- Letter
- Open Access
Self-organized dynamics of a viscous drop with interfacial nematic activity
Phys. Rev. Research 7, L012054 – Published 5 March, 2025
DOI: https://doi.org/10.1103/PhysRevResearch.7.L012054
Abstract
We study emergent dynamics in a viscous drop subject to interfacial nematic activity. Using hydrodynamic simulations, we show how the interplay of nematodynamics, activity-driven flows in the fluid bulk, and surface deformations gives rise to a sequence of self-organized behaviors of increasing complexity, from periodic braiding motions of topological defects to chaotic defect dynamics and active turbulence, along with spontaneous shape changes and translation. Our findings recapitulate qualitative features of experiments and shed light on the mechanisms underpinning morphological dynamics in active interfaces.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (60)
- F. Spira, S. Cuylen-Haering, S. Mehta, M. Samwer, A. Reversat, A. Verma, R. Oldenbourg, M. Sixt, and D. W. Gerlich, Cytokinesis in vertebrate cells initiates by contraction of an equatorial actomyosin network composed of randomly oriented filaments, eLife 6, e30867 (2017).
- A.-C. Reymann, F. Staniscia, A. Erzberger, G. Salbreux, and S. W. Grill, Cortical flow aligns actin filaments to form a furrow, eLife 5, e17807 (2016).
- P. Guillamat, C. Blanch-Mercader, G. Pernollet, K. Kruse, and A. Roux, Integer topological defects organize stresses driving tissue morphogenesis, Nat. Mater. 21, 588 (2022).
- T. B. Saw, A. Doostmohammadi, V. Nier, L. Kocgozlu, S. Thampi, Y. Toyama, P. Marcq, C. T. Lim, J. M. Yeomans, and B. Ladoux, Topological defects in epithelia govern cell death and extrusion, Nature (London) 544, 212 (2017).
- G. Duclos, C. Erlenkämper, J.-F. Joanny, and P. Silberzan, Topological defects in confined populations of spindle-shaped cells, Nat. Phys. 13, 58 (2017).
- G. Salbreux, G. Charras, and E. Paluch, Actin cortex mechanics and cellular morphogenesis, Trends Cell Biol. 22, 536 (2012).
- A. C. Martin and B. Goldstein, Apical constriction: Themes and variations on a cellular mechanism driving morphogenesis, Development 141, 1987 (2014).
- A. Mietke, F. Jülicher, and I. F. Sbalzarini, Self-organized shape dynamics of active surfaces, Proc. Natl. Acad. Sci. USA 116, 29 (2019).
- G. Salbreux, F. Jülicher, J. Prost, and A. Callan-Jones, Theory of nematic and polar active fluid surfaces, Phys. Rev. Res. 4, 033158 (2022).
- S. C. Al-Izzi and R. G. Morris, Morphodynamics of active nematic fluid surfaces, J. Fluid Mech. 957, A4 (2023).
- L. Metselaar, J. M. Yeomans, and A. Doostmohammadi, Topology and morphology of self-deforming active shells, Phys. Rev. Lett. 123, 208001 (2019).
- L. J. Ruske and J. M. Yeomans, Morphology of active deformable 3D droplets, Phys. Rev. X 11, 021001 (2021).
- D. Khoromskaia and G. Salbreux, Active morphogenesis of patterned epithelial shells, eLife 12, e75878 (2023).
- F. C. Keber, E. Loiseau, T. Sanchez, S. J. Decamp, L. Giomi, M. J. Bowick, M. C. Marchetti, Z. Dogic, and A. R. Bausch, Topology and dynamics of active nematic vesicles, Science 345, 1135 (2014).
- P. Guillamat, Ž. Kos, J. Hardoüin, J. Ignés-Mullol, M. Ravnik, and F. Sagués, Active nematic emulsions, Sci. Adv. 4, eaao1470 (2018).
- K. L. Weirich, K. Dasbiswas, T. A. Witten, S. Vaikuntanathan, and M. L. Gardel, Self-organizing motors divide active liquid droplets, Proc. Natl. Acad. Sci. USA 116, 11125 (2019).
- G. Napoli and S. Turzi, Spontaneous helical flows in active nematics lying on a cylindrical surface, Phys. Rev. E 101, 022701 (2020).
- G. Napoli and L. Vergori, Extrinsic curvature effects on nematic shells, Phys. Rev. Lett. 108, 207803 (2012).
- G. Napoli and L. Vergori, Surface free energies for nematic shells, Phys. Rev. E 85, 061701 (2012).
- R. Zhang, Y. Zhou, M. Rahimi, and J. J. De Pablo, Dynamic structure of active nematic shells, Nat. Commun. 7, 13483 (2016).
- D. Khoromskaia and G. P. Alexander, Vortex formation and dynamics of defects in active nematic shells, New J. Phys. 19, 103043 (2017).
- S. Shankar, M. J. Bowick, and M. C. Marchetti, Topological sound and flocking on curved surfaces, Phys. Rev. X 7, 031039 (2017).
- R. Green, J. Toner, and V. Vitelli, Geometry of thresholdless active flow in nematic microfluidics, Phys. Rev. Fluids 2, 104201 (2017).
- I. Nitschke, M. Nestler, S. Praetorius, H. Löwen, and A. Voigt, Nematic liquid crystals on curved surfaces: A thin film limit, Proc. Math. Phys. Eng. Sci. 474, 20170686 (2018).
- D. J. G. Pearce, P. W. Ellis, A. Fernandez-Nieves, and L. Giomi, Geometrical control of active turbulence in curved topographies, Phys. Rev. Lett. 122, 168002 (2019).
- F. L. Memarian, D. Hammar, Md. M. H. Sabbir, M. Elias, K. A. Mitchell, and L. S. Hirst, Controlling chaos: Periodic defect braiding in active nematics confined to a cardioid, Phys. Rev. Lett. 132, 228301 (2024).
- D. Gueyffier, J. Li, A. Nadim, R. Scardovelli, and S. Zaleski, Volume-of-fluid interface tracking with smoothed surface stress methods for three-dimensional flows, J. Comput. Phys. 152, 423 (1999).
- E. Johnsen and F. Ham, Preventing numerical errors generated by interface-capturing schemes in compressible multi-material flows, J. Comput. Phys. 231, 5705 (2012).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.7.L012054 for additional details on the model, simulation method and analysis, and videos of simulations corresponding to Fig. 1.
- L. Giomi, Geometry and topology of turbulence in active nematics, Phys. Rev. X 5, 031003 (2015).
- I. Nitschke, S. Reuther, and A. Voigt, Liquid crystals on deformable surfaces, Proc. Math. Phys. Eng. Sci. 476, 20200313 (2020).
- S. Kralj, R. Rosso, and E. G. Virga, Curvature control of valence on nematic shells, Soft Matter 7, 670 (2011).
- F. P. Bretherton, The motion of rigid particles in a shear flow at low Reynolds number, J. Fluid Mech. 14, 284 (1962).
- M. Firouznia, S. H. Bryngelson, and D. Saintillan, A spectral boundary integral method for simulating electrohydrodynamic flows in viscous drops, J. Comput. Phys. 489, 112248 (2023).
- M. Firouznia, S. H. Bryngelson, and D. Saintillan, Spectral boundary integral solver for electrohydrodynamic flows in viscous drops, https://github.com/mfirouzn/EHD_Drop_3D (2022).
- J.-L. Thiffeault, Braids and Dynamics (Springer Nature, 2022).
- E. Fadell and J. V. Buskirk, The braid groups of and , Duke Math. J. 29, 243 (1962).
- J. S. Birman, Braids, Links, and Mapping Class Groups (Princeton University Press, Princeton, NJ, 1974).
- P. L. Boyland, H. Aref, and M. A. Stremler, Topological fluid mechanics of stirring, J. Fluid Mech. 403, 277 (2000).
- A. Fathi, F. Laundenbach, and V. Poénaru, Thurston's Work on Surfaces (Princeton University Press, Princeton, NJ, 2021).
- M. Budišić and J. Thiffeault, Finite-time braiding exponents, Chaos 25, 087407 (2015).
- D. D'Alessandro, M. Dahleh, and I. Mezic, Control of mixing in fluid flow: A maximum entropy approach, IEEE Trans. Automat. Contr. 44, 1852 (1999).
- M. D. Finn and J.-L. Thiffeault, Topological optimization of rod-stirring devices, SIAM Rev. 53, 723 (2011).
- T. N. Shendruk, A. Doostmohammadi, K. Thijssen, and J. M. Yeomans, Dancing disclinations in confined active nematics, Soft Matter 13, 3853 (2017).
- S. A. Smith and R. Gong, Braiding dynamics in active nematics, Front. Phys. 10, 880198 (2022).
- J. Thiffeault and M. Budišić, Braidlab: A software package for braids and loops, arXiv:1410.0849.
- P. Guillamat, J. Ignés-Mullol, and F. Sagués, Taming active turbulence with patterned soft interfaces, Nat. Commun. 8, 564 (2017).
- P. W. Ellis, D. J. G. Pearce, Y. Chang, G. Goldsztein, L. Giomi, and A. Fernandez-Nieves, Curvature-induced defect unbinding and dynamics in active nematic toroids, Nat. Phys. 14, 85 (2018).
- S. Lin, W. Zhang, D. Bi, B. Li, and X. Feng, Energetics of mesoscale cell turbulence in two-dimensional monolayers, Commun. Phys. 4, 21 (2021).
- A. Doostmohammadi, J. Ignés-Mullol, J. M. Yeomans, and F. Sagués, Active nematics, Nat. Commun. 9, 3246 (2018).
- Y. Maroudas-Sacks, L. Garion, L. Shani-Zerbib, A. Livshits, E. Braun, and K. Keren, Topological defects in the nematic order of actin fibres as organization centres of hydra morphogenesis, Nat. Phys. 17, 251 (2021).
- Y. Ravichandran, M. Vogg, K. Kruse, D. J. Pearce, and A. Roux, Topology changes of hydra define actin orientation defects as organizers of morphogenesis, Sci. Adv. 11, eadr9855 (2025).
- D. Fortunato, A high-order fast direct solver for surface PDEs, SIAM J. Sci. Comput. 46, A2582 (2024).
- D. Fortunato, D. Stein, and A. Barnett, A fully adaptive, high-order, fast Poisson solver for complex two-dimensional geometries, https://danfortunato.com/papers/FullyAdaptivePoisson.pdf.
- M. Serra, L. Lemma, L. Giomi, Z. Dogic, and L. Mahadevan, Defect-mediated dynamics of coherent structures in active nematics, Nat. Phys. 19, 1355 (2023).
- C. Sinigaglia, F. Braghin, and M. Serra, Optimal control of short-time attractors in active nematics, Phys. Rev. Lett. 132, 218302 (2024).
- M. Serra, S. Streichan, M. Chuai, C. J. Weijer, and L. Mahadevan, Dynamic morphoskeletons in development, Proc. Natl. Acad. Sci. USA 117, 11444 (2020).
- E. C. Lessey, C. Guilluy, and K. Burridge, From mechanical force to RhoA activation, Biochem. 51, 7420 (2012).
- W. M. Bement, M. Leda, A. M. Moe, A. M. Kita, M. E. Larson, A. E. Golding, C. Pfeuti, K.-C. Su, A. L. Miller, A. B. Goryachev et al., Activator-inhibitor coupling between Rho signalling and actin assembly makes the cell cortex an excitable medium, Nat. Cell Biol. 17, 1471 (2015).
- J. Bischof, C. A. Brand, K. Somogyi, I. Májer, S. Thome, M. Mori, U. S. Schwarz, and P. Lénárt, A cdk1 gradient guides surface contraction waves in oocytes, Nat. Commun. 8, 849 (2017).