- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

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

Advection selects pattern in multistable emulsions of active droplets

Stefan Köstler1,2, Yicheng Qiang1, Guido Kusters1, and David Zwicker1,*

  • *Contact author: david.zwicker@ds.mpg.de
PDF

Phys. Rev. Research 8, 013107 – Published 30 January, 2026

DOI: https://doi.org/10.1103/hdls-nzyc

Abstract

Controlling the size of droplets, for example, in biological cells, is challenging because large droplets typically outcompete smaller droplets due to surface tension. This coarsening is generally accelerated by hydrodynamic effects, but active chemical reactions can suppress it. We show that the interplay of these processes leads to three different dynamical regimes: (1) Advection dominates the coalescence of small droplets, (2) diffusion leads to Ostwald ripening for intermediate sizes, and (3) reactions finally suppress coarsening. Interestingly, a range of final droplet sizes is stable, of which one is selected depending on initial conditions. Our analysis demonstrates that hydrodynamic effects control initial droplet sizes, but they do not affect the later dynamics, in contrast to passive emulsions.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (43)

  1. C. P. Brangwynne, C. R. Eckmann, D. S. Courson, A. Rybarska, C. Hoege, J. Gharakhani, F. Jülicher, and A. A. Hyman, Germline P granules are liquid droplets that localize by controlled dissolution/condensation, Science 324, 1729 (2009).
  2. A. A. Hyman, C. A. Weber, and F. Jülicher, Liquid-liquid phase separation in biology, Annu. Rev. Cell Dev. Biol. 30, 39 (2014).
  3. S. F. Banani, H. O. Lee, A. A. Hyman, and M. K. Rosen, Biomolecular condensates: Organizers of cellular biochemistry, Nat. Rev. Mol. Cell Biol. 18, 285 (2017).
  4. D. Zwicker, O. W. Paulin, and C. ter Burg, Physics of droplet regulation in biological cells, Rep. Prog. Phys. 88, 116601 (2025).
  5. E. Jambon-Puillet, A. Testa, C. Lorenz, R. W. Style, A. A. Rebane, and E. R. Dufresne, Phase-separated droplets swim to their dissolution, Nat. Commun. 15, 3919 (2024).
  6. S. Song, T. Ivanov, Thao. P. Doan-Nguyen, L. C. da Silva, J. Xie, K. Landfester, and S. Cao, Synthetic biomolecular condensates: Phase-separation control, cytomimetic modelling and emerging biomedical potential, Angew. Chem. Int. Ed. 64, e202418431 (2025).
  7. W. Ostwald, Studien über die bildung und umwandlung fester Körper: 1. Abhandlung: Übersättigung und Überkaltung, Z. Phys. Chem. 22U, 289 (1897).
  8. P. W. Voorhees, The theory of Ostwald ripening, J. Stat. Phys. 38, 231 (1985).
  9. H. Tanaka, New mechanisms of droplet coarsening in phase-separating fluid mixtures, J. Chem. Phys. 107, 3734 (1997).
  10. V. S. Nikolayev, D. Beysens, and P. Guenoun, New hydrodynamic mechanism for drop coarsening, Phys. Rev. Lett. 76, 3144 (1996).
  11. Y. Huo, X. Jiang, H. Zhang, and Y. Yang, Hydrodynamic effects on phase separation of binary mixtures with reversible chemical reaction, J. Chem. Phys. 118, 9830 (2003).
  12. J. D. Wurtz and C. F. Lee, Chemical-reaction-controlled phase separated drops: Formation, size selection, and coarsening, Phys. Rev. Lett. 120, 078102 (2018).
  13. P. C. Bressloff, Active suppression of Ostwald ripening: Beyond mean-field theory, Phys. Rev. E 101, 042804 (2020).
  14. J. Sastre, A. Thatte, A. M. Bergmann, M. Stasi, M. Tena-Solsona, C. A. Weber, and J. Boekhoven, Size control and oscillations of active droplets in synthetic cells, Nat. Commun. 16, 2003 (2024).
  15. J. Bauermann, G. Bartolucci, J. Boekhoven, F. Jülicher, and C. A. Weber, Critical transition between intensive and extensive active droplets, Phys. Rev. X 15, 041027 (2025)
  16. J. Bauermann, G. Bartolucci, C. A. Weber, and F. Jülicher, The droplet size distribution and its dynamics in chemically active emulsions, Phys. Rev. Lett. 135, 148201 (2025).
  17. R. Lefever, D. Carati, and N. Hassani, Comment on “Monte Carlo simulations of phase separation in chemically reactive binary mixtures”, Phys. Rev. Lett. 75, 1674 (1995).
  18. J. Kirschbaum and D. Zwicker, Controlling biomolecular condensates via chemical reactions, J. R. Soc. Interface 18, 20210255 (2021).
  19. C. A. Weber, D. Zwicker, F. Jülicher, and C. F. Lee, Physics of active emulsions, Rep. Prog. Phys. 82, 064601 (2019).
  20. See Supplemental Material at http://link.aps.org/supplemental/10.1103/hdls-nzyc for numerical details and additional calculations.
  21. F. Liu and N. Goldenfeld, Dynamics of phase separation in block copolymer melts, Phys. Rev. A 39, 4805 (1989).
  22. C. B. Muratov, Theory of domain patterns in systems with long-range interactions of Coulomb type, Phys. Rev. E 66, 066108 (2002).
  23. N. Ziethen and D. Zwicker, Heterogeneous nucleation and growth of sessile chemically active droplets, J. Chem. Phys. 160, 224901 (2024).
  24. S. C. Glotzer, E. A. Di Marzio, and M. Muthukumar, Reaction-controlled morphology of phase-separating mixtures, Phys. Rev. Lett. 74, 2034 (1995).
  25. J. J. Christensen, K. Elder, and H. C. Fogedby, Phase segregation dynamics of a chemically reactive binary mixture, Phys. Rev. E 54, R2212(R) (1996).
  26. D. Zwicker, A. A. Hyman, and F. Jülicher, Suppression of Ostwald ripening in active emulsions, Phys. Rev. E 92, 012317 (2015).
  27. A. Kulkarni, E. Vidal-Henriquez, and D. Zwicker, Effective simulations of interacting active droplets, Sci. Rep. 13, 733 (2023).
  28. I. M. Lifshitz and V. V. Slyozov, The kinetics of precipitation from supersaturated solid solutions, J. Phys. Chem. Solids 19, 35 (1961).
  29. C. Wagner, Theorie der alterung von niederschlägen durch Umlösen (Ostwald-Reifung), Z. Elektrochem. Ber. Bunsengesellschaft Phys. Chem. 65, 581 (1961).
  30. D. Zwicker, R. Seyboldt, C. A. Weber, A. A. Hyman, and F. Jülicher, Growth and division of active droplets provides a model for protocells, Nat. Phys. 13, 408 (2017).
  31. A. J. Wagner and M. E. Cates, Phase ordering of two-dimensional symmetric binary fluids: A droplet scaling state, Europhys. Lett. 56, 556 (2001).
  32. S. Gsell and M. Merkel, Phase separation dynamics in deformable droplets, Soft Matter 18, 2672 (2022).
  33. E. D. Siggia, Late stages of spinodal decomposition in binary mixtures, Phys. Rev. A 20, 595 (1979).
  34. R. Seyboldt and F. Jülicher, Role of hydrodynamic flows in chemically driven droplet division, New J. Phys. 20, 105010 (2018).
  35. C. Datt, J. Bauermann, N. B. Budanur, and F. Jülicher, Fluid flow and spatiotemporal chaos in chemically active emulsions, arXiv:2509.15526.
  36. P. Stansell, K. Stratford, J.-C. Desplat, R. Adhikari, and M. E. Cates, Nonequilibrium steady states in sheared binary fluids, Phys. Rev. Lett. 96, 085701 (2006).
  37. K. Stratford, J. C. Desplat, P. Stansell, and M. E. Cates, Binary fluids under steady shear in three dimensions, Phys. Rev. E 76, 030501 (2007).
  38. A. Gubbala, D. P. Arnold, A. Jena, S. Anujarerat, and S. C. Takatori, Dynamic swarms regulate the morphology and distribution of soft membrane domains, Phys. Rev. E 110, 014410 (2024).
  39. K. Furtado and J. M. Yeomans, Lattice Boltzmann simulations of phase separation in chemically reactive binary fluids, Phys. Rev. E 73, 066124 (2006).
  40. S. M. Fielding, Role of inertia in nonequilibrium steady states of sheared binary fluids, Phys. Rev. E 77, 021504 (2008).
  41. N. Ziethen, J. Kirschbaum, and D. Zwicker, Nucleation of chemically active droplets, Phys. Rev. Lett. 130, 248201 (2023).
  42. C.-Z. Zhang and Z.-G. Wang, Random isotropic structures and possible glass transitions in diblock copolymer melts, Phys. Rev. E 73, 031804 (2006).
  43. S. Köstler, Y. Qiang, G. Kusters, and D. Zwicker, Python code for “Advection selects pattern in multi-stable emulsions of active droplets”, Zenodo (2026), https://doi.org/10.5281/zenodo.18187405.

Outline

Information

Phys. Rev. Research 8, 013107– Published 30 January, 2026
  • Received 30 September 2025
  • Accepted 4 January 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by Max Planck Society.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation