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Collective dynamics and rheology of confined phoretic suspensions

Published online by Cambridge University Press:  13 June 2022

T. Traverso Open the ORCID record for T. Traverso [Opens in a new window]  and
S. Michelin Open the ORCID record for S. Michelin [Opens in a new window]
T. Traverso*
Affiliation:
LadHyX – CNRS, Ecole Polytechnique, Institut Polytechnique de Paris – 91120 Palaiseau, France
S. Michelin
Affiliation:
LadHyX – CNRS, Ecole Polytechnique, Institut Polytechnique de Paris – 91120 Palaiseau, France
*
†Email address for correspondence: [email protected]
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Abstract

Similarly to their biological counterparts, suspensions of chemically active autophoretic swimmers exhibit a non-trivial dynamics involving self-organisation processes as a result of inter-particle interactions. Using a kinetic model for a dilute suspension of autochemotactic Janus particles, we analyse the effect of a confined pressure-driven flow on these collective behaviours and the impact of chemotactic aggregation on the effective viscosity of the active fluid. Four dynamic regimes are identified when increasing the strength of the imposed pressure-driven flow, each associated with a different collective behaviour resulting from the competition of flow- and chemically induced reorientation of the swimmers together with the constraints of confinement. Interestingly, we observe that the effect of the pusher (respectively puller) hydrodynamic signature, which is known to reduce (respectively increase) the effective viscosity of a sheared suspension, is inverted upon the emergence of autochemotactic aggregation. Our results provide new insights into the role of the collective dynamics in complex environments, which are relevant to synthetic as well as biological systems.

JFM classification

Biological Fluid Dynamics: Collective behaviour Complex Fluids: Active matter
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 943 , 25 July 2022 , A21
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

REFERENCES

Alonso-Matilla, R., Ezhilan, B. & Saintillan, D. 2016 Microfluidic rheology of active particle suspensions: kinetic theory. Biomicrofluidics 10 (4), 043505.CrossRefGoogle ScholarPubMed
Anderson, J.L. 1989 Colloid transport by interfacial forces. Annu. Rev. Fluid Mech. 21 (1), 61–99.CrossRefGoogle Scholar
Arnoldi, W.E. 1951 The principle of minimized iterations in the solution of the matrix eigenvalue problem. Q. Appl. Maths 9 (1), 17–29.CrossRefGoogle Scholar
Balescu, R. 1997 Statistical Dynamics: Matter Out of Equilibrium. Imperial College Press.CrossRefGoogle Scholar
Barry, M.T., Rusconi, R., Guasto, J.S. & Stocker, R. 2015 Shear-induced orientational dynamics and spatial heterogeneity in suspensions of motile phytoplankton. J. R. Soc. Interface 12 (112), 20150791.CrossRefGoogle ScholarPubMed
Baskaran, A. & Marchetti, M.C. 2009 Statistical mechanics and hydrodynamics of bacterial suspensions. Proc. Natl Acad. Sci. USA 106 (37), 15567–15572.CrossRefGoogle ScholarPubMed
Bearon, R.N. & Hazel, A.L. 2015 The trapping in high-shear regions of slender bacteria undergoing chemotaxis in a channel. J. Fluid Mech. 771, R3.CrossRefGoogle Scholar
Berke, A.P., Turner, L., Berg, H.C. & Lauga, E. 2008 Hydrodynamic attraction of swimming microorganisms by surfaces. Phys. Rev. Lett. 101 (3), 038102.CrossRefGoogle ScholarPubMed
Blake, J.R. 1971 A spherical envelope approach to ciliary propulsion. J. Fluid Mech. 46 (1), 199–208.CrossRefGoogle Scholar
Brennen, C. & Winet, H. 1977 Fluid mechanics of propulsion by cilia and flagella. Annu. Rev. Fluid Mech. 9 (1), 339–398.CrossRefGoogle Scholar
Brotto, T., Caussin, J.-B., Lauga, E. & Bartolo, D. 2013 Hydrodynamics of confined active fluids. Phys. Rev. Lett. 110, 038101.CrossRefGoogle ScholarPubMed
Budrene, E.O. & Berg, H.C. 1991 Complex patterns formed by motile cells of Escherichia coli. Nature 349 (6310), 630–633.CrossRefGoogle ScholarPubMed
Campbell, A.I., Ebbens, S.J., Illien, P. & Golestanian, R. 2019 Experimental observation of flow fields around active janus spheres. Nat. Commun. 10 (1), 3952.CrossRefGoogle ScholarPubMed
Contino, M., Lushi, E., Tuval, I., Kantsler, V. & Polin, M. 2015 Microalgae scatter off solid surfaces by hydrodynamic and contact forces. Phys. Rev. Lett. 115, 258102.CrossRefGoogle ScholarPubMed
Dombrowski, C., Cisneros, L., Chatkaew, S., Goldstein, R.E. & Kessler, J.O. 2004 Self-concentration and large-scale coherence in bacterial dynamics. Phys. Rev. Lett. 93, 098103.CrossRefGoogle ScholarPubMed
Drescher, K., Dunkel, J., Cisneros, L.H., Ganguly, S. & Goldstein, R.E. 2011 Fluid dynamics and noise in bacterial cell–cell and cell–surface scattering. Proc. Natl Acad. Sci. USA 108 (27), 10940–10945.CrossRefGoogle ScholarPubMed
Drescher, K., Goldstein, R.E., Michel, N., Polin, M. & Tuval, I. 2010 Direct measurement of the flow field around swimming microorganisms. Phys. Rev. Lett. 105, 168101.CrossRefGoogle ScholarPubMed
Dunkel, J., Heidenreich, S., Drescher, K., Wensink, H.H., Bär, M. & Goldstein, R.E. 2013 Fluid dynamics of bacterial turbulence. Phys. Rev. Lett. 110, 228102.CrossRefGoogle ScholarPubMed
Elgeti, J. & Gompper, G. 2013 Wall accumulation of self-propelled spheres. Europhys. Lett. 101 (4), 48003.CrossRefGoogle Scholar
Ezhilan, B. & Saintillan, D. 2015 Transport of a dilute active suspension in pressure-driven channel flow. J. Fluid Mech. 777, 482–522.CrossRefGoogle Scholar
Gachelin, J., Mi no, G., Berthet, H., Lindner, A., Rousselet, A. & Clément, E. 2013 Non-Newtonian viscosity of escherichia coli suspensions. Phys. Rev. Lett. 110, 268103.CrossRefGoogle ScholarPubMed
Gao, T., Betterton, M.D., Jhang, A. & Shelley, M.J. 2017 Analytical structure, dynamics, and coarse graining of a kinetic model of an active fluid. Phys. Rev. Fluids 2, 093302.CrossRefGoogle Scholar
Garcia, X., Rafaï, S. & Peyla, P. 2013 Light control of the flow of phototactic microswimmer suspensions. Phys. Rev. Lett. 110, 138106.CrossRefGoogle ScholarPubMed
Golestanian, R., Liverpool, T.B. & Ajdari, A. 2007 Designing phoretic micro- and nano-swimmers. New J. Phys. 9, 126.CrossRefGoogle Scholar
Guasto, J.S., Rusconi, R. & Stocker, R. 2012 Fluid mechanics of planktonic microorganisms. Annu. Rev. Fluid Mech. 44, 373–400.CrossRefGoogle Scholar
Hatwalne, Y., Ramaswamy, S., Rao, M. & Simha, R.A. 2004 Rheology of active-particle suspensions. Phys. Rev. Lett. 92, 118101.CrossRefGoogle ScholarPubMed
Hong, Y., Blackman, N.M.K., Kopp, N.D., Sen, A. & Velegol, D. 2007 Chemotaxis of nonbiological colloidal rods. Phys. Rev. Lett. 99 (17), 178103.CrossRefGoogle ScholarPubMed
Howse, J.R., Jones, R.A.L., Ryan, A.J., Gough, T., Vafabakhsh, R. & Golestanian, R. 2007 Self-motile colloidal particles: from directed propulsion to random walk. Phys. Rev. Lett. 99 (4), 8–11.CrossRefGoogle ScholarPubMed
Ibele, M., Mallouk, T.E. & Sen, A. 2009 Schooling behavior of light-powered autonomous micromotors in water. Angew. Chem. Intl Ed. Engl. 121 (18), 3358–3362.CrossRefGoogle Scholar
Jülicher, F. & Prost, J. 2009 Generic theory of colloidal transport. Eur. Phys. J. E 29 (1), 27–36.CrossRefGoogle ScholarPubMed
Kanso, E. & Michelin, S. 2019 Phoretic and hydrodynamic interactions of weakly confined autophoretic particles. J. Chem. Phys. 150 (4), 044902.CrossRefGoogle ScholarPubMed
Kantsler, V., Dunkel, J., Polin, M. & Goldstein, R.E. 2013 Ciliary contact interactions dominate surface scattering of swimming eukaryotes. Proc. Natl Acad. Sci. USA 110 (4), 1187–1192.CrossRefGoogle ScholarPubMed
Kessler, J.O. 1985 Hydrodynamic focusing of motile algal cells. Nature 313 (5999), 218–220.CrossRefGoogle Scholar
Kleiser, L. & Schumann, U. 1980 Treatment of incompressibility and boundary conditions in 3-D numerical spectral simulations of plane channel flows. In Conference on Numerical Methods in Fluid Mechanics (ed. E.H. Hirschel), vol. 2, pp. 165–173.Google Scholar
Krieger, I.M. & Dougherty, T.J. 1959 A mechanism for non-Newtonian flow in suspensions of rigid spheres. Trans. Soc. Rheol. 3 (1), 137–152.CrossRefGoogle Scholar
Lambert, R.A., Picano, F., Breugem, W. & Brandt, L. 2013 Active suspensions in thin films: nutrient uptake and swimmer motion. J. Fluid Mech. 733, 528–557.CrossRefGoogle Scholar
Lauga, E. & Michelin, S. 2016 Stresslets induced by active swimmers. Phys. Rev. Lett. 117, 148001.CrossRefGoogle ScholarPubMed
Li, G., Bensson, J., Nisimova, L., Munger, D., Mahautmr, P., Tang, J.X., Maxey, M.R. & Brun, Y.V. 2011 Accumulation of swimming bacteria near a solid surface. Phys. Rev. E 84, 041932.CrossRefGoogle Scholar
Li, G. & Tang, J.X. 2009 Accumulation of microswimmers near a surface mediated by collision and rotational Brownian motion. Phys. Rev. Lett. 103 (7), 078101.CrossRefGoogle Scholar
Liebchen, B., Marenduzzo, D., Pagonabarraga, I. & Cates, M.E. 2015 Clustering and pattern formation in chemorepulsive active colloids. Phys. Rev. Lett. 115, 258301.CrossRefGoogle ScholarPubMed
Liu, Y., et al. 2020 Optimised hyperbolic microchannels for the mechanical characterisation of bio-particles. Soft Matt. 16 (43), 9844–9856.CrossRefGoogle ScholarPubMed
López, H.M., Gachelin, J., Douarche, C., Auradou, H. & Clément, E. 2015 Turning bacteria suspensions into superfluids. Phys. Rev. Lett. 115, 028301.CrossRefGoogle ScholarPubMed
Lushi, E., Goldstein, R.E. & Shelley, M.J. 2012 Collective chemotactic dynamics in the presence of self-generated fluid flows. Phys. Rev. E 86, 040902(R).CrossRefGoogle ScholarPubMed
Lushi, E., Goldstein, R.E. & Shelley, M.J. 2018 Nonlinear concentration patterns and bands in autochemotactic suspensions. Phys. Rev. E 98, 052411.CrossRefGoogle Scholar
Lushi, E., Wioland, H. & Goldstein, R.E. 2014 Fluid flows created by swimming bacteria drive self-organization in confined suspensions. Proc. Natl Acad. Sci. USA 111 (27), 9733–9738.CrossRefGoogle ScholarPubMed
Mager, D.L. 2006 Bacteria and cancer: cause, coincidence or cure? A review. J. Transl. Med. 4 (1), 1–18.CrossRefGoogle ScholarPubMed
Martin, M., Barzyk, A., Bertin, E., Peyla, P. & Rafai, S. 2016 Photofocusing: light and flow of phototactic microswimmer suspension. Phys. Rev. E 93, 051101(R).CrossRefGoogle ScholarPubMed
McDonnell, A.G., Gopesh, T.C., Lo, J., O'Bryan, M., Yeo, L.Y., Friend, J.R. & Prabhakar, R. 2015 Motility induced changes in viscosity of suspensions of swimming microbes in extensional flows. Soft Matt. 11, 4658–4668.CrossRefGoogle ScholarPubMed
Michelin, S. & Lauga, E. 2014 Phoretic self-propulsion at finite Péclet numbers. J. Fluid Mech. 747, 572–604.CrossRefGoogle Scholar
Moran, J.L. & Posner, J.D. 2017 Phoretic self-propulsion. Annu. Rev. Fluid Mech. 49, 511–540.CrossRefGoogle Scholar
Mostaghaci, B., Yasa, O., Zhuang, J. & Sitti, M. 2017 Bioadhesive bacterial microswimmers for targeted drug delivery in the urinary and gastrointestinal tracts. Adv. Sci. 4 (6), 1700058.CrossRefGoogle ScholarPubMed
Palacci, J., Abécassis, B., Cottin-Bizonne, C., Ybert, C. & Bocquet, L. 2010 Colloidal motility and pattern formation under rectified diffusiophoresis. Phys. Rev. Lett. 104 (13), 138302.CrossRefGoogle ScholarPubMed
Palacci, J., Sacanna, S., Steinberg, A.P., Pine, D.J. & Chaikin, P.M. 2013 Living crystals of light-activated colloidal surfers. Science 339 (6122), 936–940.CrossRefGoogle ScholarPubMed
Purcell, E.M. 1977 Life at low Reynolds number. Am. J. Phys. 45 (1), 3–11.CrossRefGoogle Scholar
Rafaï, S., Jibuti, L. & Peyla, P. 2010 Effective viscosity of microswimmer suspensions. Phys. Rev. Lett. 104, 098102.CrossRefGoogle ScholarPubMed
Riffell, J.A. & Zimmer, R.K. 2007 Sex and flow: the consequences of fluid shear for sperm–egg interactions. J. Expl Biol. 210 (20), 3644–3660.CrossRefGoogle ScholarPubMed
Rothschild, L. 1963 Non-random distribution of bull spermatozoa in a drop of sperm suspension. Nature 198, 1221–1222.CrossRefGoogle Scholar
Rusconi, R., Guasto, J.S. & Stocker, R. 2014 Bacterial transport suppressed by fluid shear. Nat. Phys. 10, 212–217.CrossRefGoogle Scholar
Saha, S., Golestanian, R. & Ramaswamy, S. 2014 Clusters, asters, and collective oscillations in chemotactic colloids. Phys. Rev. E 89, 062316.CrossRefGoogle ScholarPubMed
Saintillan, D. 2010 Extensional rheology of active suspensions. Phys. Rev. E 81, 056307.CrossRefGoogle ScholarPubMed
Saintillan, D. & Shelley, M.J. 2008 Instabilities, pattern formation, and mixing in active suspensions. Phys. Fluids 20 (12), 123304.CrossRefGoogle Scholar
Saintillan, D. & Shelley, M.J. 2013 Active suspensions and their nonlinear models. C. R. Phys. 14, 497–517.CrossRefGoogle Scholar
Sen, A., Ibele, M., Hong, Y. & Velegol, D. 2009 Chemo and phototactic nano/microbots. Faraday Discuss. 143, 15–27.CrossRefGoogle ScholarPubMed
Shendruk, T.N., Doostmohammadi, A., Thijssen, K. & Yeomans, J.M. 2017 Dancing disclinations in confined active nematics. Soft Matt. 13, 3853–3862.CrossRefGoogle ScholarPubMed
Spagnolie, S.E. & Lauga, E. 2012 Hydrodynamics of self-propulsion near a boundary: predictions and accuracy of far-field approximations. J. Fluid Mech. 700, 105–147.CrossRefGoogle Scholar
Steffan, R.J., Sperry, K.L., Walsh, M.T., Vainberg, S. & Condee, C.W. 1999 Field-scale evaluation of in situ bioaugmentation for remediation of chlorinated solvents in groundwater. Environ. Sci. Technol. 33 (16), 2771–2781.CrossRefGoogle Scholar
Stenhammar, J., Nardini, C., Nash, R.W., Marenduzzo, D. & Morozov, A. 2017 Role of correlations in the collective behavior of microswimmer suspensions. Phys. Rev. Lett. 119, 028005.CrossRefGoogle ScholarPubMed
Stone, H.A. & Samuel, A.D.T. 1996 Propulsion of microorganisms by surface distortions. Phys. Rev. Lett. 77, 4102–4104.CrossRefGoogle ScholarPubMed
Takagi, D., Palacci, J., Braunschweig, A.B., Shelley, M.J. & Zhang, J. 2014 Hydrodynamic capture of microswimmers into sphere-bound orbits. Soft Matt. 10, 1784–1789.CrossRefGoogle ScholarPubMed
Theillard, M. & Saintillan, D. 2019 Computational mean-field modeling of confined active fluids. J. Comput. Phys. 397, 108841.CrossRefGoogle Scholar
Theurkauff, I., Cottin-Bizonne, C., Palacci, J., Ybert, C. & Bocquet, L. 2012 Dynamic clustering in active colloidal suspensions with chemical signaling. Phys. Rev. Lett. 108, 268303.CrossRefGoogle ScholarPubMed
Traverso, T. & Michelin, S. 2020 Hydrochemical interactions in dilute phoretic suspensions: from individual particle properties to collective organization. Phys. Rev. Fluids 5, 104203.CrossRefGoogle Scholar
Tuckerman, L.S. 1989 Divergence-free velocity fields in nonperiodic geometries. J. Comput. Phys. 80 (2), 403–441.CrossRefGoogle Scholar
Tufenkji, N. 2007 Modeling microbial transport in porous media: traditional approaches and recent developments. Adv. Water Resour. 30 (6–7), 1455–1469.CrossRefGoogle Scholar
Uspal, W.E., Popescu, M.N., Dietrich, S. & Tasinkevych, M. 2015 Self-propulsion of a catalytically active particle near a planar wall: from reflection to sliding and hovering. Soft Matt. 11 (3), 434–438.CrossRefGoogle Scholar
Vennamneni, L., Nambiar, S. & Subramanian, G. 2020 Shear-induced migration of microswimmers in pressure-driven channel flow. J. Fluid Mech. 890, A15.CrossRefGoogle Scholar
Wang, W., Duan, W., Sen, A. & Mallouk, T.E. 2013 Catalytically powered dynamic assembly of rod-shaped nanomotors and passive tracer particles. Proc. Natl Acad. Sci. USA 110 (44), 17744–17749.CrossRefGoogle ScholarPubMed
Wioland, H., Lushi, H. & Goldstein, R.E. 2016 Directed collective motion of bacteria under channel confinement. New J. Phys. 18 (7), 075002.CrossRefGoogle Scholar
Wioland, H., Woodhouse, F.G., Dunkel, J., Kessler, J.O. & Goldstein, R.E. 2013 Confinement stabilizes a bacterial suspension into a spiral vortex. Phys. Rev. Lett. 110, 268102.CrossRefGoogle ScholarPubMed
Yadav, V., Duan, W., Butler, P.J. & Sen, A. 2015 Anatomy of nanoscale propulsion. Annu. Rev. Biophys. 44, 77–100.CrossRefGoogle ScholarPubMed
Ying, Y., Pourrahimi, A.M., Sofer, Z., Matějková, S. & Pumera, M. 2019 Radioactive uranium preconcentration via self-propelled autonomous microrobots based on metal–organic frameworks. ACS Nano 13 (10), 11477–11487.CrossRefGoogle ScholarPubMed