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Shape matters: a Brownian microswimmer in a channel

Published online by Cambridge University Press:  06 April 2021

Hongfei Chen Open the ORCID record for Hongfei Chen [Opens in a new window]  and
Jean-Luc Thiffeault Open the ORCID record for Jean-Luc Thiffeault [Opens in a new window]
Hongfei Chen*
Affiliation:
Department of Mathematics, University of Wisconsin – Madison, 480 Lincoln Dr., Madison, WI53706, USA
Jean-Luc Thiffeault*
Affiliation:
Department of Mathematics, University of Wisconsin – Madison, 480 Lincoln Dr., Madison, WI53706, USA
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

We consider the active Brownian particle model for a two-dimensional microswimmer with fixed speed, whose direction of swimming changes according to a Brownian process. The probability density for the swimmer obeys a Fokker–Planck equation defined on the configuration space, whose structure depends on the swimmer's shape, centre of rotation and domain of swimming. We enforce zero probability flux at the boundaries of configuration space. At first neglecting hydrodynamic interactions, we derive a reduced equation for a swimmer in an infinite channel, in the limit of small rotational diffusivity, and find that the invariant density depends strongly on the swimmer's precise shape and centre of rotation. We also give a formula for the mean reversal time: the expected time taken for a swimmer to completely reverse direction in the channel. Using homogenization theory, we find an expression for the effective longitudinal diffusivity of a swimmer in the channel, and show that it is bounded by the mean reversal time. Finally, we include hydrodynamic interactions with walls, and examine the role of shape.

JFM classification

Biological Fluid Dynamics: Micro-organism dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 916 , 10 June 2021 , A15
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Ai, B., Chen, Q., He, Y., Li, F. & Zheng, W. 2013 Rectification and diffusion of self-propelled particles in a two-dimensional corrugated channel. Phys. Rev. E 88, 062129.CrossRefGoogle Scholar
Alonso-Matilla, R., Ezhilan, B. & Saintillan, D. 2016 Microfluidic rheology of active particle suspensions: kinetic theory. Biomicrofluidics 10, 043505.CrossRefGoogle ScholarPubMed
Alonso-Matilla, R. & Saintillan, D. 2019 Interfacial instabilities in active viscous films. J. Non-Newtonian Fluid Mech. 259, 57–64.CrossRefGoogle Scholar
Bearon, R.N., Hazel, A.L. & Thorn, G.J. 2011 The spatial distribution of gyrotactic swimming micro-organisms in laminar flow fields. J. Fluid Mech. 680, 602–635.CrossRefGoogle Scholar
Bechinger, C., Di Leonardo, R., Löwen, H., Reichhardt, C., Volpe, G. & Volpe, G. 2016 Active particles in complex and crowded environments. Rev. Mod. Phys. 88, 045006.CrossRefGoogle Scholar
Berke, A.P., Turner, L., Berg, H.C. & Lauga, E. 2008 Hydrodynamic attraction of swimming microorganisms by surfaces. Phys. Rev. Lett. 101, 038102.CrossRefGoogle ScholarPubMed
Bianchi, S., Saglimbeni, F. & Di Leonardo, R. 2017 Holographic imaging reveals the mechanism of wall entrapment in swimming bacteria. Phys. Rev. X 7, 011010.Google Scholar
Bricard, A., Caussin, J.-B., Savoie, D.D.C., Chikkadi, V., Shitara, K., Chepizhko, O., Peruani, F., Saintillan, D. & Bartolo, D. 2015 Emergent vortices in populations of confined colloidal rollers. Nat. Commun. 6, 7470.CrossRefGoogle Scholar
Bruna, M. & Chapman, S.J. 2013 Diffusion of finite-size particles in confined geometries. Bull. Math. Biol. 76 (4), 947–982.CrossRefGoogle ScholarPubMed
Burada, P.S., Hänggi, P., Marchesoni, F., Schmid, G. & Talkner, P. 2009 Diffusion in confined geometries. ChemPhysChem 10 (1), 45–54.CrossRefGoogle ScholarPubMed
Caprini, L. & Marconi, U. 2018 Active particles under confinement and effective force generation among surfaces. Soft Matt. 14, 9044–9054.CrossRefGoogle ScholarPubMed
Cates, M.E. & Tailleur, J. 2013 When are active Brownian particles and run-and-tumble particles equivalent? Consequences for motility-induced phase separation. Europhys. Lett. 101, 20010.CrossRefGoogle Scholar
Chen, Y., Wang, Z., Chu, K., Chen, H., Sheng, Y. & Tsao, H. 2018 Hydrodynamic interaction induced breakdown of the state properties of active fluids. Soft Matt. 14, 5319–5326.CrossRefGoogle ScholarPubMed
Childress, S. & Soward, A.M. 1989 Scalar transport and alpha-effect for a family of cat's-eye flows. J. Fluid Mech. 205, 99–133.CrossRefGoogle Scholar
Chilukuri, S., Collins, C.H. & Underhill, P.T. 2014 Impact of external flow on the dynamics of swimming microorganisms near surfaces. J. Phys.: Condens. Matter 26, 115101.Google 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 (25), 258102.CrossRefGoogle ScholarPubMed
Costanzo, A., Di Leonardo, R., Ruocco, G. & Angelani, L. 2012 Transport of self-propelling bacteria in micro-channel flow. J. Phys.: Condens. Matter 24, 065101.Google ScholarPubMed
Crowdy, D.G. & Or, Y. 2010 Two-dimensional point singularity model of a low-Reynolds-number swimmer near a wall. Phys. Rev. E 81, 036313.CrossRefGoogle Scholar
Crowdy, D.G. & Samson, O. 2011 Hydrodynamic bound states of a low-Reynolds-number swimmer near a gap in a wall. J. Fluid Mech. 667, 309–335.CrossRefGoogle Scholar
Daddi-Moussa-Ider, A., Lisicki, M., Hoell, C. & Löwen, H. 2018 Swimming trajectories of a three-sphere microswimmer near a wall. J. Chem. Phys. 148, 134904.CrossRefGoogle Scholar
Denissenko, P., Kanstler, V., Smith, D.J. & Kirkman-Brown, J. 2012 Human spermatozoa migration in micro channels reveals boundary-following navigation. Proc. Natl Acad. Sci. USA 109, 8007–8010.CrossRefGoogle Scholar
DiLuzio, W.R., Turner, L., Mayer, M., Garstecki, P., Weibel, D.B., Berg, H.C. & Whitesides, G.M. 2005 Escherichia coli swim on the right-hand side. Nature 435, 1271–1274.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, 10940–10945.CrossRefGoogle ScholarPubMed
Elgeti, J. & Gompper, G. 2009 Self-propelled rods near surfaces. Europhys. Lett. 85, 38002.CrossRefGoogle Scholar
Elgeti, J. & Gompper, G. 2013 Wall accumulation of self-propelled spheres. Europhys. Lett. 101, 48003.CrossRefGoogle Scholar
Elgeti, J. & Gompper, G. 2015 Run-and-tumble dynamics of self-propelled particles in confinement. Europhys. Lett. 109, 58003.CrossRefGoogle Scholar
Elgeti, J. & Gompper, G. 2016 Microswimmers near surfaces. Eur. Phys. J. Spec. Top. 225, 2333–2352.CrossRefGoogle Scholar
Evans, A.A. & Lauga, E. 2010 Propulsion by passive filaments and active flagella near boundaries. Phys. Rev. E 82, 041915.CrossRefGoogle ScholarPubMed
Ezhilan, B., Alonso-Matilla, R. & Saintillan, D. 2015 On the distribution and swim pressure of run-and-tumble particles in confinement. J. Fluid Mech. 781, R4.CrossRefGoogle Scholar
Ezhilan, B., Pahlavan, A.A. & Saintillan, D. 2012 Chaotic dynamics and oxygen transport in thin films of aerotactic bacteria. Phys. Fluids 24, 091701.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
Fauci, L.J. & McDonald, A. 1995 Sperm motility in the presence of boundaries. Bull. Math. Biol. 57, 679–699.CrossRefGoogle ScholarPubMed
Frymier, P.D., Ford, R.M., Berg, H.C. & Cummings, P.T. 1995 Three-dimensional tracking of motile bacteria near a solid planar surface. Proc. Natl Acad. Sci. USA 92, 6195–6199.CrossRefGoogle Scholar
Gachelin, J., Miño, G., Berthet, H., Lindner, A., Rousselet, A. & Clément, É. 2013 Non-newtonian viscosity of Escherichia coli suspensions. Phys. Rev. Lett. 110, 268103.CrossRefGoogle ScholarPubMed
Grebenkov, D.S. 2016 Universal formula for the mean first passage time in planar domains. Phys. Rev. Lett. 117, 260201.CrossRefGoogle ScholarPubMed
Happel, J. & Brenner, H. 1983 Low Reynolds Number Hydrodynamics. Martinus Nijhoff (Kluwer).Google Scholar
Hernandez-Ortiz, J.P., Stoltz, C.G. & Graham, M.D. 2005 Transport and collective dynamics in suspensions of confined swimming particles. Phys. Rev. Lett. 95, 204501.CrossRefGoogle ScholarPubMed
Hernandez-Ortiz, J.P., Underhill, P.T. & Graham, M.D. 2009 Dynamics of confined suspensions of swimming particles. J. Phys.: Condens. Matter 21, 204107.Google ScholarPubMed
Hill, J., Kalkanci, O., McMurry, J.L. & Koser, H. 2007 Hydrodynamic surface interactions enablei Escherichia coli to seek efficient routes to swim upstream. Phys. Rev. Lett. 98, 068101.CrossRefGoogle ScholarPubMed
Holcman, D. & Schuss, Z. 2014 The narrow escape problem. SIAM Rev. 56 (2), 213–257.CrossRefGoogle Scholar
Kaiser, A., Wensink, H.H. & Löwen, H. 2012 How to capture active particles. Phys. Rev. Lett. 108, 268307.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
Katz, D.F. 1974 Propulsion of microorganisms near solid boundaries. J. Fluid Mech. 64, 33–49.CrossRefGoogle Scholar
Katz, D.F. & Blake, J.R. 1975 flagellar motions near walls. Swimming Flying Nat. 1, 173–184.Google Scholar
Katz, D.F., Blake, J.R. & Paverifontana, S.L. 1975 On the movement of slender bodies near plane boundaries at low Reynolds number. J. Fluid Mech. 72, 529–540.CrossRefGoogle Scholar
Kaynan, U. & Yariv, E. 2017 Stokes resistance of a cylinder near a slippery wall. Phys. Rev. Fluids 2, 104103.CrossRefGoogle Scholar
Kim, M.Y., Drescher, K., Park, O.S., Bassler, B. & Stone, H.A. 2014 Filaments in curved streamlines: rapid formation of Staphylococcus aureus biofilm streamers. New J. Phys. 16, 065024.Google ScholarPubMed
Koumakis, N., Maggi, C. & Di Leonardo, R. 2014 Directed transport of active particles over asymmetric energy barriers. Soft Matt. 10, 5695–5701.CrossRefGoogle ScholarPubMed
Krochak, P.J., Olson, J.A. & Martinez, D.M. 2010 Near-wall estimates of the concentration and orientation distribution of a semi-dilute rigid fibre suspension in Poiseuille flow. J. Fluid Mech. 653, 431–462.CrossRefGoogle Scholar
Kurella, V., Tzou, J.C., Coombs, D. & Ward, M.J. 2015 Asymptotic analysis of first passage time problems inspired by ecology. Bull. Math. Biol. 77 (1), 83–125.CrossRefGoogle Scholar
Kurzthaler, C. & Franosch, T. 2017 Intermediate scattering function of an anisotropic Brownian circle swimmer. Soft Matt. 13, 6396–6406.CrossRefGoogle ScholarPubMed
Kurzthaler, C., Leitmann, S. & Franosch, T. 2016 Intermediate scattering function of an anisotropic active Brownian particle. Sci. Rep. 6, 36702.CrossRefGoogle ScholarPubMed
Lambert, G., Liao, D. & Austin, R.H. 2010 Collective escape of chemotactic swimmers through microscopic ratchets. Phys. Rev. Lett. 104, 168102.CrossRefGoogle ScholarPubMed
Lauga, E. 2006 Swimming in circles: motion of bacteria near solid boundaries. Biophys. J. 90, 400–412.CrossRefGoogle ScholarPubMed
Lauga, E. & Powers, T.R. 2009 The hydrodynamics of swimming microorganisms. Rep. Prog. Phys. 72, 096601.CrossRefGoogle Scholar
Lee, C.F. 2013 Active particles under confinement: aggregation at the wall and gradient formation inside a channel. New J. Phys. 15, 055007.CrossRefGoogle Scholar
Lee, M., Szuttor, K. & Holm, C. 2019 A computational model for bacterial run-and-tumble motion. J. Chem. Phys. 17, 174111.CrossRefGoogle Scholar
Lefauve, A. & Saintillan, D. 2014 Globally aligned states and hydrodynamic traffic jams in confined suspensions of active asymmetric particles. Phys. Rev. E 89, 021002.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., Tam, L. & Tanf, J. 2008 Amplified effect of Brownian motion in bacterial near-surface swimming. Proc. Natl Acad. Sci. USA 105, 18355–18359.CrossRefGoogle ScholarPubMed
Li, G. & Tang, J.X. 2009 Accumulation of microswimmers near a surface mediated by collision and rotational Brownian motion. Phys. Rev. Lett. 103, 078101.CrossRefGoogle Scholar
Li, G.-J. & Ardekani, A.M. 2014 Hydrodynamic interaction of microswimmers near a wall. Phys. Rev. E 90, 013010.CrossRefGoogle Scholar
Lopez, D. & Lauga, E. 2014 Dynamics of swimming bacteria at complex interfaces. Phys. Fluids 26, 071902.CrossRefGoogle Scholar
Lushi, E. 2016 Stability and dynamics of anisotropically-tumbling chemotactic swimmers. Phys. Rev. E 94, 022414.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.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., Kantsler, V. & Goldstein, R.E. 2017 Scattering of biflagellate microswimmers from surfaces. Phys. Rev. E 96 (2), 023102.CrossRefGoogle ScholarPubMed
Lushi, E. & Vlahovska, P.M. 2015 Periodic and chaotic orbits of plane-confined micro-rotors in creeping flows. J. Nonlinear Sci. Appl. 25, 1111–1123.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
Majda, A.J. & Kramer, P.R. 1999 Simplified models for turbulent diffusion: theory, numerical modelling and physical phenomena. Phys. Rep. 314 (4–5), 237–574.CrossRefGoogle Scholar
Malgaretti, P. & Stark, H. 2017 Model microswimmers in channels with varying cross section. J. Chem. Phys. 146, 174901.CrossRefGoogle ScholarPubMed
Marchetti, M.C., Joanny, J.F., Ramaswamy, S., Liverpool, T.B., Prost, J., Rao, M. & Simha, R.A. 2013 Hydrodynamics of soft active matter. Rev. Mod. Phys. 85, 1143–1189.CrossRefGoogle Scholar
Marcotte, F., Doering, C.R., Thiffeault, J.-L & Young, W.R. 2018 Optimal heat transfer and optimal exit times. SIAM J. Appl. Maths 78 (1), 591–608.CrossRefGoogle Scholar
Martens, K., Angelani, L., Di Leonardo, R. & Bocquet, L. 2012 Probability distributions for the run-and-tumble bacterial dynamics: an analogy to the Lorentz model. Europhys. Lett. 35, 1–6.Google ScholarPubMed
Mathijssen, A.J.T.M., Doostmohammadi, A., Yeomans, J.M. & Shendruk, T.N. 2016 Hotspots of boundary accumulation: dynamics and statistics of microswimmers in flowing films. J. R. Soc. Interface 13, 20150936.CrossRefGoogle Scholar
McCarty, P. & Horsthemke, W. 1988 Effective diffusion for steady two-dimensional flow. Phys. Rev. A 37 (6), 2112–2117.CrossRefGoogle Scholar
Mirzakhanloo, M. & Alam, M.-R. 2018 Flow characteristics of Chlamydomonas result in purely hydrodynamic scattering. Phys. Rev. E 98 (1), 012603.CrossRefGoogle ScholarPubMed
Mok, R., Dunkel, J. & Kantsler, V. 2019 Geometric control of bacterial surface accumulation. Phys. Rev. E 99, 052607.CrossRefGoogle ScholarPubMed
Molaei, M., Barry, M., Stocker, R. & Sheng, J. 2014 Failed escape: solid surfaces prevent tumbling of Escherichia coli. Phys. Rev. Lett. 113, 068103.CrossRefGoogle ScholarPubMed
Nash, R.W., Adhikari, R., Tailleur, J. & Cates, M.E. 2010 Run-and-tumble particles with hydrodynamics: sedimentation, trapping, and upstream swimming. Phys. Rev. Lett. 104, 258101.CrossRefGoogle ScholarPubMed
Nikola, N., Solon, A.P., Kafri, Y., Kardar, M., Tailleur, J. & Voituriez, R. 2016 Active particles with soft and curved walls: equation of state, ratchets, and instabilities. Phys. Rev. Lett. 117, 098001.CrossRefGoogle ScholarPubMed
Nitsche, J.M. & Brenner, H. 1990 On the formulation of boundary conditions for rigid non spherical Brownian particles near solid walls: applications to orientation-specific reactions with immobilized enzymes. J. Colloid Interface Sci. 138, 21–41.CrossRefGoogle Scholar
Obuse, K. & Thiffeault, J.-L. 2012 A low-Reynolds-number treadmilling swimmer near a semi-infinite wall. In IMA Volume on Natural Locomotion in Fluids and on Surfaces: Swimming, Flying, and Sliding (ed. S. Childress, A. Hosoi, W.W. Schultz & J. Wang), pp. 197–206. Springer.CrossRefGoogle Scholar
Paksa, A., et al. 2016 Repulsive cues combined with physical barriers and cell–cell adhesion determine progenitor cell positioning during organogenesis. Nat. Commun. 7, 11288.CrossRefGoogle ScholarPubMed
Pavliotis, G.A. 2014 Stochastic Processes and Applications. Springer.CrossRefGoogle Scholar
Razin, N., Voituriez, R., Elgeti, J. & Gov, N.S. 2017 Generalized Archimedes’ principle in active fluids. Phys. Rev. E 96, 032606.CrossRefGoogle ScholarPubMed
Redner, G.S., Hagan, M.F. & Baskaran, A. 2013 Structure and dynamics of a phase-separating active colloidal fluid. Phys. Rev. Lett. 110, 055701.CrossRefGoogle ScholarPubMed
Redner, S. 2001 A Guide to First-Passage Processes. Cambridge University Press.CrossRefGoogle Scholar
Rothschild, L. 1963 Non-random distribution of bull spermatozoa in a drop of sperm suspension. Nature 198, 1221–1222.CrossRefGoogle Scholar
Rusconi, R., Lecuyer, S., Guglielmini, L. & Stone, H.A. 2010 Laminar flow around corners triggers the formation of biofilm streamers. J. R. Soc. Interface 7, 1293–1299.CrossRefGoogle ScholarPubMed
Sagues, F. & Horsthemke, W. 1986 Diffusive transport in spatially periodic hydrodynamic flows. Phys. Rev. A 34 (5), 4136–4143.CrossRefGoogle ScholarPubMed
Saintillan, D. 2010 The dilute rheology of swimming suspensions: a simple kinetic model. Expl Mech. 50, 1275–1281.CrossRefGoogle Scholar
Saintillan, D., Shaqfeh, E.S.G. & Darve, E. 2006 a Effect of flexibility on the shear-induced migration of short-chain polymers in parabolic channel flow. J. Fluid Mech. 557, 297–306.CrossRefGoogle Scholar
Saintillan, D., Shaqfeh, E.S.G. & Darve, E. 2006 b The growth of concentration fluctuations in dilute dispersions of orientable and deformable particles under sedimentation. J. Fluid Mech. 553, 347–388.CrossRefGoogle Scholar
Saintillan, D. & Shelley, M.J. 2007 Orientational order and instabilities in suspensions of self-locomoting rods. Phys. Rev. Lett. 99, 058102.CrossRefGoogle ScholarPubMed
Saintillan, D. & Shelley, M.J. 2008 Instabilities and pattern formation in active particle suspensions: kinetic theory and continuum simulations. Phys. Rev. Lett. 100, 178103.CrossRefGoogle ScholarPubMed
Saintillan, D. & Shelley, M.J. 2011 Emergence of coherent structures and large-scale flows in motile suspensions. J. R. Soc. Interface 9, 571–585.CrossRefGoogle ScholarPubMed
Saintillan, D. & Shelley, M.J. 2013 Active suspensions and their nonlinear models. C. R. Phys. 14, 497–517.CrossRefGoogle Scholar
Schaar, K., Zöttl, A. & Stark, H. 2015 Detention times of microswimmers close to surfaces: influence of hydrodynamic interactions and noise. Phys. Rev. Lett. 115 (3), 038101.CrossRefGoogle ScholarPubMed
Sepúlveda, N. & Soto, R. 2017 Wetting transitions displayed by persistent active particles. Phys. Rev. Lett. 119, 078001.CrossRefGoogle ScholarPubMed
Sepúlveda, N. & Soto, R. 2018 Universality of active wetting transitions. Phys. Rev. E 98, 052141.CrossRefGoogle Scholar
Shum, H., Gaffney, E. & Smith, D. 2010 Modelling bacterial behaviour close to a no-slip plane boundary: the influence of bacterial geometry. Proc. R. Soc. A 466, 1725–1748.CrossRefGoogle Scholar
Sipos, O., Nagy, K., Di Leonardo, R. & Galajda, P. 2015 Hydrodynamic trapping of swimming bacteria by convex walls. Phys. Rev. Lett. 114, 258104.CrossRefGoogle ScholarPubMed
Solon, A.P., Fily, Y., Baskaran, A., Cates, M.E., Kafri, Y., Kardar, M. & Tailleur, J. 2015 Pressure is not a state function for generic active fluids. Nat. Phys. 11, 673–678.CrossRefGoogle Scholar
Spagnolie, S.E. & Lauga, E. 2012 Hydrodynamics of self-propulsion near boundaries: predictions and accuracy of far-field approximations. J. Fluid Mech. 700, 105–147.CrossRefGoogle Scholar
Spagnolie, S.E., Moreno-Flores, G.R., Bartolo, D. & Lauga, E. 2015 Geometric capture and escape of a microswimmer colliding with an obstacle. Soft Matt. 11, 3396–3411.CrossRefGoogle ScholarPubMed
Speck, T. 2020 Collective forces in scalar active matter. Soft Matt. 16, 2652–2663.CrossRefGoogle ScholarPubMed
Stenhammar, J., Marenduzzo, D., Allen, R.J. & Cates, M.E. 2014 Phase behaviour of active Brownian particles: the role of dimensionality. Soft Matt. 10, 1489–1499.CrossRefGoogle Scholar
Swan, J.W. & Brady, J.F. 2007 Simulation of hydrodynamically interacting particles near a no-slip boundary. Phys. Fluids 19, 113306.CrossRefGoogle Scholar
Tailleur, J. & Cates, M.E. 2009 Sedimentation, trapping, and rectification of dilute bacteria. Europhys. Lett. 86, 60002.CrossRefGoogle Scholar
Takagi, D., Palacci, J., Braunschweig, A., Shelley, M. & Zhang, J. 2014 Hydrodynamic capture of microswimmers into sphere-bound orbits. Soft Matt. 10, 1784–1789.CrossRefGoogle ScholarPubMed
Takatori, S.C., Yan, W. & Brady, J.F. 2014 Swim pressure: stress generation in active matter. Phys. Rev. Lett. 113, 028103.CrossRefGoogle ScholarPubMed
van Teeffelen, S. & Löwen, H. 2008 Dynamics of a Brownian circle swimmer. Phys. Rev. E 78, 020101.CrossRefGoogle ScholarPubMed
ten Hagen, B., Wittkowski, R. & Löwen, H. 2011 Brownian dynamics of a self-propelled particle in shear flow. Phys. Rev. E 84, 031105.CrossRefGoogle ScholarPubMed
ten Hagen, B., Wittkowski, R., Takagi, D., Kümmel, F., Bechinger, C. & Löwen, H. 2015 Can the self-propulsion of anisotropic microswimmers be described by using forces and torques. J. Phys.: Condens. Matter 27, 194110.Google ScholarPubMed
Theers, M., Westphal, E., Qi, K., Winkler, R.G. & Gompper, G. 2018 Clustering of microswimmers: interplay of shape and hydrodynamics. Soft Matt. 14, 8590–8603.CrossRefGoogle ScholarPubMed
Theillard, M., Matilla, R.A. & Saintillan, D. 2017 Geometric control of active collective motion. Soft Matt. 13, 363–375.CrossRefGoogle ScholarPubMed
Tian, W., Gu, Y., Guo, Y. & Chen, K. 2017 Anomalous boundary deformation induced by enclosed active particles. Chin. Phys. B 26, 100502.CrossRefGoogle Scholar
Volpe, G., Buttinoni, I., Vogt, D., Kümmerer, H.J. & Bechinger, C. 2011 Microswimmers in patterned environments. Soft Matt. 7, 8810–8815.CrossRefGoogle Scholar
Volpe, G., Gigan, S. & Volpe, G. 2014 Simulation of the active Brownian motion of a microswimmer. Am. J. Phys. 82 (7), 659–664.CrossRefGoogle Scholar
Wagner, C., Hagan, M. & Baskaran, A. 2019 Response of active Brownian particles to boundary driving. Phys. Rev. E 100, 042610.CrossRefGoogle ScholarPubMed
Wagner, C., Hagan, M.F. & Baskaran, A. 2017 Steady-state distributions of ideal active Brownian particles under confinement and forcing. J. Stat. Mech. 4 (4), 043203.CrossRefGoogle Scholar
Ward, M.J. & Keller, J.B. 1993 Strong localized perturbations of eigenvalue problems. SIAM J. Appl. Maths 53 (3), 770–798.CrossRefGoogle Scholar
Wensink, H.H. & Löwen, H. 2008 Aggregation of self-propelled colloidal rods near confining walls. Phys. Rev. E 78, 031409.CrossRefGoogle ScholarPubMed
Wioland, H., Lushi, E. & Goldstein, R.E. 2016 Directed collective motion of bacteria under channel confinement. New J. Phys. 18, 081001.CrossRefGoogle Scholar
Woolley, D.M. 2003 Motility of spermatozoa at surfaces. Reproduction 126, 259–270.CrossRefGoogle ScholarPubMed
Yan, W. & Brady, J.F. 2015 The force on a boundary in active matter. J. Fluid Mech. 785, R1.CrossRefGoogle Scholar
Yariv, E. & Schnitzer, O. 2014 Ratcheting of Brownian swimmers in periodically corrugated channels: a reduced Fokker–Planck approach. Phys. Rev. E 90, 032115.CrossRefGoogle ScholarPubMed
Yeo, K., Lushi, E. & Vlahovska, P.M. 2015 Collective dynamics in a binary mixture of hydrodynamically coupled micro-rotors. Phys. Rev. Lett. 114, 188301.CrossRefGoogle Scholar
Zargar, R., Najafi, A. & Miri, M. 2009 Three-sphere low-Reynolds-number swimmer near a wall. Phys. Rev. E 80, 026308.CrossRefGoogle Scholar
Zöttl, A. & Stark, H. 2016 Emergent behavior in active colloids. J. Phys.: Condens. Matter 28, 253001.Google Scholar