme: The role of fluctuation-induced hydrodynamic coupling, Europhys. Lett. 119, 40002 (2017).
  11. J. Losa, S. Leupold, D. Alonso-Martinez, P. Vainikka, S. Thallmair, K. M. Tych, S. J. Marrink, and M. Heinemann, Perspective: A stirring role for metabolism in cells, Mol. Syst. Biol. 18, e10822 (2022).
  12. E. Lauga, Bacterial hydrodynamics, Annu. Rev. Fluid Mech. 48, 105 (2016).
  13. R. Golestanian, Enhanced diffusion of enzymes that catalyze exothermic reactions, Phys. Rev. Lett. 115, 108102 (2015).
  14. T. Adeleke-Larodo, P. Illien, and R. Golestanian, Fluctuation-induced hydrodynamic coupling in an asymmetric, anisotropic dumbbell, Eur. Phys. J. E 42, 39 (2019).
  15. N. Tyagi and B. J. Cherayil, Effects of reactivity on mobility: Insights from an exactly solvable two-state model, J. Stat. Mech. (2021) 083204.
  16. A. Suma, G. Gonnella, G. Laghezza, A. Lamura, A. Mossa, and L. F. Cugliandolo, Dynamics of a homogeneous active dumbbell system, Phys. Rev. E 90, 052130 (2014).
  17. M. Dennison, R. Kapral, and H. Stark, Diffusion in systems crowded by active force-dipole molecules, Soft Matter 13, 3741 (2017).
  18. Y. Koyano, H. Kitahata, and A. S. Mikhailov, Diffusion in crowded colloids of particles cyclically changing their shapes, Europhys. Lett. 128, 40003 (2019).
  19. K. Klett, A. G. Cherstvy, J. Shin, I. M. Sokolov, and R. Metzler, Non-Gaussian, transiently anomalous, and ergodic self-diffusion of flexible dumbbells in crowded two-dimensional environments: Coupled translational and rotational motions, Phys. Rev. E 104, 064603 (2021).
  20. J. C. Crocker, M. T. Valentine, E. R. Weeks, T. Gisler, P. D. Kaplan, A. G. Yodh, and D. A. Weitz, Two-point microrheology of inhomogeneous soft materials, Phys. Rev. Lett. 85, 888 (2000).
  21. E. M. Furst and T. M. Squires, Microrheology (Oxford University Press, Oxford, 2017).
  22. X.-L. Wu and A. Libchaber, Particle diffusion in a quasi-two-dimensional bacterial bath, Phys. Rev. Lett. 84, 3017 (2000).
  23. H. Ebata, K. Umeda, K. Nishizawa, W. Nagao, S. Inokuchi, Y. Sugino, T. Miyamoto, and D. Mizuno, Activity-dependent glassy cell mechanics I: Mechanical properties measured with active microrheology, Biophys. J. 122, 1781 (2023).
  24. T. M. Muenker, G. Knotz, M. Krüger, and T. Betz, Accessing activity and viscoelastic properties of artificial and living systems from passive measurement, Nat. Mater. 23, 1283 (2024).
  25. S. Sahoo, S. P. Singh, and S. Thakur, Enhanced self-propulsion of a sphere-dimer in viscoelastic fluid, Soft Matter 15, 2170 (2019).
  26. B. Liebchen, P. Monderkamp, B. ten Hagen, and H. Löwen, Viscotaxis: Microswimmer navigation in viscosity gradients, Phys. Rev. Lett. 120, 208002 (2018).
  27. K. K. Kumar, J. Caspers, F. Ginot, M. Krüger, and C. Bechinger, Memory-induced alignment of colloidal dumbbells, Sci. Rep. 13, 17409 (2023).
  28. A. Torrik, A. Naji, and M. Zarif, Dimeric colloidal inclusion in a chiral active bath: Effective interactions and chirality-induced torque, Phys. Rev. E 104, 064610 (2021).
  29. B. Liebchen and D. Levis, Chiral active matter, Europhys. Lett. 139, 67001 (2022).
  30. J. Mecke, J. O. Nketsiah, R. Li, and Y. Gao, Emergent phenomena in chiral active matter, National Sci. Open 3, 20230086 (2024).
  31. D. Banerjee, A. Souslov, A. G. Abanov, and V. Vitelli, Odd viscosity in chiral active fluids, Nat. Commun. 8, 1573 (2017).
  32. Y. Hosaka and S. Komura, Nonequilibrium transport induced by biological nanomachines, Biophys. Rev. Lett. 17, 51 (2022).
  33. M. Fruchart, C. Scheibner, and V. Vitelli, Odd viscosity and odd elasticity, Annu. Rev. Condens. Matter Phys. 14, 471 (2023).
  34. T. Khain, C. Scheibner, M. Fruchart, and V. Vitelli, Stokes flows in three-dimensional fluids with odd and parity-violating viscosities, J. Fluid Mech. 934, A23 (2022).
  35. Z. Zhao, B. Wang, S. Komura, M. Yang, F. Ye, and R. Seto, Emergent stripes of active rotors in shear flows, Phys. Rev. Res. 3, 043229 (2021).
  36. M. F. Lapa and T. L. Hughes, Swimming at low Reynolds number in fluids with odd, or Hall, viscosity, Phys. Rev. E 89, 043019 (2014).
  37. S. Ganeshan and A. G. Abanov, Odd viscosity in two-dimensional incompressible fluids, Phys. Rev. Fluids 2, 094101 (2017).
  38. T. Khain, M. Fruchart, C. Scheibner, T. A. Witten, and V. Vitelli, Trading particle shape with fluid symmetry: On the mobility matrix in 3-D chiral fluids, J. Fluid Mech. 992, A5 (2024).
  39. Y. Hosaka, R. Golestanian, and A. Vilfan, Lorentz reciprocal theorem in fluids with odd viscosity, Phys. Rev. Lett. 131, 178303 (2023).
  40. A. Aggarwal, E. Kirkinis, and M. O. de la Cruz, Thermocapillary migrating odd viscous droplets, Phys. Rev. Lett. 131, 198201 (2023).
  41. R. Lier, Slip-induced odd viscous flow past a cylinder, Phys. Rev. Fluids 9, 094101 (2024).
  42. P. Matus, R. Lier, and P. Surówka, Molecular modeling of odd viscoelastic fluids, Phys. Rev. E 110, 044605 (2024).
  43. X. M. de Wit, M. Fruchart, T. Khain, F. Toschi, and V. Vitelli, Pattern formation by turbulent cascades, Nature (London) 627, 515 (2024).
  44. P. Chen, S. Weady, S. Atis, T. Matsuzawa, M. J. Shelley, and W. T. Irvine, Self-propulsion, flocking and chiral active phases from particles spinning at intermediate Reynolds numbers, Nat. Phys. 21, 146 (2025).
  45. J. C. Everts and B. Cichocki, Dissipative effects in odd viscous stokes flow around a single sphere, Phys. Rev. Lett. 132, 218303 (2024).
  46. Y. Hosaka, M. Chatzittofi, R. Golestanian, and A. Vilfan, Chirotactic response of microswimmers in fluids with odd viscosity, Phys. Rev. Res. 6, L032044 (2024).
  47. Y. Hosaka, S. Komura, and D. Andelman, Hydrodynamic lift of a two-dimensional liquid domain with odd viscosity, Phys. Rev. E 104, 064613 (2021).
  48. A. Daddi-Moussa-Ider, A. Vilfan, and Y. Hosaka, Analytical solution for the hydrodynamic resistance of a disk in a compressible fluid layer with odd viscosity on a rigid substrate, J. Chem. Phys. 162, 064103 (2025).
  49. A. Daddi-Moussa-Ider, Y. Hosaka, E. Tjhung, and A. Vilfan, Hydrodynamic flow field and frictional resistance coefficient of a disk rotating steadily in a compressible fluid layer with odd viscosity on a rigid substrate, J. Phys. Soc. Jpn. 94, 044401 (2025).
  50. J. E. Avron, Odd viscosity, J. Stat. Phys. 92, 543 (1998).
  51. T. Markovich and T. C. Lubensky, Odd viscosity in active matter: Microscopic origin and 3D effects, Phys. Rev. Lett. 127, 048001 (2021).
  52. J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics (Springer, Netherlands, 1983).
  53. L. L. Jia, W. T. M. Irvine, and M. J. Shelley, Incompressible active phases at an interface. Part 1. Formulation and axisymmetric odd flows, J. Fluid Mech. 951, A36 (2022).
  54. H. Yuan and M. O. de la Cruz, Stokesian dynamics with odd viscosity, Phys. Rev. Fluids 8, 054101 (2023).
  55. A. Najafi and R. Golestanian, Simple swimmer at low Reynolds number: Three linked spheres, Phys. Rev. E 69, 062901 (2004).
  56. J. Agudo-Canalejo, T. Adeleke-Larodo, P. Illien, and R. Golestanian, Synchronization and enhanced catalysis of mechanically coupled enzymes, Phys. Rev. Lett. 127, 208103 (2021).
  57. M. Chatzittofi, J. Agudo-Canalejo, and R. Golestanian, Mechanistic rules for de novo design of enzymes, Chem Catalysis 5, 101394 (2025).
  58. Z. Tang, J. Wu, S. Wu, W. Tang, J.-R. Zhang, W. Zhu, J.-J. Zhu, and Z. Chen, Single molecule–driven nanomotors reveal the dynamic-disordered chemomechanical transduction of active enzymes, Sci. Adv. 11, eads0446 (2025).
  59. Our definition of the viscosity tensor or the stress tensor with odd viscosity is equivalent to that in Ref. [51] with ℓ=−2ηoẑ, in Ref. [34] with η1o=−2η2o=ηo, in Ref. [54] with μo=ηo/2, and in Ref. [45] with ηo=−ηo/2.
  60. E. M. Purcell, Life at low Reynolds number, Am. J. Phys. 45, 3 (1977).
  61. J. S. Lintuvuori, A. Würger, and K. Stratford, Hydrodynamics defines the stable swimming direction of spherical squirmers in a nematic liquid crystal, Phys. Rev. Lett. 119, 068001 (2017).
  62. G. E. Uhlenbeck and L. S. Ornstein, On the theory of the Brownian motion, Phys. Rev. 36, 823 (1930).
  63. L. Cocconi, H. Alston, J. Romano, and T. Bertrand, The OU2 process: Characterising dissipative confinement in noisy traps, New J. Phys. 26, 103016 (2024).
  64. L. L. Bonilla, Active Ornstein-Uhlenbeck particles, Phys. Rev. E 100, 022601 (2019).
  65. D. Martin, J. O'Byrne, M. E. Cates, E. Fodor, C. Nardini, J. Tailleur, and F. van Wijland, Statistical mechanics of active Ornstein-Uhlenbeck particles, Phys. Rev. E 103, 032607 (2021).
  66. Y. Hosaka, S. Komura, and A. S. Mikhailov, Mechanochemical enzymes and protein machines as hydrodynamic force dipoles: The active dimer model, Soft Matter 16, 10734 (2020).
  67. M. Chatzittofi, J. Agudo-Canalejo, and R. Golestanian, Nonlinear response theory of molecular machines, Europhys. Lett. 147, 21002 (2024).
  68. K. Yasuda, K. Ishimoto, A. Kobayashi, L.-S. Lin, I. Sou, Y. Hosaka, and S. Komura, Time-correlation functions for odd Langevin systems, J. Chem. Phys. 157, 095101 (2022).
  69. Y. Oh and Y. Baek, Effects of the self-propulsion parity on the efficiency of a fuel-consuming active heat engine, Phys. Rev. E 108, 024602 (2023).
  70. M. K. Johnsrud and R. Golestanian, Generalized fluctuation dissipation relations for active field theories, Phys. Rev. Res. 7, L032053 (2025).
  71. E. Lauga, Enhanced diffusion by reciprocal swimming, Phys. Rev. Lett. 106, 178101 (2011).
  72. V. Soni, E. S. Bililign, S. Magkiriadou, S. Sacanna, D. Bartolo, M. J. Shelley, and W. T. M. Irvine, The odd free surface flows of a colloidal chiral fluid, Nat. Phys. 15, 1188 (2019).
  73. P. L. Muzzeddu, E. Kalz, A. Gambassi, A. Sharma, and R. Metzler, Self-diffusion anomalies of an odd tracer in soft-core media, New J. Phys. 27, 033025 (2025).
  74. E. Kalz, H. D. Vuijk, I. Abdoli, J.-U. Sommer, H. Löwen, and A. Sharma, Collisions enhance self-diffusion in odd-diffusive systems, Phys. Rev. Lett. 129, 090601 (2022).
  75. E. Kalz, H. D. Vuijk, J.-U. Sommer, R. Metzler, and A. Sharma, Oscillatory force autocorrelations in equilibrium odd-diffusive systems, Phys. Rev. Lett. 132, 057102 (2024).
  76. R. Shinde, J. U. Sommer, H. Löwen, and A. Sharma, Strongly enhanced dynamics of a charged rouse dimer by an external magnetic field, PNAS Nexus 1, pgac119 (2022).
  77. J. Rotne and S. Prager, Variational treatment of hydrodynamic interaction in polymers, J. Chem. Phys. 50, 4831 (1969).
  78. H. Yamakawa, Transport properties of polymer chains in dilute solution: Hydrodynamic interaction, J. Chem. Phys. 53, 436 (1970).
  79. R. Golestanian and A. Ajdari, Analytic results for the three-sphere swimmer at low Reynolds number, Phys. Rev. E 77, 036308 (2008).
  80. K. Yasuda, Y. Hosaka, and S. Komura, Generalized three-sphere microswimmers, J. Phys. Soc. Jpn. 92, 121008 (2023).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation