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Liquid Crystals Reviews Volume 8, 2020 - Issue 2
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Review

Design of nematic liquid crystals to control microscale dynamics

Oleg D. LavrentovichAdvanced Materials and Liquid Crystal Institute, Department of Physics, Materials Science Graduate Program, Kent State University, Kent, OH, USACorrespondence[email protected]
ORCID Iconhttps://orcid.org/0000-0002-0128-0708View further author information
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Pages 59-129 | Received 17 Dec 2020, Accepted 11 Apr 2021, Published online: 26 May 2021

References

  • Yang D-K, Wu S-T. Fundamentals of liquid crystal devices. Chichester, England: Wiley; 2006; p. 394.
  • de Gennes PG, Prost J. The physics of liquid crystals. Oxford: Clarendon Press; 1993; p. 598.
  • Ramaswamy S. The mechanics and statistics of active matter. Annu Rev Condens Matter Phys. 2010;1:323–345.
  • Marchetti MC, Joanny JF, Ramaswamy S, et al. Hydrodynamics of soft active matter. Rev Mod Phys. 2013;85:1143–1189.
  • Aranson IS. Active colloids. Phys Usp. 2013;56:79–92.
  • Doostmohammadi A, Ignés-Mullol J, Yeomans JM, et al. Active nematics. Nat Commun. 2018;9:3246.
  • Lane N. The unseen world: reflections on Leeuwenhoek (1677) ‘Concerning little animals’. Philos Trans R Soc B Biol Sci. 2015;370:20140344.
  • Gest H. The discovery of microorganisms by Robert Hooke and Antoni Van Leeuwenhoek, fellows of the Royal Society. Notes Rec R Soc Lond. 2004;58:187–201.
  • Brown R. A brief account of microscopical observations on the particles contained in the pollen of plants and the general existence of active molecules in organic and inorganic bodies. Edinburgh New Philos J. 1828;4:358–371.
  • Berg HC. Random walks in biology: new and expanded edition. Princeton (NJ): Princeton University Press; 2018.
  • Lauga E, Powers TR. The hydrodynamics of swimming microorganisms. Rep Prog Phys. 2009;72:096601.
  • Lauga E. Bacterial hydrodynamics. Annu Rev Fluid Mech. 2016;48:105–130.
  • Takatori SC, Brady JF. Forces, stresses and the (thermo?) dynamics of active matter. Curr Opin Colloid Interface Sci. 2016;21:24–33.
  • Reichhardt CJO, Reichhardt C. Ratchet effects in active matter systems. Annu Rev Condens Matter Phys. 2017;8(8):51–75.
  • Needleman D, Dogic Z. Active matter at the interface between materials science and cell biology. Nature Rev Mater. 2017;2:17048.
  • Ramaswamy S. Active matter. J Stat Mech Theory Exp. 2017;2017:054002.
  • Liebchen B, Lowen H. Synthetic chemotaxis and collective behavior in active matter. Acc Chem Res. 2018;51:2982–2990.
  • Villa K, Pumera M. Fuel-free light-driven micro/nanomachines: artificial active matter mimicking nature. Chem Soc Rev. 2019;48:4966–4978.
  • Varnerey FJ, Benet E, Blue L, et al. Biological active matter aggregates: inspiration for smart colloidal materials. Adv Colloid Interface Sci. 2019;263:38–51.
  • Dou Y, Dhatt-Gauthier K, Bishop KJM. Thermodynamic costs of dynamic function in active soft matter. Curr Opin Solid State Mater Sci. 2019;23:28–40.
  • Doostmohammadi A, Yeomans JM. Coherent motion of dense active matter. Eur Phys J Spec Top. 2019;227:2401–2411.
  • Pishvar M, Harne RL. Foundations for soft, smart matter by active mechanical metamaterials. Adv Sci. 2020;7:2001384.
  • Liu WJ, Chen X, Lu XL, et al. From passive inorganic oxides to active matters of micro/nanomotors. Adv Funct Mater. 2020;30:2003195.
  • Wang W, Lv XL, Moran JL, et al. A practical guide to active colloids: choosing synthetic model systems for soft matter physics research. Soft Matter. 2020;16:3846–3868.
  • Shaebani MR, Wysocki A, Winkler RG, et al. Computational models for active matter. Nature Rev Phys. 2020;2:181–199.
  • Ghosh A, Xu WN, Gupta N, et al. Active matter therapeutics. Nano Today. 2020;31:100836.
  • Speck T. Collective forces in scalar active matter. Soft Matter. 2020;16:2652–2663.
  • Cichos F, Gustavsson K, Mehlig B, et al. Machine learning for active matter. Nature Mach Intell. 2020;2:94–103.
  • Bar M, Grossmann R, Heidenreich S, et al. Self-propelled rods: insights and perspectives for active matter. Annu Rev Condens Matter Phys. 2020;11:441–466.
  • Zhang R, Mozaffari A, de Pablo JJ. Autonomous materials systems from active liquid crystals. Nature Rev Mater. 2021. https://doi.org/10.1038/s41578-41020-00272-x.
  • Turiv T, Lazo I, Brodin A, et al. Effect of collective molecular reorientations on Brownian motion of colloids in nematic liquid crystal. Science. 2013;342:1351–1354.
  • Mandle RJ, Cowling SJ, Goodby JW. A nematic to nematic transformation exhibited by a rod-like liquid crystal. Phys Chem Chem Phys. 2017;19:11429–11435.
  • Mertelj A, Cmok L, Sebastian N, et al. Splay nematic phase. Phys Rev X. 2018;8:041025.
  • Nishikawa H, Shiroshita K, Higuchi H, et al. A fluid liquid-crystal material with highly polar order. Adv Mater. 2017;29:1702354.
  • Chen X, Korblova E, Dong DP, et al. First-principles experimental demonstration of ferroelectricity in a thermotropic nematic liquid crystal: polar domains and striking electro-optics. Proc Natl Acad Sci USA. 2020;117:14021–14031.
  • Jákli A, Lavrentovich OD, Selinger JV. Physics of liquid crystals of bent-shaped molecules. Rev Mod Phys. 2018;90:045004.
  • Morales-Navarrete H, Nonaka H, Scholich A, et al. Liquid-crystal organization of liver tissue. eLife. 2019;8:e44860.
  • Kleman M, Lavrentovich OD. Soft matter physics: an introduction. New York: Springer; 2003; Partially Ordered Systems, p. 638.
  • Buka Á, Éber N, Pesch W, et al. Convective patterns in liquid crystals driven by electric field – an overview of the onset behavior, self-assembly. Pattern Formation Growth Phenom Nano-Syst. 2006;218:55–82.
  • Kai S, Zimmermann W. Pattern dynamics in the electrohydrodynamics of nematic liquid-crystals – defect patterns, transition to turbulence and magnetic-field effects. Prog Theor Phys Suppl. 1989;99:458–492.
  • Éber N, Salamon P, Buka Á. Electrically induced patterns in nematics and how to avoid them. Liq Cryst Rev. 2016;4:102–135.
  • Guyon E, Hulin J-P, Petit L, et al. Physical hydrodynamics. New York: Oxford University Press; 2001; p. 506.
  • Helfrich W. Conduction-induced alignment of nematic liquid crystals – basic model and stability considerations. J Chem Phys. 1969;51:4092–4105.
  • Kurik MV, Lavrentovich OD. Defects in liquid-crystals – homotopy-theory and experimental investigations. Uspekhi Fizicheskikh Nauk. [Sov. Phys]. 1988;31:196–224.
  • Li BX, Borshch V, Xiao RL, et al. Electrically-driven three-dimensional solitary waves as director bullets in nematic liquid crystals. Nat Commun. 2018;9:2912.
  • Li BX, Xiao RL, Paladugu S, et al. Three-dimensional solitary waves with electrically tunable direction of propagation in nematics. Nat Commun. 2019;10:3749.
  • Shen Y, Dierking I. Dynamics of electrically driven solitons in nematic and cholesteric liquid crystals. Commun Phys. 2020;3:14.
  • Li BX, Xiao RL, Shiyanovskii SV, et al. Soliton-induced liquid crystal enabled electrophoresis. Phys Rev Res. 2020;2:013178.
  • Lam L, Prost J. Solitons in liquid crystals. New York: Springer-Verlag; 1992; p. 338.
  • Lavrentovich OD, Kleman M. Cholesteric liquid crystals: defects and topology. In: Kitzerow H-S, Bahr C, editors. Chirality in liquid crystals. New York: Springer-Verlag; 2001. p. 115–158.
  • Kleman M. Points, lines and walls in liquid crystals, magnetic systems and various ordered media. Chichester: Wiley; 1983; p. 322.
  • Belavin AA, Polyakov AM. Metastable States of 2-dimensional isotropic ferromagnets. JETP Lett. 1975;22:245–247.
  • Bogdanov AN, Rossler UK, Shestakov AA. Skyrmions in nematic liquid crystals. Phys Rev E. 2003;67:016602.
  • Dauxois T, Peyrard M. Physics of solitons. Cambridge, UK: Cambridge University Press; 2006; p. 422.
  • Lin L, Shu CQ, Xu G. Generation and detection of propagating solitons in shearing liquid-crystals. J Stat Phys. 1985;39:633–652.
  • Zhu GZ, Liu XZ, Bai NB. Director waves and their accompanying flow. Phys Lett A. 1986;117:229–233.
  • Gleeson JT, Palffy-Muhoray P, Van Saarloos W. Propagation of excitations induced by shear-flow in nematic liquid-crystals. Phys Rev A. 1991;44:2588–2595.
  • Čopar S, Kos Ž, Emersic T, et al. Microfluidic control over topological states in channel-confined nematic flows. Nat Commun. 2020;11:59.
  • Derrick GH. Comments on nonlinear wave equations as models for elementary particles. J Math Phys. 1964;5:1252–1254.
  • Haas WEL, Adams JE. New optical storage mode in liquid-crystals. Appl Phys Lett. 1974;25:535–537.
  • Haas WEL, Adams JE. Electrically variable diffraction in spherulitic liquid-crystals. Appl Phys Lett. 1974;25:263–264.
  • Kawachi M, Kogure O, Kato Y. Bubble-domain texture of a liquid-crystal. Jpn J Appl Phys. 1974;13:1457–1458.
  • Bouligand Y, Derrida B, Poenaru V, et al. Distortions with double topological character – case of cholesterics. J Phys. 1978;39:863–867.
  • Smalyukh II, Senyuk BI, Palffy-Muhoray P, et al. Electric-field-induced nematic-cholesteric transition and three-dimensional director structures in homeotropic cells. Phys Rev E. 2005;72:061707.
  • Smalyukh II, Lansac Y, Clark NA, et al. Three-dimensional structure and multistable optical switching of triple-twisted particle-like excitations in anisotropic fluids. Nat Mater. 2010;9:139–145.
  • Ackerman PJ, Boyle T, Smalyukh II. Squirming motion of baby skyrmions in nematic fluids. Nat Commun. 2017;8:673.
  • Sohn HRO, Ackerman PJ, Boyle TJ, et al. Dynamics of topological solitons, knotted streamlines, and transport of cargo in liquid crystals. Phys Rev E. 2018;97:052701.
  • Tai JSB, Smalyukh II. Three-dimensional crystals of adaptive knots. Science. 2019;365:1449–1453.
  • Guo YB, Afghah S, Xiang J, et al. Cholesteric liquid crystals in rectangular microchannels: skyrmions and stripes. Soft Matter. 2016;12:6312–6320.
  • Nych A, Fukuda J-I, Ognysta U, et al. Spontaneous formation and dynamics of half-skyrmions in a chiral liquid-crystal film. Nat Phys. 2017;13:1215–1220.
  • Posnjak G, Čopar S, Muševič I. Points, skyrmions and torons in chiral nematic droplets. Sci Rep. 2016;6:26361.
  • Leonov AO, Dragunov IE, Rossler UK, et al. Theory of skyrmion states in liquid crystals. Phys Rev E. 2014;90:042502.
  • Afghah S, Selinger JV. Theory of helicoids and skyrmions in confined cholesteric liquid crystals. Phys Rev E. 2017;96:012708.
  • Ryabchun A, Bobrovsky A. Cholesteric liquid crystal materials for tunable diffractive optics. Adv Opt Mater. 2018;6:1800335.
  • Smalyukh II. Review: knots and other new topological effects in liquid crystals and colloids. Rep Prog Phys. 2020;83:106601.
  • Cladis PE, Kleman M. Cholesteric domain texture. Mol Cryst Liq Cryst. 1972;16:1–20.
  • Oswald P, Baudry J, Pirkl S. Static and dynamic properties of cholesteric fingers in electric field. Phys Rep Rev Sect Phys Lett. 2000;337:67–96.
  • Oswald P, Dequidt A, Poy G. Chapter 3: thermomechanical effects in liquid crystals. In: P Pieranski, MH Godinho, editor. Liquid crystals: New perspectives. London, UK: ISTE Ltd and John Wiley & Sons, Inc.; 2021. p. 117–191.
  • Press MJ, Arrott AS. Static strain waves in cholesteric liquid-crystals – response to magnetic and electric-fields. Mol Cryst Liq Cryst. 1976;37:81–99.
  • Baudry J, Pirkl S, Oswald P. Looped finger transformation in frustrated cholesteric liquid crystals. Phys Rev E. 1999;59:5562–5571.
  • Gil L, Gilli JM. Surprising dynamics of some cholesteric liquid crystal patterns. Phys Rev Lett. 1998;80:5742–5745.
  • Shiyanovskii SV, Smalyukh II, Lavrentovich OD. Computer simulations and fluorescence confocal polarizing microscopy of structures in cholesteric liquid crystals. In: OD Lavrentovich, P Pasini, C Zannoni, S Zumer, editor. Defects in liquid crystals: computer simulations, theory and experiments. Dordrecht: Kluwer Academic Publishers; 2001. p. 229–270.
  • Gartland EC, Huang H, Lavrentovich OD, et al. Electric-field induced transitions in a cholesteric liquid-crystal film with negative dielectric anisotropy. J Comput Theor Nanosci. 2010;7:709–725.
  • Durey G, Sohn HRO, Ackerman PJ, et al. Topological solitons, cholesteric fingers and singular defect lines in Janus liquid crystal shells. Soft Matter. 2020;16:2669–2682.
  • Voloschenko D, Lavrentovich OD. Optical vortices generated by dislocations in a cholesteric liquid crystal. Opt Lett. 2000;25:317–319.
  • Shiyanovskii SV, Voloschenko D, Ishikawa T, et al. Director structures of cholesteric diffraction gratings. Mol Cryst Liq Cryst. 2001;358:225–236.
  • Smalyukh II, Shiyanovskii SV, Lavrentovich OD. Three-dimensional imaging of orientational order by fluorescence confocal polarizing microscopy. Chem Phys Lett. 2001;336:88–96.
  • Smalyukh II, Lavrentovich OD. Three-dimensional director structures of defects in Grandjean-Cano wedges of cholesteric liquid crystals studied by fluorescence confocal polarizing microscopy. Phys Rev E. 2002;66:051703.
  • Friedel J, Kleman M. Application of dislocation theory to liquid crystals (National Bureau of Standards special publication no. 317). In: RDWJA Simmons, R Bullough, editor. Fundamental aspects of dislocation theory. Washington, D.C.: US National Bureau of Standards; 1970. p. 607–636.
  • Akahane T, Tako T. Molecular alignment of bubble domains in cholesteric-nematic mixtures. Jpn J Appl Phys. 1976;15:1559–1560.
  • Dzyaloshinskii IE. Theory of helicoidal structures in antiferromagnets. Nonmetals, Sov Phys JETP-USSR. 1964;19:960–971.
  • Manton N, Sutcliffe P. Topological solitons (Cambridge, Cambridge, U.K.; New York, 2004), Cambridge monographs on mathematical physics, p. 493.
  • Fukuda J-I, Žumer S. Quasi-two-dimensional skyrmion lattices in a chiral nematic liquid crystal. Nat Commun. 2011;2:246.
  • Skyrme TH. A Non-linear field theory. Proc R Soc Lond Ser A Math Phys Sci. 1961;260:127–138.
  • Duzgun A, Selinger JV, Saxena A. Comparing skyrmions and merons in chiral liquid crystals and magnets. Phys Rev E. 2018;97:062706.
  • Sohn HRO, Vlasov SM, Uzdin VM, et al. Real-space observation of skyrmion clusters with mutually orthogonal skyrmion tubes. Phys Rev B. 2019;100:104401.
  • Machon T, Alexander GP. Woven nematic defects, skyrmions, and the Abelian sandpile model. Phys Rev Lett. 2018;121:237801.
  • Machon T, Alexander GP. Umbilic lines in orientational order. Phys Rev X. 2016;6:011033.
  • De Matteis G, Martina L, Turco V. Skyrmion States in chiral liquid crystals. Theor Math Phys. 2018;196:1150–1163.
  • Fukuda J, Žumer S. Reflection spectra and near-field images of a liquid crystalline half-skyrmion lattice. Opt Express. 2018;26:1174–1184.
  • Duzgun A, Saxena A, Selinger JV. Alignment-induced reconfigurable walls for patterning and assembly of liquid crystal skyrmions. Phys Rev Res. 2021;3:L012005.
  • Duzgun A, Nisoli C. Skyrmion spin ice in liquid crystals. Phys Rev Lett. 2021;126:047801.
  • Gilli JM, Gil L. Static and dynamic textures obtained under an electric-field in the neighborhood of the winding transition of a strongly confined cholesteric. Liq Cryst. 1994;17:1–15.
  • Gil L, Thiberge S. Is the electromechanical coupling the driving force for the perpendicular drift of first class cholesteric finger? J Phys II. 1997;7:1499–1508.
  • Ribiere P, Oswald P, Pirkl S. Crawling and spiraling of cholesteric fingers in electric-field. J Phys II. 1994;4:127–143.
  • Baudry J, Pirkl S, Oswald P. Effect of the electric conductivity on the drift velocity of the cholesteric fingers of the second type in confined geometry. Phys Rev E. 1999;60:2990–2993.
  • Tarasov OS, Krekhov AP, Kramer L. Dynamics of cholesteric structures in an electric field. Phys Rev E. 2003;68:031708.
  • Sohn HRO, Liu CDD, Smalyukh II. Schools of skyrmions with electrically tunable elastic interactions. Nat Commun. 2019;10.
  • Peccianti M, Assanto G. Nematicons. Phys Rep Rev Sect Phys Lett. 2012;516:147–208.
  • Burgess IB, Peccianti M, Assanto G, et al. Accessible light bullets via synergetic nonlinearities. Phys Rev Lett. 2009;102:203903.
  • Peccianti M, Burgess IB, Assanto G, et al. Space-time bullet trains via modulation instability and nonlocal solitons. Opt Express. 2010;18:5934–5941.
  • Assanto G. Nematicons: reorientational solitons from optics to photonics. Liq Cryst Rev. 2018;6:170–194.
  • Laudyn UA, Kwasny M, Karpierz MA, et al. Electro-optic quenching of nematicon fluctuations. Opt Lett. 2019;44:167–170.
  • Madani A, Beeckman J, Neyts K. Theoretical study of reorientation and torque of liquid crystal molecules under influence of external electric field and experimentally generation of spatial optical soliton beam and getting a sharp switching in chiral nematic liquid crystal. Optik (Stuttg). 2013;124:3983–3986.
  • Tabiryan NV, Sukhov AV, Zeldovich BY. Orientational optical nonlinearity of liquid-crystals. Mol Cryst Liq Cryst. 1986;136:1–139.
  • Stegeman GI, Segev M. Optical spatial solitons and their interactions: universality and diversity. Science. 1999;286:1518–1523.
  • Towers IN, Malomed BA, Wise FW. Light bullets in quadratic media with normal dispersion at the second harmonic. Phys Rev Lett. 2003;90:123902.
  • Mihalache D, Mazilu D, Lederer F, et al. Stable spatiotemporal solitons in bessel optical lattices. Phys Rev Lett. 2005;95:023902.
  • Mihalache D, Mazilu D, Lederer F, et al. Three-dimensional spatiotemporal optical solitons in nonlocal nonlinear media. Phys Rev E. 2006;73:025601.
  • Minardi S, Eilenberger F, Kartashov YV, et al. Three-Dimensional light bullets in arrays of waveguides. Phys Rev Lett. 2010;105:263901.
  • Lahav O, Kfir O, Sidorenko P, et al. Three-dimensional spatiotemporal pulse-train solitons. Phys Rev X. 2017;7:041051.
  • Malomed BA, Mihalache D, Wise F, et al. Spatiotemporal optical solitons. J Opt B Quantum Semiclassical Opt. 2005;7:R53–R72.
  • Malomed B, Torner L, Wise F, et al. On multidimensional solitons and their legacy in contemporary atomic, molecular and optical physics. J Phys B At Mol Opt Phys. 2016;49:170502.
  • Silberberg Y. Collapse of optical pulses. Opt Lett. 1990;15:1282–1284.
  • Mcleod R, Blair S, Wagner K. Asymmetric light bullet dragging logic. Opt Comput. 1995;139:657–660.
  • Purwins HG, Bödeker HU, Amiranashvili S. Dissipative solitons. Adv Phys. 2010;59:485–701.
  • Descalzi O, Clerc MG, Residori S, et al. Localized states in physics: solitons and patterns. New York: Springer; 2011.
  • Knobloch E. Spatial localization in dissipative systems. Annu Rev Condens Matter Phys. 2015;6:325–359.
  • Bödeker HU, Röttger MC, Liehr AW, et al. Noise-covered drift bifurcation of dissipative solitons in a planar gas-discharge system. Phys Rev E. 2003;67:056220.
  • Aya S, Araoka F. Kinetics of motile solitons in nematic liquid crystals. Nat Commun. 2020;11:3248.
  • Earls A, Calderer MC. Three-dimensional solitons in nematic liquid crystals, Part I: Linear analysis; 2019. arXiv:1910.05959v1.
  • Pikin SA. On the structural instability of a nematic in an alternating electric field and Its connection with convection and the flexoelectric effect. J Surf Invest. 2019;13:1078–1082.
  • de Gennes PG, Prost J. The physics of liquid crystals. Oxford: Clarendon Press; 1995.
  • Dubois-Violette E, de Gennes PG, Parodi O. Hydrodynamic instabilities of nematic liquid crystals under A. C. electric fields. J Phys France. 1971;32:305–317.
  • Meyer RB. Piezoelectric effects in liquid crystals. Phys Rev Lett. 1969;22:918–920.
  • Prost J, Marcerou JP. On the microscopic interpretation of flexoelectricity. J Phys. 1977;38:315–324.
  • Krekhov A, Pesch W, Éber N, et al. Nonstandard electroconvection and flexoelectricity in nematic liquid crystals. Phys Rev E. 2008;77:021705.
  • Krekhov A, Pesch W, Buka Á. Flexoelectricity and pattern formation in nematic liquid crystals. Phys Rev E. 2011;83:051706.
  • Shen Y, Dierking I. Dynamic dissipative solitons in nematics with positive anisotropies. Soft Matter. 2020;16:5325–5333.
  • Garbovskiy Y. Conventional and unconventional ionic phenomena in tunable soft materials made of liquid crystals and nanoparticles. Nano Express. 2021;2:012004.
  • Whitesides GM. The origins and the future of microfluidics. Nature. 2006;442:368–373.
  • Stone HA, Stroock AD, Ajdari A. Engineering flows in small devices: microfluidics toward a lab-on-a-chip. Annu Rev Fluid Mech. 2004;36:381–411.
  • Psaltis D, Quake SR, Yang CH. Developing optofluidic technology through the fusion of microfluidics and optics. Nature. 2006;442:381–386.
  • deMello AJ. Control and detection of chemical reactions in microfluidic systems. Nature. 2006;442:394–402.
  • Karlinsey JM. Sample introduction techniques for microchip electrophoresis: a review. Anal Chim Acta. 2012;725:1–13.
  • Sajeesh P, Sen AK. Particle separation and sorting in microfluidic devices: a review. Microfluid Nanofluidics. 2014;17:1–52.
  • El-Ali J, Sorger PK, Jensen KF. Cells on chips. Nature. 2006;442:403–411.
  • Craighead H. Future lab-on-a-chip technologies for interrogating individual molecules. Nature. 2006;442:387–393.
  • Morgan H, Green NG. AC Electrokinetics: colloids and nanoparticles (Research Studies Press Ltd., Baldock, 2003), Vol. 2, Microtechnology and Microsystems series, p. 324.
  • Russel WB, Saville DA, Schowalter WR. Colloidal dispersions. Cambridge: Cambridge University Press; 1989; p. 526.
  • Ramos A. Electrokinetics and Electrohydrodynamics in Microsystems (Springer, Wien, 2011), Vol. 530, CISM Courses and Lectures, p. 298.
  • Dukhin SS, Mishchuk NA, Tarovskii AA, et al. Electrophoresis of the 2nd kind. Colloid J USSR. 1987;49:544–545.
  • Dukhin SS, Mishchuk NA, Takhistov PV. Electroosmosis of the 2nd Kind and unrestricted current increase in the mixed monolayer of an Ion-exchanger. Colloid J USSR. 1989;51:540–542.
  • Squires TM, Bazant MZ. Induced-charge electro-osmosis. J Fluid Mech. 2004;509:217–252.
  • Squires TM, Bazant MZ. Breaking symmetries in induced-charge electro-osmosis and electrophoresis. J Fluid Mech. 2006;560:65–101.
  • Gangwal S, Cayre OJ, Bazant MZ, et al. Induced-charge electrophoresis of metallodielectric particles. Phys Rev Lett. 2008;100:058302.
  • Bazant MZ, Squires TM. Induced-charge electrokinetic phenomena. Curr Opin Colloid Interface Sci. 2010;15:203–213.
  • Bazant MZ, Squires TM. Induced-charge electrokinetic phenomena: theory and microfluidic applications. Phys Rev Lett. 2004;92:066101.
  • Zhao CL, Yang C. Electrokinetics of non-Newtonian fluids: a review. Adv Colloid Interface Sci. 2013;201:94–108.
  • Ramos A, Morgan H, Green NG, et al. AC electric-field-induced fluid flow in microelectrodes. J Colloid Interface Sci. 1999;217:420–422.
  • Murtsovkin VA, Mantrov GI. Steady flows in the Neighborhood of a drop of mercury with the application of a Variable external electric-field. Colloid J USSR. 1991;53:240–244.
  • Gamayunov NI, Mantrov GI, Murtsovkin VA. Study of flows induced in the vicinity of conducting particles by an external electric-field. Colloid J USSR. 1992;54:20–23.
  • Peng CH, Lazo I, Shiyanovskii SV, et al. Induced-charge electro-osmosis around metal and Janus spheres in water: patterns of flow and breaking symmetries. Phys Rev E. 2014;90:051002.
  • Harnett CK, Templeton J, Dunphy-Guzman KA, et al. Model based design of a microfluidic mixer driven by induced charge electroosmosis. Lab Chip. 2008;8:565–572.
  • Levitan JA, Devasenathipathy S, Studer V, et al. Experimental observation of induced-charge electro-osmosis around a metal wire in a microchannel. Colloids Surf A. 2005;267:122–132.
  • Canpolat C, Qian SZ, Beskok A. Micro-PIV measurements of induced-charge electro-osmosis around a metal rod. Microfluid Nanofluidics. 2013;14:153–162.
  • Canpolat C, Zhang MK, Rosen W, et al. Induced-charge electroosmosis around touching metal rods. J Fluids Eng Trans ASME. 2013;135:021103.
  • Boymelgreen A, Yossifon G, Park S, et al. Spinning Janus doublets driven in uniform ac electric fields. Phys Rev E. 2014;89:011003.
  • Yariv E. Induced-charge electrophoresis of nonspherical particles. Phys Fluids. 2005;17:051702.
  • Zhao H, Bau HH. On the effect of induced electro-osmosis on a cylindrical particle next to a surface. Langmuir. 2007;23:4053–4063.
  • Saintillan D, Darve E, Shaqfeh ESG. Hydrodynamic interactions in the induced-charge electrophoresis of colloidal rod dispersions. J Fluid Mech. 2006;563:223–259.
  • Zhao H, Bau HH. Microfluidic chaotic stirrer utilizing induced-charge electro-osmosis. Phys Rev E. 2007;75:066217.
  • Lavrentovich OD, Lazo I, Pishnyak OP. Nonlinear electrophoresis of dielectric and metal spheres in a nematic liquid crystal. Nature. 2010;467:947–950.
  • Lazo I, Lavrentovich OD. Liquid-crystal-enabled electrophoresis of spheres in a nematic medium with negative dielectric anisotropy. Phil Trans R Soc A. 2013;371:20120255.
  • Lazo I, Peng CH, Xiang J, et al. Liquid crystal-enabled electro-osmosis through spatial charge separation in distorted regions as a novel mechanism of electrokinetics. Nat Commun. 2014;5:5033.
  • Lavrentovich OD. Liquid crystal-enabled electrophoresis and electro-osmosis. In: JPF Lagerwall, G Scalia, editors. Liquid crystals with nano and microparticles. New Jersey: World Scientific; 2017. p. 415–457.
  • Ramaswamy S, Nityananda R, Raghunathan VA, et al. Power-law forces between particles in a nematic. Mol Cryst Liquid Cryst Sci Technol Sect A. 1996;288:175–180.
  • Kuksenok OV, Ruhwandl RW, Shiyanovskii SV, et al. Director structure around a colloid particle suspended in a nematic liquid crystal. Phys Rev E. 1996;54:5198–5203.
  • Poulin P, Stark H, Lubensky TC, et al. Novel colloidal interactions in anisotropic fluids. Science. 1997;275:1770–1773.
  • Stark H. Saturn-ring defects around microspheres suspended in nematic liquid crystals: an analogy between confined geometries and magnetic fields. Phys Rev E. 2002;66:032701.
  • Gu YD, Abbott NL. Observation of Saturn-ring defects around solid microspheres in nematic liquid crystals. Phys Rev Lett. 2000;85:4719–4722.
  • Stark H. Physics of colloidal dispersions in nematic liquid crystals. Phys Rep Rev Sect Phys Lett. 2001;351:387–474.
  • Volovik GE, Lavrentovich OD. Topological dynamics of defects: boojums in nematic drops. Sov Phys JETP. 1983;58:1159–1166.
  • Peng C, Turiv T, Guo Y, et al. Sorting and separation of microparticles by surface properties using liquid crystal-enabled electro-osmosis. Liq Cryst. 2018;45:1936–1943.
  • Peng C, Lavrentovich OD. Chapter 2: control of micro-particles with liquid crystals, in liquid crystals: New perspectives. In: P Pieranski, MH Godinho, London, UK: ISTE Ltd and John Wiley & Sons, Inc; 2021. p. 81–116.
  • Lintuvuori JS, Würger A, Stratford K. Hydrodynamics defines the stable swimming direction of spherical squirmers in a nematic liquid crystal. Phys Rev Lett. 2017;119:068001.
  • Peng CH, Guo YB, Conklin C, et al. Liquid crystals with patterned molecular orientation as an electrolytic active medium. Phys Rev E. 2015;92:052502.
  • Calderer MC, Golovaty D, Lavrentovich O, et al. Modeling of nematic electrolytes and nonlinear electroosmosis. SIAM J Appl Math. 2016;76:2260–2285.
  • Tovkach OM, Calderer MC, Golovaty D, et al. Electro-osmosis in nematic liquid crystals. Phys Rev E. 2016;94:012702.
  • Tovkach OM, Conklin C, Calderer MC, et al. Q-tensor model for electrokinetics in nematic liquid crystals. Phys Rev Fluids. 2017;2:053302.
  • Conklin C, Tovkach OM, Viñals J, et al. Electrokinetic effects in nematic suspensions: single-particle electro-osmosis and interparticle interactions. Phys Rev E. 2018;98:022703.
  • Paladugu S, Conklin C, Viñals J, et al. Nonlinear electrophoresis of colloids controlled by anisotropic conductivity and permittivity of liquid-crystalline electrolyte. Phys Rev Appl. 2017;7:034033.
  • Hernàndez-Navarro S, Tierno P, Ignés-Mullol J, et al. AC electrophoresis of microdroplets in anisotropic liquids: transport, assembling and reaction. Soft Matter. 2013;9:7999–8004.
  • Hernàndez-Navarro S, Tierno P, Ignés-Mullol J, et al. Liquid-crystal enabled electrophoresis: scenarios for driving and reconfigurable assembling of colloids. Eur Phys J Spec Top. 2015;224:1263–1273.
  • Ignés-Mullol J, Sagués F. Active, self-motile, and driven emulsions. Curr Opin Colloid Interface Sci. 2020;49:16–26.
  • Ryzhkova AV, Podgornov FV, Haase W. Nonlinear electrophoretic motion of dielectric microparticles in nematic liquid crystals. Appl Phys Lett. 2010;96:151901.
  • Simonova TS, Dukhin SS. Nonlinear polarization of diffusion part of thin double-layer of a spherical-particle. Colloid J USSR. 1976;38:65–70.
  • Dukhin AS, Dukhin SS. Aperiodic capillary electrophoresis method using an alternating current electric field for separation of macromolecules. Electrophoresis. 2005;26:2149–2153.
  • Stotz S. Field dependence of the electrophoretic mobility of particles suspended in low-conductivity liquids. J Colloid Interface Sci. 1978;65:118–130.
  • Sahu DK, Kole S, Ramaswamy S, et al. Omnidirectional transport and navigation of Janus particles through a nematic liquid crystal film. Phys Rev Res. 2020;2:032009(R).
  • Simonov IN, Shilov VN. Theory of low-frequency dielectric-dispersion of a suspension of ideally polarizable spherical-particles. Colloid J USSR. 1977;39:775–780.
  • Hernàndez-Navarro S, Tierno P, Farrera JA, et al. Reconfigurable swarms of nematic colloids controlled by photoactivated surface patterns. Angew Chem, Int Ed. 2014;53:10696–10700.
  • Straube AV, Pages JM, Ortiz-Ambriz A, et al. Assembly and transport of nematic colloidal swarms above photo-patterned defects and surfaces. New J Phys. 2018;20:075006.
  • Lavrentovich OD. Active colloids in liquid crystals. Curr Opin Colloid Interface Sci. 2016;21:97–109.
  • Guo Y, Jiang M, Peng C, et al. High-resolution and high-throughput plasmonic photopatterning of complex molecular orientations in liquid crystals. Adv Mater. 2016;28:2353–2358.
  • Guo YB, Jiang M, Peng CH, et al. Designs of plasmonic metamasks for photopatterning molecular orientations in liquid crystals. Crystals (Basel). 2017;7:8.
  • Peng CH, Guo YB, Turiv T, et al. Patterning of lyotropic chromonic liquid crystals by photoalignment with photonic metamasks. Adv Mater. 2017;29:1606112.
  • Peng C, Turiv T, Guo Y, et al. Control of colloidal placement by modulated molecular orientation in nematic cells. Sci Adv. 2016;2:e1600932.
  • Peng C, Turiv T, Zhang R, et al. Controlling placement of nonspherical (boomerang) colloids in nematic cells with photopatterned director. J Phys: Condens Matter. 2017;29:014005.
  • Peng CH, Lavrentovich OD. Liquid crystals-enabled AC electrokinetics. Micromachines (Basel). 2019;10:45.
  • Hernàndez-Navarro S, Tierno P, Ignés-Mullol J, et al. Nematic colloidal swarms assembled and transported on photosensitive surfaces. IEEE Trans Nanobioscience. 2015;14:267–271.
  • Conklin C, Viñals J. Electrokinetic flows in liquid crystal thin films with fixed anchoring. Soft Matter. 2017;13:725–739.
  • Conklin C, Viñals J, Valls OT. A connection between living liquid crystals and electrokinetic phenomena in nematic fluids. Soft Matter. 2018;14:4641–4648.
  • Korniychuk PP, Gabovich AM, Singer K, et al. Transient and steady electric currents through a liquid crystal cell. Liq Cryst. 2010;37:1171–1181.
  • Peng C, Turiv T, Guo Y, et al. Command of active matter by topological defects and patterns. Science. 2016;354:882–885.
  • Jákli A, Senyuk B, Liao GX, et al. Colloidal micromotor in smectic A liquid crystal driven by DC electric field. Soft Matter. 2008;4:2471–2474.
  • Bricard A, Caussin JB, Desreumaux N, et al. Emergence of macroscopic directed motion in populations of motile colloids. Nature. 2013;503:95–98.
  • Bricard A, Caussin JB, Das D, et al. Emergent vortices in populations of colloidal rollers. Nat Commun. 2015;6:7470.
  • Geyer D, Morin A, Bartolo D. Sounds and hydrodynamics of polar active fluids. Nat Mater. 2018;17:789–793.
  • Vicsek T, Czirok A, Benjacob E, et al. Novel type of Phase-Transition in a system of Self-Driven particles. Phys Rev Lett. 1995;75:1226–1229.
  • Koizumi R, Turiv T, Genkin MM, et al. Control of bacterial swirls by spiral nematic vortices: transition from individual to collective motion and contraction, expansion, and stable circulation of bacterial swirls. Phys Rev Res. 2020;2:033060.
  • Warner M, Terentjev EM. Liquid crystal elastomers. Oxford: Clarendon Press; 2007; p. 408.
  • White TJ, Broer DJ. Programmable and adaptive mechanics with liquid crystal polymer networks and elastomers. Nat Mater. 2015;14:1087–1098.
  • Ambulo CP, Tasmim S, Wang SF, et al. Processing advances in liquid crystal elastomers provide a path to biomedical applications. J Appl Phys. 2020;128:140901.
  • Ula SW, Traugutt NA, Volpe RH, et al. Liquid crystal elastomers: an introduction and review of emerging technologies. Liq Cryst Rev. 2018;6:78–107.
  • Babakhanova G, Turiv T, Guo YB, et al. Liquid crystal elastomer coatings with programmed response of surface profile. Nat Commun. 2018;9:456.
  • Simha RA, Ramaswamy S. Hydrodynamic fluctuations and instabilities in ordered suspensions of self-propelled particles. Phys Rev Lett. 2002;89:058101.
  • Thomsen DL, Keller P, Naciri J, et al. Liquid crystal elastomers with mechanical properties of a muscle. Macromolecules. 2001;34:5868–5875.
  • Warner M, Modes CD, Corbett D. Curvature in nematic elastica responding to light and heat. Proc R Soc A Math Phys Eng Sci. 2010;466:2975–2989.
  • McConney ME, Martinez A, Tondiglia VP, et al. Topography from topology: photoinduced surface features generated in liquid crystal polymer networks. Adv Mater. 2013;25:5880–5885.
  • de Haan LT, Schenning APHJ, Broer DJ. Programmed morphing of liquid crystal networks. Polymer (Guildf). 2014;55:5885–5896.
  • Ware TH, McConney ME, Wie JJ, et al. Voxelated liquid crystal elastomers. Science. 2015;347:982–984.
  • Xia Y, Cedillo-Servin G, Kamien RD, et al. Guided folding of nematic liquid crystal elastomer Sheets into 3D via patterned 1D microchannels. Adv Mater. 2016;28:9637–9643.
  • Mostajeran C, Warner M, Ware TH, et al. Encoding Gaussian curvature in glassy and elastomeric liquid crystal solids. Proc R Soc A Math Phys Eng Sci. 2016;472:20160112.
  • Ambulo CP, Burroughs JJ, Boothby JM, et al. Four-dimensional printing of liquid crystal elastomers. ACS Appl Mater Interfaces. 2017;9:37332–37339.
  • Godman NP, Kowalski BA, Auguste AD, et al. Synthesis of elastomeric liquid Crystalline Polymer Networks via chain transfer. ACS Macro Lett. 2017;6:1290–1295.
  • Gelebart AH, Mulder DJ, Varga M, et al. Making waves in a photoactive polymer film. Nature. 2017;546:632–635.
  • Modes CD, Bhattacharya K, Warner M. Disclination-mediated thermo-optical response in nematic glass sheets. Phys Rev E. 2010;81:060701.
  • Modes CD, Warner M. Blueprinting nematic glass: systematically constructing and combining active points of curvature for emergent morphology. Phys Rev E. 2011;84:021711.
  • Aharoni H, Sharon E, Kupferman R. Geometry of thin nematic elastomer sheets. Phys Rev Lett. 2014;113:257801.
  • Aharoni H, Xia Y, Zhang XY, et al. Universal inverse design of surfaces with thin nematic elastomer sheets. Proc Natl Acad Sci USA. 2018;115:7206–7211.
  • Liu DQ, Broer DJ. Liquid crystal polymer networks: switchable surface topographies. Liq Cryst Rev. 2013;1:20–28.
  • Stumpel JE, Broer DJ, Schenning APHJ. Stimuli-responsive photonic polymer coatings. Chem Commun. 2014;50:15839–15848.
  • Kim H, Gibson J, Maeng JM, et al. Responsive, 3D electronics enabled by liquid crystal elastomer substrates. ACS Appl Mater Interfaces. 2019;11:19506–19513.
  • Babakhanova G, Schenning APHJ, Broer DJ, et al. Surface structures of hybrid aligned liquid crystal network coatings containing reverse tilt domains. Emerging Liquid Cryst Technol XIV. 2019;10941:109410I.
  • Babakhanova G, Yu H, Chaganava I, et al. Controlled placement of microparticles at the water-liquid crystal elastomer interface. ACS Appl Mater Interfaces. 2019;11:15007–15013.
  • Gelebart AH, Jan Mulder D, Varga M, et al. Making waves in a photoactive polymer film. Nature. 2017;546:632–636.
  • Serak S, Tabiryan N, Vergara R, et al. Liquid crystalline polymer cantilever oscillators fueled by light. Soft Matter. 2010;6:779–783.
  • Liu DQ, Liu L, Onck PR, et al. Reverse switching of surface roughness in a self-organized polydomain liquid crystal coating. Proc Natl Acad Sci USA. 2015;112:3880–3885.
  • Feng W, Broer DJ, Liu DQ. Oscillating Chiral-Nematic fingerprints wipe away dust. Adv Mater. 2018;30:1704970.
  • Akinoglu EM, de Haan LT, Li SR, et al. Nanoid canyons on-demand: electrically switchable surface topography in liquid crystal networks. ACS Appl Mater Interfaces. 2018;10:37743–37748.
  • Visschers FLL, Gojzewski H, Vancso GJ, et al. Oscillating surfaces fueled by a continuous AC electric field. Adv Mater Interfaces. 2019;6:1901292.
  • van der Kooij HM, Semerdzhiev SA, Buijs J, et al. Morphing of liquid crystal surfaces by emergent collectivity. Nat Commun. 2019;10:3501.
  • Kusters GLA, Verheul IP, Tito NB, et al. Dynamical Landau-de Gennes theory for electrically-responsive liquid crystal networks. Phys Rev E. 2020;102:042703.
  • Dai M, Picot OT, Verjans JMN, et al. Humidity-responsive bilayer actuators based on a liquid-crystalline polymer network. ACS Appl Mater Interfaces. 2013;5:4945–4950.
  • de Haan LT, Verjans JMN, Broer DJ, et al. Humidity-responsive liquid crystalline polymer actuators with an asymmetry in the molecular trigger that bend, fold, and curl. J Am Chem Soc. 2014;136:10585–10588.
  • Verpaalen RCP, Souren AEJ, Debije MG, et al. Unravelling humidity-gated, temperature responsive bilayer actuators. Soft Matter. 2020;16:2753–2759.
  • Wani OM, Verpaalen R, Zeng H, et al. An artificial nocturnal flower via humidity-gated photoactuation in liquid crystal networks. Adv Mater. 2019;31:e1805985.
  • Turiv T, Krieger J, Babakhanova G, et al. Topology control of human fibroblast cells monolayer by liquid crystal elastomer. Sci Adv. 2020;6:eaaz6485.
  • Liu DQ, Bastiaansen CWM, den Toonder JMJ, et al. Photo-switchable surface topologies in chiral nematic coatings. Angew Chem, Int Ed. 2012;51:892–896.
  • Stumpel JE, Ziolkowski B, Florea L, et al. Photoswitchable ratchet surface topographies based on self-protonating spiropyran-NIPAAM hydrogels. ACS Appl Mater Interfaces. 2014;6:7268–7274.
  • Babakhanova G, Golestani YM, Baza H, et al. Dynamically morphing microchannels in liquid crystal elastomer coatings containing disclinations. J Appl Phys. 2020;128:184702.
  • Lebar A, Kutnjak Z, Žumer S, et al. Evidence of supercritical behavior in liquid single crystal elastomers. Phys Rev Lett. 2005;94:197801.
  • Lebar A, Cordoyiannis G, Kutnjak Z, et al. The isotropic-to-nematic conversion in liquid crystalline elastomers. Liq Cryst Elastomers: Mater Appl. 2012;250:147–185.
  • Narayan V, Ramaswamy S, Menon N. Long-lived giant number fluctuations in a swarming granular nematic. Science. 2007;317:105–108.
  • Kawaguchi K, Kageyama R, Sano M. Topological defects control collective dynamics in neural progenitor cell cultures. Nature. 2017;545:327–331.
  • Duclos G, Erlenkamper C, Joanny JF, et al. Topological defects in confined populations of spindle-shaped cells. Nat Phys. 2017;13:58–62.
  • Genkin MM, Sokolov A, Lavrentovich OD, et al. Topological defects in a living nematic ensnare swimming bacteria. Phys Rev X. 2017;7:011029.
  • Sanchez T, Chen DTN, DeCamp SJ, et al. Spontaneous motion in hierarchically assembled active matter. Nature. 2012;491:431–434.
  • Keber FC, Loiseau E, Sanchez T, et al. Topology and dynamics of active nematic vesicles. Science. 2014;345:1135–1139.
  • DeCamp SJ, Redner GS, Baskaran A, et al. Orientational order of motile defects in active nematics. Nat Mater. 2015;14:1110–1115.
  • Zhou S, Sokolov A, Lavrentovich OD, et al. Living liquid crystals. Proc Natl Acad Sci USA. 2014;111:1265–1270.
  • Zhang R, Kumar N, Ross JL, et al. Interplay of structure, elasticity, and dynamics in actin-based nematic materials. Proc Natl Acad Sci USA. 2018;115:E124–E133.
  • Kumar N, Zhang R, de Pablo JJ, et al. Tunable structure and dynamics of active liquid crystals. Sci Adv. 2018;4:eaat7779.
  • Tan AJ, Roberts E, Smith SA, et al. Topological chaos in active nematics. Nat Phys. 2019;15:1033–1039.
  • Rivas DP, Shendruk TN, Henry RR, et al. Driven topological transitions in active nematic films. Soft Matter. 2020;16:9331–9338.
  • Copenhagen K, Alert R, Wingreen NS, et al. Topological defects promote layer formation in Myxococcus Xanthus colonies. Nat Phys. 2021;17:211–215.
  • Giomi L, Bowick MJ, Mishra P, et al. Defect dynamics in active nematics. Phil Trans R Soc A. 2014;372:20130365.
  • Pismen LM. Dynamics of defects in an active nematic layer. Phys Rev E. 2013;88:050502.
  • Vromans AJ, Giomi L. Orientational properties of nematic disclinations. Soft Matter. 2016;12:6490–6495.
  • Tang XZ, Selinger JV. Orientation of topological defects in 2D nematic liquid crystals. Soft Matter. 2017;13:5481–5490.
  • Cortese D, Eggers J, Liverpool TB. Pair creation, motion, and annihilation of topological defects in two-dimensional nematic liquid crystals. Phys Rev E. 2018;97:022704.
  • Shankar S, Ramaswamy S, Marchetti MC, et al. Defect unbinding in active nematics. Phys Rev Lett. 2018;121:108002.
  • Tang XZ, Selinger JV. Theory of defect motion in 2D passive and active nematic liquid crystals. Soft Matter. 2019;15:587–601.
  • Shankar S, Marchetti MC. Hydrodynamics of active defects: from order to chaos to defect ordering. Phys Rev X. 2019;9:041047.
  • Patelli A, Djafer-Cherif I, Aranson IS, et al. Understanding dense active nematics from microscopic models. Phys Rev Lett. 2019;123:258001.
  • Norton MM, Grover P, Hagan MF, et al. Optimal control of active nematics. Phys Rev Lett. 2020;125:178005.
  • Li ZY, Zhang DQ, Lin SZ, et al. Pattern formation and defect ordering in active chiral nematics. Phys Rev Lett. 2020;125:098002.
  • Meacock OJ, Doostmohammadi A, Foster KR, et al. Bacteria solve the problem of crowding by moving slowly. Nat Phys. 2021;17:205–210.
  • Wang MF, Li YN, Yokoyama H. Artificial web of disclination lines in nematic liquid crystals. Nat Commun. 2017;8:388.
  • Babakhanova G, Krieger J, Li BX, et al. Cell alignment by smectic liquid crystal elastomer coatings withnanogrooves. J Biomed Mater Res A. 2020: 1223–1230.
  • Fournier JB, Dozov I, Durand G. Surface frustration and texture instability in smectic-a liquid-crystals. Phys Rev A. 1990;41:2252–2255.
  • Lavrentovich OD, Kleman M, Pergamenshchik VM. Nucleation of focal conic domains in smectic A liquid-crystals. J Phys II. 1994;4:377–404.
  • Yoon DK, Choi MC, Kim YH, et al. Internal structure visualization and lithographic use of periodic toroidal holes in liquid crystals. Nat Mater. 2007;6:866–870.
  • Choi MC, Pfohl T, Wen Z, et al. Ordered patterns of liquid crystal toroidal defects by microchannel confinement. Proc Natl Acad Sci U S A. 2004;101:17340–17344.
  • Designolle V, Herminghaus S, Pfohl T, et al. AFM study of defect-induced depressions of the smectic-A/air interface. Langmuir. 2006;22:363–368.
  • Michel JP, Lacaze E, Alba M, et al. Optical gratings formed in thin smectic films frustrated on a single crystalline substrate. Phys Rev E Stat Nonlin Soft Matter Phys. 2004;70:011709.
  • Zappone B, Lacaze E, Ayeb H, et al. Self-ordered arrays of linear defects and virtual singularities in thin smectic-A films (vol 7, pg 1161, 2011). Soft Matter. 2011;7:11550–11550.
  • Coursault D, Grand J, Zappone B, et al. Linear self-assembly of nanoparticles within liquid crystal defect arrays. Adv Mater. 2012;24:1461–1465.
  • Blanc C, Coursault D, Lacaze E. Ordering nano- and microparticles assemblies with liquid crystals. Liq Cryst Rev. 2013;1:83–109.
  • Kim YH, Yoon DK, Choi MC, et al. Confined self-assembly of toric focal conic domains (The effects of confined geometry on the feature size of toric focal conic domains). Langmuir. 2009;25:1685–1691.
  • Zappone B, Lacaze E. Surface-frustrated periodic textures of smectic – a liquid crystals on crystalline surfaces. Phys Rev E. 2008;78:061704.
  • Guo W, Bahr C. Influence of anchoring strength on focal conic domains in smectic films. Phys Rev E. 2009;79:011707.
  • Gonzalez-Rodriguez D, Guevorkian K, Douezan S, et al. Soft matter models of developing tissues and tumors. Science. 2012;338:910–917.
  • Prost J, Julicher F, Joanny JF. Active gel physics. Nat Phys. 2015;11:111–117.
  • Hakim V, Silberzan P. Collective cell migration: a physics perspective. Rep Prog Phys. 2017;80:076601.
  • Mohammed D, Charras G, Vercruysse E, et al. Substrate area confinement is a key determinant of cell velocity in collective migration. Nat Phys. 2019;15:858–866.
  • Mehes E, Vicsek T. Collective motion of cells: from experiments to models. Integr Biol. 2014;6:831–854.
  • Ilina O, Friedl P. Mechanisms of collective cell migration at a glance. J Cell Sci. 2009;122:3203–3208.
  • Keller R. Shaping the vertebrate body plan by polarized embryonic cell movements. Science. 2002;298:1950–1954.
  • Farooqui R, Fenteany G. Multiple rows of cells behind an epithelial wound edge extend cryptic lamellipodia to collectively drive cell-sheet movement. J Cell Sci. 2005;118:51–63.
  • Friedl P, Gilmour D. Collective cell migration in morphogenesis, regeneration and cancer. Nat Rev Mol Cell Biol. 2009;10:445–457.
  • Chuai M, Hughes D, Weijer CJ. Collective epithelial and mesenchymal cell migration during gastrulation. Curr Genomics. 2012;13:267–277.
  • Cetera M, Juan GRRS, Oakes PW, et al. Epithelial rotation promotes the global alignment of contractile actin bundles during Drosophila egg chamber elongation. Nat Commun. 2014;5:5511.
  • Ghabrial AS, Krasnow MA. Social interactions among epithelial cells during tracheal branching morphogenesis. Nature. 2006;441:746–749.
  • Peyret G, Mueller R, d’Alessandro J, et al. Sustained oscillations of epithelial cell sheets. Biophys J. 2019;117:464–478.
  • Ridley AJ, Schwartz MA, Burridge K, et al. Cell migration: integrating signals from front to back. Science. 2003;302:1704–1709.
  • Mayor R, Etienne-Manneville S. The front and rear of collective cell migration. Nat Rev Mol Cell Biol. 2016;17:97–109.
  • Friedl P, Alexander S. Cancer invasion and the microenvironment: plasticity and reciprocity. Cell. 2011;147:992–1009.
  • Wong IY, Javaid S, Wong EA, et al. Collective and individual migration following the epithelial-mesenchymal transition. Nat Mater. 2014;13:1063–1071.
  • Vedula SRK, Leong MC, Lai TL, et al. Emerging modes of collective cell migration induced by geometrical constraints. Proc Natl Acad Sci USA. 2012;109:12974–12979.
  • Nia HDT, Munn LL, Jain RK. Physical traits of cancer. Science. 2020;370:eaaz0868.
  • Kemkemer R, Teichgraber V, Schrank-Kaufmann S, et al. Nematic order-disorder state transition in a liquid crystal analogue formed by oriented and migrating amoeboid cells. Eur Phys J E. 2000;3:101–110.
  • Kemkemer R, Kling D, Kaufmann D, et al. Elastic properties of nematoid arrangements formed by amoeboid cells. Eur Phys J E. 2000;1:215–225.
  • Duvert M, Bouligand Y, Salat C. The liquid-crystalline nature of the cytoskeleton in epidermal-cells of the chaetognath sagitta. Tissue Cell. 1984;16:469–481.
  • Bouligand Y. Liquid crystals and biological morphogenesis: ancient and new questions. C R Chim. 2008;11:281–296.
  • Bouligand Y. Liquid crystals and morphogenesis. In: P Bourgine, A Lesne, editor. Morphogenesis: origin of patterns and shapes. Berlin: Springer-Verlag; 2011. p. 49–86.
  • Saw TB, Doostmohammadi A, Nier V, et al. Topological defects in epithelia govern cell death and extrusion. Nature. 2017;544:212–216.
  • Théry M. Micropatterning as a tool to decipher cell morphogenesis and functions. J Cell Sci. 2010;123:4201–4213.
  • Saw TB, Xi W, Ladoux B, et al. Biological tissues as active nematic liquid crystals. Adv Mater. 2018;30:1802579.
  • Maroudas-Sacks Y, Garion L, Shani-Zerbib L, et al. Topological defects in the nematic order of actin fibres as organization centres of Hydra morphogenesis. Nat Phys. 2021;17:251–259.
  • Bade ND, Kamien RD, Assoian RK, et al. Edges impose planar alignment in nematic monolayers by directing cell elongation and enhancing migration. Soft Matter. 2018;14:6867–6874.
  • Ladoux B, Fardin M-A. Living proof of effective defects. Nat Phys. 2021;17:172–173.
  • Penrose LS. Dermatoglyphic topology. Nature. 1965;205:544–546.
  • Duclos G, Garcia S, Yevick HG, et al. Perfect nematic order in confined monolayers of spindle-shaped cells. Soft Matter. 2014;10:2346–2353.
  • Blanch-Mercader C, Yashunsky V, Garcia S, et al. Turbulent dynamics of epithelial cell cultures. Phys Rev Lett. 2018;120:208101.
  • Ladoux B, Mege RM. Mechanobiology of collective cell behaviours. Nat Rev Mol Cell Biol. 2017;18:743–757.
  • Deforet M, Hakim V, Yevick HG, et al. Emergence of collective modes and tri-dimensional structures from epithelial confinement. Nat Commun. 2014;5:3747.
  • Doxzen K, Vedula SRK, Leong MC, et al. Guidance of collective cell migration by substrate geometry. Integr Biol. 2013;5:1026–1035.
  • Guillamat P, Blanch-Mercader C, Kruse K, et al. Integer topological defects organize stresses driving tissue morphogenesis; 2020. https://www.biorxiv.org/content/10.1101/2020.06.02.129262v1.
  • Nelson DR. Toward a tetravalent chemistry of colloids. Nano Lett. 2002;2:1125–1129.
  • Williams RD. 2 Transitions in tangentially anchored nematic droplets. J Phys A: Math Gen. 1986;19:3211–3222.
  • Lavrentovich OD, Sergan VV. Parity-Breaking Phase-Transition in tangentially anchored nematic drops. Nuovo Cimento Soc Ital Fis D. 1990;12:1219–1222.
  • Koning V, Lopez-Leon T, Darmon A, et al. Spherical nematic shells with a threefold valence. Phys Rev E. 2016;94:012703.
  • Urbanski M, Reyes CG, Noh J, et al. Liquid crystals in micron-scale droplets, shells and fibers. J Phys Condensed Matter. 2017;29:133003.
  • Noh J, Wang YW, Liang HL, et al. Dynamic tuning of the director field in liquid crystal shells using block copolymers. Phys Rev Res. 2020;2:033160.
  • Sharma A, Jampani VSR, Lagerwall JPF. Realignment of liquid crystal shells driven by temperature-dependent surfactant solubility. Langmuir. 2019;35:11132–11140.
  • Durey G, Ishii Y, Lopez-Leon T. Temperature-driven anchoring transitions at liquid crystal/water interfaces. Langmuir. 2020;36:9368–9376.
  • Khoromskaia D, Alexander GP. Vortex formation and dynamics of defects in active nematic shells. New J Phys. 2017;19:103043.
  • Zhang YH, Deserno M, Tu ZC. Dynamics of active nematic defects on the surface of a sphere. Phys Rev E. 2020;102:012607.
  • Brown AT. A theoretical phase diagram for an active nematic on a spherical surface. Soft Matter. 2020;16:4682–4691.
  • Ellis PW, Pearce DJG, Chang YW, et al. Curvature-induced defect unbinding and dynamics in active nematic toroids. Nat Phys. 2018;14:85–90.
  • Pearce DJG, Ellis PW, Fernandez-Nieves A, et al. Geometrical control of active turbulence in curved topographies. Phys Rev Lett. 2019;122:168002.
  • Chiccoli C, Feruli I, Lavrentovich OD, et al. Topological defects in schlieren textures of biaxial and uniaxial nematics. Phys Rev E Stat Nonlin Soft Matter Phys. 2002;66:030701.
  • Mueller R, Yeomans JM, Doostmohammadi A. Emergence of active nematic behavior in monolayers of isotropic cells. Phys Rev Lett. 2019;122:048004.
  • Pomp W, Schakenraad K, Balcioglu HE, et al. Cytoskeletal anisotropy controls geometry and forces of adherent cells. Phys Rev Lett. 2018;121:178101.
  • Duclos G, Blanch-Mercader C, Yashunsky V, et al. Spontaneous shear flow in confined cellular nematics. Nat Phys. 2018;14:728–733.
  • Duclos G, Blanch-Mercader C, Yashunsky V, et al. Author correction: spontaneous shear flow in confined cellular nematics (vol 14, pg 728, 2018). Nat Phys. 2019;15:868.
  • Leoni M, Sens P. Polarization of cells and soft objects driven by mechanical interactions: consequences for migration and chemotaxis. Phys Rev E. 2015;91:022720.
  • Jain S, Cachoux VML, Narayana GHNS, et al. The role of single-cell mechanical behaviour and polarity in driving collective cell migration. Nat Phys. 2020;16:802–809.
  • Erzberger A, Jacobo A, Dasgupta A, et al. Mechanochemical symmetry breaking during morphogenesis of lateral-line sensory organs. Nat Phys. 2020;16:949–957.
  • Loiseau E, Gsell S, Nommick A, et al. Active mucus-cilia hydrodynamic coupling drives self-organization of human bronchial epithelium. Nat Phys. 2020;16:1158–1164.
  • Schnell U, Carroll TJ. Planar cell polarity of the kidney. Exp Cell Res. 2016;343:258–266.
  • Trepat X, Wasserman MR, Angelini TE, et al. Physical forces during collective cell migration. Nat Phys. 2009;5:426–430.
  • Reffay M, Petitjean L, Coscoy S, et al. Orientation and polarity in Collectively Migrating cell structures: statics and dynamics. Biophys J. 2011;100:2566–2575.
  • Butler MT, Wallingford JB. Planar cell polarity in development and disease. Nat Rev Mol Cell Biol. 2017;18:375–388.
  • Ramaswamy S, Simha RA, Toner J. Active nematics on a substrate: giant number fluctuations and long-time tails. Europhys Lett. 2003;62:196–202.
  • Zhang R, Redford SA, Ruijgrok PV, et al. Spatiotemporal control of liquid crystal structure and dynamics through activity patterning. Nat Mater. 2021. doi:10.1038/s41563-41020-00901-41564.
  • Green R, Toner J, Vitelli V. Geometry of thresholdless active flow in nematic microfluidics. Phys Rev Fluids. 2017;2:104201.
  • Turiv T, Koizumi R, Thijssen K, et al. Polar jets of swimming bacteria condensed by a patterned liquid crystal. Nat Phys. 2020;16:481–487.
  • Toner J, Tu YH. Flocks, herds, and schools: a quantitative theory of flocking. Physical Review E. 1998;58:4828–4858.
  • Chaté H, Ginelli F, Montagne R. Simple model for active nematics: quasi-long-range order and giant fluctuations. Phys Rev Lett. 2006;96:180602.
  • Zhang HP, Be’er A, Florin EL, et al. Collective motion and density fluctuations in bacterial colonies. Proc Natl Acad Sci USA. 2010;107:13626–13630.
  • Schaller V, Bausch AR. Topological defects and density fluctuations in collectively moving systems. Proc Natl Acad Sci USA. 2013;110:4488–4493.
  • Giomi L, Bowick MJ, Ma X, et al. Defect annihilation and proliferation in active nematics. Phys Rev Lett. 2013;110:228101.
  • Giomi L. Geometry and Topology of turbulence in active nematics. Phys Rev X. 2015;5:031003.
  • Angelini TE, Hannezo E, Trepat X, et al. Cell migration driven by cooperative substrate deformation patterns. Phys Rev Lett. 2010;104:168104.
  • Angelini TE, Hannezo E, Trepat X, et al. Glass-like dynamics of collective cell migration. Proc Natl Acad Sci USA. 2011;108:4714–4719.
  • Tambe DT, Hardin CC, Angelini TE, et al. Collective cell guidance by cooperative intercellular forces. Nat Mater. 2011;10:469–475.
  • Maitra A, Srivastava P, Marchetti MC, et al. A nonequilibrium force can stabilize 2D active nematics. Proc Natl Acad Sci USA. 2018;115:6934–6939.
  • Julicher F, Eaton S. Emergence of tissue shape changes from collective cell behaviours. Semin Cell Dev Biol. 2017;67:103–112.
  • Lo CM, Wang HB, Dembo M, et al. Cell movement is guided by the rigidity of the substrate. Biophys J. 2000;79:144–152.
  • Janmey PA, Miller RT. Mechanisms of mechanical signaling in development and disease. J Cell Sci. 2011;124:9–18.
  • Schwarz US, Safran SA. Physics of adherent cells. Rev Mod Phys. 2013;85:1327–1381.
  • Szabo B, Kornyei Z, Zach J, et al. Auto-reverse nuclear migration in bipolar mammalian cells on micropatterned surfaces. Cell Motil Cytoskeleton. 2004;59:38–49.
  • Gupta M, Doss BL, Kocgozlu L, et al. Cell shape and substrate stiffness drive actin-based cell polarity. Phys Rev E. 2019;99:012412.
  • Wan LQ, Ronaldson K, Park M, et al. Micropatterned mammalian cells exhibit phenotype-specific left-right asymmetry. Proc Natl Acad Sci USA. 2011;108:12295–12300.
  • Jiang XY, Bruzewicz DA, Wong AP, et al. Directing cell migration with asymmetric micropatterns. Proc Natl Acad Sci USA. 2005;102:975–978.
  • Petitjean L, Reffay M, Grasland-Mongrain E, et al. Velocity fields in a Collectively Migrating epithelium. Biophys J. 2010;98:1790–1800.
  • Tang XZ, Selinger JV. Alignment of a topological defect by an activity gradient. Phys Rev E. 2021;103:022703.
  • Kim DH, Han K, Gupta K, et al. Mechanosensitivity of fibroblast cell shape and movement to anisotropic substratum topography gradients. Biomaterials. 2009;30:5433–5444.
  • Rianna C, Rossano L, Kollarigowda RH, et al. Spatio-temporal control of dynamic topographic patterns on azopolymers for cell culture applications. Adv Funct Mater. 2016;26:7572–7580.
  • Molitoris JM, Paliwal S, Sekar RB, et al. Precisely parameterized experimental and computational models of tissue organization. Integr Biol (UK). 2016;8:230–242.
  • Endresen KD, Kim B, Serra F. Topological defects of integer charge in cell monolayers; 2019. Arxiv, 1912.03271v03271.
  • Endresen KD, Kim M, Pittman M, et al. Topological defects of integer charge in cell monolayers. Soft Matter. 2021. https://doi.org/10.1039/D1031SM00100K.
  • Callens SJP, Uyttendaele RJC, Fratila-Apachitei LE, et al. Substrate curvature as a cue to guide spatiotemporal cell and tissue organization. Biomaterials. 2020;232:119739.
  • Baptista D, Teixeira L, van Blitterswijk C, et al. Overlooked? underestimated? Effects of substrate curvature on cell behavior. Trends Biotechnol. 2019;37:838–854.
  • Bade ND, Xu TN, Kamien RD, et al. Gaussian curvature directs stress fiber orientation and cell migration. Biophys J. 2018;114:1467–1476.
  • Sussman DM. Interplay of curvature and rigidity in shape-based models of confluent tissue. Phys Rev Res. 2020;2:023417.
  • Agarwal A, Huang E, Palecek S, et al. Optically responsive and mechanically tunable colloid-in-liquid crystal gels that support growth of fibroblasts. Adv Mater. 2008;20:4804–4809.
  • Martella D, Parmeggiani C. Advances in cell scaffolds for tissue engineering: the value of liquid crystalline elastomers. Chem: A Eur J. 2018;24:12206–12220.
  • Martella D, Paoli P, Pioner JM, et al. Liquid crystalline networks toward regenerative medicine and tissue repair. Small. 2017;13:1702677.
  • Prevot ME, Andro H, Alexander SLM, et al. Liquid crystal elastomer foams with elastic properties specifically engineered as biodegradable brain tissue scaffolds. Soft Matter. 2018;14:354–360.
  • Agrawal A, Chen HY, Kim H, et al. Electromechanically responsive liquid crystal elastomer nanocomposites for active cell culture. ACS Macro Lett. 2016;5:1386–1390.
  • Gao YX, Mori T, Manning S, et al. Biocompatible 3D liquid crystal elastomer cell Scaffolds and foams with primary and secondary porous architecture. ACS Macro Lett. 2016;5:14–19.
  • Lowe AM, Abbott NL. Liquid crystalline materials for biological applications. Chem Mater. 2012;24:746–758.
  • Agrawal A, Adetiba O, Kim H, et al. Stimuli-responsive liquid crystal elastomers for dynamic cell culture. J Mater Res. 2015;30:453–462.
  • Kocer G, Ter Schiphorst J, Hendrikx M, et al. Light-responsive hierarchically structured liquid crystal Polymer Networks for harnessing cell adhesion and migration. Adv Mater. 2017;29:1606407.
  • Martella D, Pattelli L, Matassini C, et al. Liquid crystal-induced myoblast alignment. Adv Healthc Mater. 2019;8:1801489.
  • Jiang JH, Dhakal NP, Guo YB, et al. Controlled dynamics of neural tumor cells by templated liquid Crystalline Polymer networks. Adv Healthc Mater. 2020;9:2000487.
  • Skinner BM, Johnson EEP. Nuclear morphologies: their diversity and functional relevance. Chromosoma. 2017;126:195–212.
  • Nishiguchi D, Nagai KH, Chaté H, et al. Long-range nematic order and anomalous fluctuations in suspensions of swimming filamentous bacteria. Phys Rev E. 2017;95:020601.
  • Harris AR, Peter L, Bellis J, et al. Characterizing the mechanics of cultured cell monolayers. Proc Natl Acad Sci USA. 2012;109:16449–16454.
  • Trushko A, Di Meglio I, Merzouki A, et al. Buckling of an epithelium growing under spherical confinement. Dev Cell. 2020;54:655–668.
  • Fouchard J, Wyatt TPJ, Proag A, et al. Curling of epithelial monolayers reveals coupling between active bending and tissue tension. Proc Natl Acad Sci USA. 2020;117:9377–9383.
  • Cladis PE, Kleman M. Non-Singular disclinations of strength S = + 1 in nematics. J Phys. 1972;33:591–598.
  • Meyer RB. Existence of even indexed disclinations in nematic liquid-crystals. Philos Mag. 1973;27:405–424.
  • Purcell EM. Life at low reynolds-number. Am J Phys. 1977;45:3–11.
  • Lauga E. Life around the scallop theorem. Soft Matter. 2011;7:3060–3065.
  • Di Leonardo R, Angelani L, Dell’Arciprete D, et al. Bacterial ratchet motors. Proc Natl Acad Sci USA. 2010;107:9541–9545.
  • Thutupalli S, Seemann R, Herminghaus S. Swarming behavior of simple model squirmers. New J Phys. 2011;13:073021.
  • Bechinger C, Di Leonardo R, Lowen H, et al. Active particles in complex and crowded environments. Rev Mod Phys. 2016;88:045006.
  • Sokolov A, Apodaca MM, Grzybowski BA, et al. Swimming bacteria power microscopic gears. Proc Natl Acad Sci USA. 2010;107:969–974.
  • Arlt J, Martinez VA, Dawson A, et al. Painting with light-powered bacteria. Nat Commun. 2018;9:768.
  • Moran J, Posner J. Microscopic self-propelled particles could one day be used to clean up wastewater or deliver drugs in the body. Phys Today. 2019;72:45–50.
  • Howse JR, Jones RAL, Ryan AJ, et al. Self-motile colloidal particles: from directed propulsion to random walk. Phys Rev Lett. 2007;99:048102.
  • Ramos G, Cordero ML, Soto R. Bacteria driving droplets. Soft Matter. 2020;16:1359–1365.
  • Baker RD, Montenegro-Johnson T, Sediako AD, et al. Shape-programmed 3D printed swimming microtori for the transport of passive and active agents. Nat Commun. 2019;10:4932.
  • Lydon J. Chromonic liquid crystalline phases. Liq Cryst. 2011;38:1663–1681.
  • Park HS, Lavrentovich OD. Lyotropic chromonic liquid crystals: emerging applications. In: Q Li, editor. Liquid crystals beyond displays: chemistry, physics, and applications. Hoboken, NJ: Wiley; 2012. p. 449–484.
  • Woolverton CJ, Gustely E, Li L, et al. Liquid crystal effects on bacterial viability. Liq Cryst. 2005;32:417–423.
  • Lydon J. Chromonic mesophases. Curr Opin Colloid Interface Sci. 2004;8:480–490.
  • Lydon J. Chromonic review. J Mater Chem. 2010;20:10071–10099.
  • Kim Y-K, Shiyanovskil SV, Lavrentovich OD. Morphogenesis of defects and tactoids during isotropic–nematic phase transition in self-assembled lyotropic chromonic liquid crystals. J Phys: Condens Matter. 2013;25:404202.
  • Smalyukh II, Butler J, Shrout JD, et al. Elasticity-mediated nematiclike bacterial organization in model extracellular DNA matrix. Phys Rev E. 2008;78:030701.
  • Kumar A, Galstian T, Pattanayek SK, et al. The motility of bacteria in an anisotropic liquid environment. Mol Cryst Liq Cryst. 2013;574:33–39.
  • Mushenheim PC, Trivedi RR, Weibel DB, et al. Using liquid crystals to reveal how mechanical anisotropy changes interfacial behaviors of motile bacteria. Biophys J. 2014;107:255–265.
  • Mushenheim PC, Trivedi RR, Roy SS, et al. Effects of confinement, surface-induced orientation and strain on dynamic behavior of bacteria in thin liquid crystalline films. Soft Matter. 2015;11:6821–6831.
  • Mushenheim PC, Trivedi RR, Tuson HH, et al. Dynamic self-assembly of motile bacteria in liquid crystals. Soft Matter. 2014;10:79–86.
  • Sokolov A, Zhou S, Lavrentovich OD, et al. Individual behavior and pairwise interactions between microswimmers in anisotropic liquid. Phys Rev E. 2015;91:013009.
  • Zhao JG, Gulan U, Horie T, et al. Advances in biological liquid crystals. Small. 2019;15:1900019.
  • Cisneros LH, Kessler JO, Ortiz R, et al. Unexpected bipolar flagellar arrangements and long-range flows driven by bacteria near solid boundaries. Phys Rev Lett. 2008;101:168102.
  • Drescher K, Dunkel J, Cisneros LH, et al. Fluid dynamics and noise in bacterial cell-cell and cell-surface scattering. Proc Natl Acad Sci USA. 2011;108:10940–10945.
  • Darnton NC, Turner L, Rojevsky S, et al. On torque and tumbling in swimming Escherichia coli. J Bacteriol. 2007;189:1756–1764.
  • Chattopadhyay S, Moldovan R, Yeung C, et al. Swimming efficiency of bacterium Escherichia coli. Proc Natl Acad Sci USA. 2006;103:13712–13717.
  • Fahrner KA, Ryu WS, Berg HC. Biomechanics: bacterial flagellar switching under load. Nature. 2003;423:938.
  • Reid SW, Leake MC, Chandler JH, et al. The maximum number of torque-generating units in the flagellar motor of Escherichia coli is at least 11. Proc Natl Acad Sci USA. 2006;103:8066–8071.
  • Berry RM, Berg HC. Absence of a barrier to backwards rotation of the bacterial flagellar motor demonstrated with optical tweezers. Proc Natl Acad Sci USA. 1997;94:14433–14437.
  • Hu JL, Yang MC, Gompper G, et al. Modelling the mechanics and hydrodynamics of swimming E. coli. Soft Matter. 2015;11:7867–7876.
  • Genkin MM, Sokolov A, Aranson IS. Spontaneous topological charging of tactoids in a living nematic. New J Phys. 2018;20:043027.
  • Brochard F, de Gennes PG. Theory of magnetic suspensions in liquid crystals. J Phys. 1970;31:691–708.
  • Smith CJ, Denniston C. Elastic response of a nematic liquid crystal to an immersed nanowire. J Appl Phys. 2007;101:014305.
  • Zhou S, Tovkach O, Golovaty D, et al. Dynamic states of swimming bacteria in a nematic liquid crystal cell with homeotropic alignment. New J Phys. 2017;19:055006.
  • Nazarenko VG, Boiko OP, Park HS, et al. Surface alignment and Anchoring Transitions in nematic lyotropic chromonic liquid crystal. Phys Rev Lett. 2010;105:017801.
  • Shiyanovskii SV, Lavrentovich OD, Schneider T, et al. Lyotropic chromonic liquid crystals for biological sensing applications. Mol Cryst Liq Cryst. 2005;434:587–598.
  • Tasinkevych M, Mondiot F, Mondain-Monval O, et al. Dispersions of ellipsoidal particles in a nematic liquid crystal. Soft Matter. 2014;10:2047–2058.
  • McGinn CK, Laderman LI, Zimmermann N, et al. Planar anchoring strength and pitch measurements in achiral and chiral chromonic liquid crystals using 90-degree twist cells. Phys Rev E. 2013;88:062513.
  • Chi H, Potomkin M, Zhang L, et al. Surface anchoring controls orientation of a microswimmer in nematic liquid crystal. Commun Phys. 2020;3:162.
  • Daddi-Moussa-Ider A, Menzel AM. Dynamics of a simple model microswimmer in an anisotropic fluid: implications for alignment behavior and active transport in a nematic liquid crystal. Phys Rev Fluids. 2018;3:094102.
  • Crowley TL, Bottrill C, Mateer D, et al. Lyotropic chromonic liquid crystals: neutron scattering studies of shear-induced orientation and reorientation. Colloids Surf A. 1997;129:95–115.
  • Kostko AF, Cipriano BH, Pinchuk OA, et al. Salt effects on the phase behavior, structure, and rheology of chromonic liquid crystals. J Phys Chem B. 2005;109:19126–19133.
  • Zhou S, Neupane K, Nastishin YA, et al. Elasticity, viscosity, and orientational fluctuations of a lyotropic chromonic nematic liquid crystal disodium cromoglycate. Soft Matter. 2014;10:6571–6581.
  • Cha YJ, Gim MJ, Ahn H, et al. Orthogonal liquid crystal alignment layer: templating speed-dependent orientation of chromonic liquid crystals. ACS Appl Mater Interfaces. 2017;9:18355–18361.
  • Baza H, Turiv T, Li B-X, et al. Shear-induced polydomain structures of nematic lyotropic chromonic liquid crystal disodium cromoglycate. Soft Matter. 2020;16: 8565–8576.
  • Mondiot F, Chandran SP, Mondain-Monval O, et al. Shape-induced dispersion of colloids in anisotropic fluids. Phys Rev Lett. 2009;103:238303.
  • Gotze IO, Gompper G. Mesoscale simulations of hydrodynamic squirmer interactions. Phys Rev E. 2010;82:041921.
  • Pergamenshchik VM, Uzunova VA. Dipolar colloids in nematostatics: tensorial structure, symmetry, different types, and their interaction. Phys Rev E. 2011;83:021701.
  • Uzunova VA, Pergamenshchik VM. Chiral dipole induced by azimuthal anchoring on the surface of a planar elastic quadrupole. Phys Rev E. 2011;84:031702.
  • Senyuk B, Glugla D, Smalyukh II. Rotational and translational diffusion of anisotropic gold nanoparticles in liquid crystals controlled by varying surface anchoring. Phys Rev E. 2013;88:062507.
  • Patteson AE, Gopinath A, Goulian M, et al. Running and tumbling with E-coli in polymeric solutions. Sci Rep. 2015;5:15761.
  • Trivedi RR, Maeda R, Abbott NL, et al. Bacterial transport of colloids in liquid crystalline environments. Soft Matter. 2015;11:8404–8408.
  • Kos Ž, Ravnik M. Elementary flow field profiles of micro-swimmers in weakly anisotropic nematic fluids: stokeslet, stresslet, rotlet and source flows. Fluids. 2018;3:15.
  • Krieger MS, Spagnolie SE, Powers TR. Locomotion and transport in a hexatic liquid crystal. Phys Rev E. 2014;90:052503.
  • Dombrowski C, Cisneros L, Chatkaew S, et al. Self-concentration and large-scale coherence in bacterial dynamics. Phys Rev Lett. 2004;93:098103.
  • Mendelson NH, Bourque A, Wilkening K, et al. Organized cell swimming motions in Bacillus subtilis colonies: patterns of short-lived whirls and jets. J Bacteriol. 1999;181:600–609.
  • Sokolov A, Aranson IS, Kessler JO, et al. Concentration dependence of the collective dynamics of swimming bacteria. Phys Rev Lett. 2007;98:158102.
  • Cisneros LH, Kessler JO, Ganguly S, et al. Dynamics of swimming bacteria: transition to directional order at high concentration. Phys Rev E. 2011;83:061907.
  • Wensink HH, Dunkel J, Heidenreich S, et al. Meso-scale turbulence in living fluids. Proc Natl Acad Sci USA. 2012;109:14308–14313.
  • Dunkel J, Heidenreich S, Drescher K, et al. Fluid dynamics of bacterial turbulence. Phys Rev Lett. 2013;110:228102.
  • Ishikawa T, Sekiya G, Imai Y, et al. Hydrodynamic interactions between two swimming bacteria. Biophys J. 2007;93:2217–2225.
  • Wolgemuth CW. Collective swimming and the dynamics of bacterial turbulence. Biophys J. 2008;95:1564–1574.
  • Tan TH, Liu JH, Miller PW, et al. Topological turbulence in the membrane of a living cell. Nat Phys. 2020;16:657–662.
  • Ramaswamy S, Rao M. Active-filament hydrodynamics: instabilities, boundary conditions and rheology. New J Phys. 2007;9:423.
  • Liverpool TB, Marchetti MC. Instabilities of isotropic solutions of active polar filaments. Phys Rev Lett. 2003;90:138102.
  • Marenduzzo D, Orlandini E, Cates ME, et al. Steady-state hydrodynamic instabilities of active liquid crystals: hybrid lattice Boltzmann simulations. Phys Rev E. 2007;76:031921.
  • Saintillan D, Shelley MJ. Instabilities, pattern formation, and mixing in active suspensions. Phys Fluids. 2008;20:123304.
  • Alert R, Joanny JF, Casademunt J. Universal scaling of active nematic turbulence. Nat Phys. 2020;16:682–688.
  • Guillamat P, Ignés-Mullol J, Sagués F. Control of active liquid crystals with a magnetic field. Proc Natl Acad Sci USA. 2016;113:5498–5502.
  • Guillamat P, Ignés-Mullol J, Sagués F. Taming active turbulence with patterned soft interfaces. Nat Commun. 2017;8:564.
  • Hardouin J, Hughes R, Doostmohammadi A, et al. Reconfigurable flows and defect landscape of confined active nematics. Commun Phys. 2019;2:121.
  • Chandrakar P, Varghese M, Aghvami AA, et al. Confinement controls the bend instability of three-dimensional active liquid crystals. Phys Rev Lett. 2020;125:257801.
  • Martinez-Prat B, Ignés-Mullol J, Casademunt J, et al. Selection mechanism at the onset of active turbulence. Nat Phys. 2019;15:362–366.
  • Voituriez R, Joanny JF, Prost J. Spontaneous flow transition in active polar gels. Europhys Lett. 2005;70:404–410.
  • Vicsek T, Zafeiris A. Collective motion. Phys Rep: Rev Sect Phys Lett. 2012;517:71–140.
  • Toner J, Tu YH. Long-Range order in a 2-dimensional dynamical XY model – How birds fly together. Phys Rev Lett. 1995;75:4326–4329.
  • Sokolov A, Aranson IS. Physical properties of collective motion in suspensions of bacteria. Phys Rev Lett. 2012;109:248109.
  • Thampi SP, Golestanian R, Yeomans JM. Velocity correlations in an active nematic. Phys Rev Lett. 2013;111:118101.
  • Thampi SP, Golestanian R, Yeomans JM. Active nematic materials with substrate friction. Phys Rev E. 2014;90:062307.
  • Gao T, Blackwell R, Glaser MA, et al. Multiscale polar theory of microtubule and motor-protein assemblies. Phys Rev Lett. 2015;114:048101.
  • Huber L, Suzuki R, Kruger T, et al. Emergence of coexisting ordered states in active matter systems. Science. 2018;361:255–258.
  • Denk J, Frey E. Pattern-induced local symmetry breaking in active-matter systems. Proc Natl Acad Sci USA. 2020;117:31623–31630.
  • Ahmadi A, Liverpool TB, Marchetti MC. Nematic and polar order in active filament solutions. Phys Rev E. 2005;72:060901.
  • Ahmadi A, Marchetti MC, Liverpool TB. Hydrodynamics of isotropic and liquid crystalline active polymer solutions. Phys Rev E. 2006;74:061913.
  • Grossmann R, Aranson IS, Peruani F. A particle-field approach bridges phase separation and collective motion in active matter. Nat Commun. 2020;11:5365.
  • Sokolov A, Mozaffari A, Zhang R, et al. Emergence of radial tree of bend stripes in active nematics. Phys Rev X. 2019;9:031014.
  • Loisy A, Eggers J, Liverpool TB. Tractionless self-propulsion of active drops. Phys Rev Lett. 2019;123:248006.
  • Srivastava P, Mishra P, Marchetti MC. Negative stiffness and modulated states in active nematics. Soft Matter. 2016;12:8214–8225.
  • Putzig E, Redner GS, Baskaran A, et al. Instabilities, defects, and defect ordering in an overdamped active nematic. Soft Matter. 2016;12:3854–3859.
  • Joshi A, Putzig E, Baskaran A, et al. The interplay between activity and filament flexibility determines the emergent properties of active nematics. Soft Matter. 2019;15:94–101.
  • Ingham CJ, Kalisman O, Finkelshtein A, et al. Mutually facilitated dispersal between the nonmotile fungus aspergillus fumigatus and the swarming bacterium paenibacillus vortex. Proc Natl Acad Sci USA. 2011;108:19731–19736.
  • Shklarsh A, Finkelshtein A, Ariel G, et al. Collective navigation of cargo-carrying swarms. Interface Focus. 2012;2:786–798.
  • Finkelshtein A, Roth D, Ben Jacob E, et al. Bacterial swarms recruit cargo bacteria To pave the Way in toxic environments. Mbio. 2015;6:e00074–e00015.
  • Lele PP, Hosu BG, Berg HC. Dynamics of mechanosensing in the bacterial flagellar motor. Proc Natl Acad Sci USA. 2013;110:11839–11844.
  • Wu KT, Hishamunda JB, Chen DTN, et al. Transition from turbulent to coherent flows in confined three-dimensional active fluids. Science. 2017;355:eaal1979.
  • Maass CC, Krüger C, Herminghaus S, et al. Swimming droplets. Annu Rev Condens Matter Phys. 2016;7:171–193.
  • Schmitt M, Stark H. Swimming active droplet: a theoretical analysis. EPL. 2013;101:44008.
  • Jin CY, Kruger C, Maass CC. Chemotaxis and autochemotaxis of self-propelling droplet swimmers. Proc Natl Acad Sci USA. 2017;114:5089–5094.
  • Jin CY, Vachier J, Bandyopadhyay S, et al. Fine balance of chemotactic and hydrodynamic torques: when microswimmers orbit a pillar just once. Phys Rev E. 2019;100:040601.
  • Meredith CH, Moerman PG, Groenewold J, et al. Predator-prey interactions between droplets driven by non-reciprocal oil exchange. Nat Chem. 2020;12:1136–1142.
  • Najafi A, Golestanian R. Simple swimmer at low Reynolds number: three linked spheres. Phys Rev E. 2004;69:062901.
  • Avron JE, Kenneth O, Oaknin DH. Pushmepullyou: an efficient micro-swimmer. New J Phys. 2005;7:234.
  • Kruse K, Joanny JF, Julicher F, et al. Contractility and retrograde flow in lamellipodium motion. Phys Biol. 2006;3:130–137.
  • Keren K, Pincus Z, Allen GM, et al. Mechanism of shape determination in motile cells. Nature. 2008;453:475–480.
  • Ziebert F, Swaminathan S, Aranson IS. Model for self-polarization and motility of keratocyte fragments. J R Soc Interface. 2012;9:1084–1092.
  • Tjhung E, Marenduzzo D, Cates ME. Spontaneous symmetry breaking in active droplets provides a generic route to motility. Proc Natl Acad Sci USA. 2012;109:12381–12386.
  • Khoromskaia D, Alexander GP. Motility of active fluid drops on surfaces. Phys Rev E. 2015;92:062311.
  • Tjhung E, Tiribocchi A, Marenduzzo D, et al. A minimal physical model captures the shapes of crawling cells. Nat Commun. 2015;6:5420.
  • Giomi L, DeSimone A. Spontaneous division and motility in active nematic droplets. Phys Rev Lett. 2014;112:147802.
  • Callan-Jones AC, Voituriez R. Active gel model of amoeboid cell motility. New J Phys. 2013;15:025022.
  • Recho P, Putelat T, Truskinovsky L. Contraction-driven cell motility. Phys Rev Lett. 2013;111:108102.
  • Whitfield CA, Hawkins RJ. Instabilities, motion and deformation of active fluid droplets. New J Phys. 2016;18:123016.
  • Yoshinaga N. Self-propulsion of an active polar drop. J Chem Phys. 2019;150:184904.
  • Lushi E, Wioland H, Goldstein RE. Fluid flows created by swimming bacteria drive self-organization in confined suspensions. Proc Natl Acad Sci USA. 2014;111:9733–9738.
  • Tsang ACH, Kanso E. Circularly confined microswimmers exhibit multiple global patterns. Phys Rev E. 2015;91:043008.
  • Čopar S, Aplinc J, Kos Ž, et al. Topology of three-dimensional active nematic turbulence confined to droplets. Phys Rev X. 2019;9:031051.
  • Hardouin JM, Laurent J, Lopez-Leon T, et al. Active microfluidic transport in two-dimensional handlebodies. Soft Matter. 2020;16:9230–9241.
  • Gao T, Betterton MD, Jhang AS, et al. Analytical structure, dynamics, and coarse graining of a kinetic model of an active fluid. Phys Rev Fluids. 2017;2:093302.
  • Reigh SY, Zhu LL, Gallaire F, et al. Swimming with a cage: low-reynolds-number locomotion inside a droplet. Soft Matter. 2017;13:3161–3173.
  • Huang ZH, Omori T, Ishikawa T. Active droplet driven by a collective motion of enclosed microswimmers. Phys Rev E. 2020;102:022603.
  • Gao T, Li ZR. Self-driven droplet powered by active nematics. Phys Rev Lett. 2017;119:108002.
  • Rajabi M, Hend B, Turiv T, et al. Directional self-locomotion of active droplets enabled by nematic environment. Nat Phys. 2021;17:260–266.
  • Adrian RJ. Particle-imaging techniques for experimental fluid-mechanics. Annu Rev Fluid Mech. 1991;23:261–304.
  • Grant I. Particle image velocimetry: a review. Proc Inst Mech Eng Part C: J Mech Eng Sci. 1997;211:55–76.
  • Vladescu ID, Marsden EJ, Schwarz-Linek J, et al. Filling an emulsion drop with motile bacteria. Phys Rev Lett. 2014;113:268101.
  • Fily Y, Baskaran A, Hagan MF. Dynamics of self-propelled particles under strong confinement. Soft Matter. 2014;10:5609–5617.
  • Wioland H, Woodhouse FG, Dunkel J, et al. Confinement stabilizes a bacterial suspension into a spiral vortex. Phys Rev Lett. 2013;110:268102.
  • Kim YK, Noh J, Nayani K, et al. Soft matter from liquid crystals. Soft Matter. 2019;15:6913–6929.
  • Stark H, Ventzki D. Non-linear Stokes drag of spherical particles in a nematic solvent. Europhys Lett. 2002;57:60–66.
  • Zhang R, Roberts T, Aranson IS, et al. Lattice Boltzmann simulation of asymmetric flow in nematic liquid crystals with finite anchoring. J Chem Phys. 2016;144:084905.
  • Marenduzzo D, Orlandini E, Yeomans JM. Interplay between shear flow and elastic deformations in liquid crystals. J Chem Phys. 2004;121:582–591.
  • Gettelfinger BT, Moreno-Razo JA, Koenig GM, et al. Flow induced deformation of defects around nanoparticles and nanodroplets suspended in liquid crystals. Soft Matter. 2010;6:896–901.
  • Elgeti J, Winkler RG, Gompper G. Physics of microswimmers-single particle motion and collective behavior: a review. Rep Prog Phys. 2015;78:056601.
  • Stanton MM, Trichet-Paredes C, Sanchez S. Applications of three-dimensional (3D) printing for microswimmers and bio-hybrid robotics. Lab Chip. 2015;15:1634–1637.
  • Tsang ACH, Demir E, Ding Y, et al. Roads to Smart artificial microswimmers. Adv Intell Syst. 2020;2:1900137.
  • Ricotti L, Trimmer B, Feinberg AW, et al. Biohybrid actuators for robotics: a review of devices actuated by living cells. Sci Rob. 2017;2:eaaq0495.
  • Lavrentovich OD. Transport of particles in liquid crystals. Soft Matter. 2014;10:1264–1283.
  • Shi J, Powers TR. Swimming in an anisotropic fluid: how speed depends on alignment angle. Phys Rev Fluids. 2017;2:123102.
  • Lavrentovich OD. Ferroelectric nematic liquid crystal, a century in waiting. Proc Natl Acad Sci USA. 2020;117:14629–14631.
  • Mandle RJ, Mertelj A. Orientational order in the splay nematic ground state. Phys Chem Chem Phys. 2019;21:18769–18772.
  • Sebastian N, Cmok L, Mandle RJ, et al. Ferroelectric-Ferroelastic phase transition in a nematic liquid crystal. Phys Rev Lett. 2020;124:037801.
  • Rosseto MP, Selinger JV. Theory of the splay nematic phase: single versus double splay. Phys Rev E. 2020;101:052707.
  • Born M. Über anisotrope Flüssigkeiten. Versuch einer Theorie der flüssigen Kristalle und des elektrischen Kerr-Effects in Flüssigkeiten/On anisotropic fluids. The test of a theory of fluid crystals and of electrical Kerr effects in fluids, Sitzungsberichte Der Koniglich Preussischen Akademie Der Wissenschaften, 614–650 (1916).
  • Martin LW, Rappe AM. Thin-film ferroelectric materials and their applications. Nat Rev Mater. 2017;2:16087.
  • Hindmarsh MB, Kibble TWB. Cosmic strings. Rep Prog Phys. 1995;58:477–562.
  • Makinen JT, Dmitriev VV, Nissinen J, et al. Half-quantum vortices and walls bounded by strings in the polar-distorted phases of topological superfluid He-3. Nat Commun. 2019;10:237.
  • Volovik GE, Zhang K. String monopoles, vortex skyrmions, and nexus objects in the polar distorted B phase of 3 He. Phys Rev Res. 2020;2:023263.
  • Zhang K. One-dimensional nexus objects, network of Kibble-Lazarides-Shafi string walls, and their spin dynamic response in polar-distorted B-phase of 3He. Phys Rev Res. 2020;2:043356.
  • Whitfield CA, Adhyapak TC, Tiribocchi A, et al. Hydrodynamic instabilities in active cholesteric liquid crystals. Eur Phys J E. 2017;40:50.
  • Kole SJ, Alexander GP, Ramaswamy S, et al. Active cholesterics: odder than odd elasticity; 2020. arXiv:2012.14321.
  • Carenza LN, Gonnella G, Marenduzzo D, et al. Rotation and propulsion in 3D active chiral droplets. Proc Natl Acad Sci USA. 2019;116:22065–22070.
  • Carenza LN, Gonnella G, Marenduzzo D, et al. Chaotic and periodical dynamics of active chiral droplets. Phys A: Stat Mech Appl. 2020;559:125025.
  • Adhyapak TC, Ramaswamy S, Toner J. Live soap: stability, order, and fluctuations in apolar active smectics. Phys Rev Lett. 2013;110:118102.
  • Romanczuk P, Chaté H, Chen LM, et al. Emergent smectic order in simple active particle models. New J Phys. 2016;18:063015.
  • Kumar N, Gupta RK, Soni H, et al. Trapping and sorting active particles: motility-induced condensation and smectic defects. Phys Rev E. 2019;99:032605.
  • Ferreiro-Cordova C, Toner J, Lowen H, et al. Long-time anomalous swimmer diffusion in smectic liquid crystals. Phys Rev E. 2018;97:062606.
  • Thijssen K, Metselaar L, Yeomans JM, et al. Active nematics with anisotropic friction: the decisive role of the flow aligning parameter. Soft Matter. 2020;16:2065–2074.

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