Abstract
Active suspensions, of which a bath of swimming microorganisms is a paradigmatic example, denote large collections of individual particles or macromolecules capable of converting fuel into mechanical work and microstructural stresses. Such systems, which have excited much research in the last decade, exhibit complex dynamical behaviors such as large-scale correlated motions and pattern formation due to hydrodynamic interactions. In this chapter, we summarize efforts to model these systems using particle simulations and continuum kinetic theories. After reviewing results from experiments and simulations, we present a general kinetic model for a suspension of self-propelled rodlike particles and discuss its stability and nonlinear dynamics. We then address extensions of this model that capture the effect of steric interactions in concentrated systems, the impact of confinement and interactions with boundaries, and the effect of the suspending medium rheology. Finally, we discuss new active systems such as those that involve the interactions of biopolymers with immersed motor proteins and surface-bound suspensions of chemically powered particles.
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References
I. Aranson, Physics 6, 61 (2013)
H.P. Zhang, A. Be’er, E.L. Florin, H.L. Swinney, Proc. Natl. Acad. Sci. USA 107, 13626 (2010)
T. Sanchez, D. Chen, S. DeCamp, M. Heymann, Z. Dogic, Nature 491, 431 (2012)
V. Schaller, C. Weber, C. Semmrich, E. Frey, A.R. Bausch, Nature 467, 73 (2010)
S. Thutupalli, R. Seeman, S. Herminghaus, New J. Phys. 13, 073021 (2011)
C.A. Weber, T. Hanke, J. Deseigne, S. Léonard, O. Dauchot, E. Frey, H. Chaté, Phys. Rev. Lett. 110, 208001 (2013)
S. Ramaswamy, Annu. Rev. Condens. Matt. 1, 323 (2010)
M.C. Marchetti, J.F. Joanny, S. Ramaswamy, T.B. Liverpool, J. Prost, M. Rao, R. Aditi Simha. Rev. Mod. Phys. 85, 1143 (2013)
D. Saintillan, M.J. Shelley, C.R. Physique 14, 497 (2013)
C. Dombrowski, L. Cisneros, S. Chatkaew, R.E. Goldstein, J.O. Kessler, Phys. Rev. Lett. 93, 098103 (2004)
L.H. Cisneros, J.O. Kessler, S. Ganguly, R.E. Goldstein, Phys. Rev. E 83, 061907 (2011)
J. Dunkel, S. Heidenreich, K. Drescher, H.H. Wensink, M. Bar, R.E. Goldstein, Phys. Rev. Lett. 110, 228102 (2013)
S. Köhler, V. Schaller, A.R. Bausch, PLoS ONE 6, e23798 (2011)
T. Shinar, M. Mana, F. Piano, M. Shelley, Proc. Natl. Acad. Sci. 108, 10508 (2011)
F. Woodhouse, R.E. Goldstein, Proc. Natl. Acad. Sci. USA 110, 14132 (2013)
F. Nedelec, T. Surrey, A.C. Maggs, S. Leibler, Nature 389, 305 (1997)
Y. Sumino, K.H. Nagai, Y. Shitaka, D. Tanaka, K. Yoshikawa, H. Chaté, K. Oiwa, Nature 483, 448 (2012)
W.F. Paxton, K.C. Kistler, C.C. Olmeda, A. Sen, S.K.S. Angelo, Y. Cao, T.E. Mallouk, P.E. Lammert, V.H. Crespi, J. Am. Chem. Soc. 126, 13424 (2004)
J.R. Howse, R.A.L. Jones, A.J. Ryan, T. Gough, R. Vafabakhsh, R. Golestanian, Phys. Rev. Lett. 99, 048102 (2007)
S.J. Ebbens, J.R. Howse, Soft Matter 6, 726 (2010)
D. Takagi, A. Braunschweig, J. Zhang, M. Shelley, Phys. Rev. Lett. 110, 038301 (2013)
A. Bricard, J.B. Caussin, N. Desreumaux, O. Dauchot, D. Bartolo, Nature 503, 95 (2013)
A. Kudrolli, G. Lumay, D. Volfson, L.S. Tsimring, Phys. Rev. Lett. 100, 058001 (2008)
J. Deseigne, O. Dauchot, H. Chaté, Phys. Rev. Lett. 105, 098001 (2010)
T. Vicsek, A. Zafeiris, Phys. Rep. 517, 71 (2012)
N.H. Mendelson, A. Bourque, K. Wilkening, K.R. Anderson, J.C. Watkins, J. Bacteriol. 181, 600 (1999)
I. Tuval, L. Cisneros, C. Dombrowski, C.W. Wolgemuth, J.O. Kessler, R.E. Goldstein, Proc. Natl. Acad. Sci. USA 102, 2277 (2005)
A. Sokolov, R.E. Goldstein, F.I. Feldchtein, I.S. Aranson, Phys. Rev. E 80, 031903 (2009)
X.L. Wu, A. Libchaber, Phys. Rev. Lett. 84, 3017 (2000)
K.C. Leptos, J.S. Guasto, J.P. Gollub, A.I. Pesci, R.E. Goldstein, Phys. Rev. Lett. 103, 198103 (2009)
G.L. Miño, J. Dunstan, A. Rousselet, E. Clément, R. Soto, J. Fluid Mech. 729, 423 (2013)
J. Orozco, B. Jurado-Sánchez, G. Wagner, W. Gao, R. Vazquez-Duhalt, S. Sattayasamitsathit, M. Galarnyk, A. Cortés, D. Saintillan, J. Wang, Langmuir 30, 5082 (2014)
M.J. Kim, K.S. Breuer, Anal. Chem. 79, 955 (2007)
H. Kurtuldu, J.S. Guasto, K.A. Johnson, J.P. Gollub, Phys. Rev. Lett. 108, 10391 (2011)
A. Sokolov, I.S. Aranson, Phys. Rev. Lett. 103, 148101 (2009)
L. Giomi, T.B. Liverpool, M.C. Marchetti, Phys. Rev. E 81, 051908 (2010)
D. Saintillan, Exp. Mech. 50, 1275 (2010)
J. Gachelin, G. Miño, H. Berthet, A. Lindner, A. Rousselet, E. Clément, Phys. Rev. Lett. 110, 268103 (2013)
E. Lauga, T.R. Powers, Rep. Prog. Phys. 72, 096601 (2009)
E.M. Purcell, Am. J. Phys. 45, 3 (1977)
C. Brennen, H. Winet, Annu. Rev. Fluid Mech. 9, 339 (1977)
K. Drescher, J. Dunkel, L.H. Cisneros, S. Ganguly, R.E. Goldstein, Proc. Natl. Acad. Sci. USA 108, 10940 (2011)
J.S. Guasto, K.A. Johnson, J.P. Gollub, Phys. Rev. Lett. 105, 168102 (2010)
S. Kim, S.J. Karrila, Microhydrodynamics: Principles and Selected Applications (Dover, NewYork, 2005)
K. Drescher, R.E. Goldstein, N. Michel, M. Polin, I. Tuval, Phys. Rev. Lett. 105, 168101 (2010)
S. Fürthauer, S. Ramaswamy, Phys. Rev. Lett. 111, 238102 (2013)
M. Leoni, T.B. Liverpool, Phys. Rev. Lett. 112, 148104 (2014)
T. Ishikawa, M.P. Simmonds, T.J. Pedley, J. Fluid Mech. 568, 119 (2006)
Q. Liao, G. Subramanian, M.P. DeLisa, D.L. Koch, M. Wu, Phys. Fluids 19, 061701 (2007)
V. Gyrya, I.S. Aranson, L.V. Berlyand, D. Karpeev, Bull. Math. Bio. 72, 148 (2010)
J.P. Hernández-Ortiz, C.G. Stoltz, M.D. Graham, Phys. Rev. Lett. 95, 204501 (2005)
J.P. Hernández-Ortiz, P.T. Underhill, M.D. Graham, J. Phys.: Condens. Matter 21, 204107 (2009)
J.R. Blake, J. Fluid Mech. 46, 199 (1971)
T. Ishikawa, T.J. Pedley, J. Fluid Mech. 588, 437 (2007)
T. Ishikawa, J.T. Locsei, T.J. Pedley, Phys. Rev. E 82, 021408 (2010)
T. Ishikawa, T.J. Pedley, Phys. Rev. Lett. 100, 088103 (2008)
T. Ishikawa, J.T. Locsei, T.J. Pedley, J. Fluid Mech. 615, 401 (2008)
A.A. Evans, T. Ishikawa, T. Yamaguchi, E. Lauga, Phys. Fluids 23, 111702 (2011)
D. Saintillan, M. Shelley, J.R. Soc. Interface 9, 571 (2012)
D. Saintillan, M. Shelley, Phys. Rev. Lett. 99, 058102 (2007)
R.A. Simha, S. Ramaswamy, Phys. Rev. Lett. 89, 058101 (2002)
I.S. Aranson, A. Sokolov, J.O. Kessler, R.E. Goldstein, Phys. Rev. E 75, 040901 (2007)
C. Wolgemuth, J. Biophys.95, 1564 (2008)
S. Mishra, A. Baskaran, M.C. Marchetti, Phys. Rev. E 81, 061916 (2010)
J. Dunkel, S. Heidenreich, M. Bär, R.E. Goldstein, New J. Phys. 15, 045016 (2013)
D. Saintillan, M. Shelley, Phys. Rev. Lett. 100, 178103 (2008)
D. Saintillan, M. Shelley, Phys. Fluids 20, 123304 (2008)
A. Alizadeh Pahlavan, D. Saintillan, Phys. Fluids 23, 011901 (2011)
B. Ezhilan, A. Alizadeh Pahlavan, D. Saintillan, Phys. Fluids 24, 091701 (2012)
E. Lushi, R.E. Goldstein, M.J. Shelley, Phys. Rev. E 86, 040902 (2012)
B. Ezhilan, M.J. Shelley, D. Saintillan, Phys. Fluids 25, 070607 (2013)
M. Doi, S.F. Edwards, The Theory of Polymer Dynamics (Oxford University Press, Oxford, 1986)
D.L. Koch, E.S.G. Shaqfeh, J. Fluid Mech. 209, 521 (1989)
G. Subramanian, D.L. Koch, J. Fluid Mech. 632, 359 (2009)
G.B. Jeffery, Proc. R. Soc. Lond. A 102, 161 (1922)
F.P. Bretherton, J. Fluid Mech. 14, 284 (1962)
G.K. Batchelor, J. Fluid Mech. 44, 419 (1970)
M. Garcia, S. Berti, P. Peyla, S. Rafaï, Phys. Rev. E 83, 035301 (2011)
H. Brenner, J. Colloid Interface Sci. 71, 189 (1979)
H. Brenner, PhysicoChem. Hydrodyn. 1, 91 (1980)
H.C. Berg, Random Walks in Biology (Princeton University Press, Princeton, 1983)
P. Underhill, J. Hernández-Ortiz, M. Graham, Phys. Rev. Lett. 100, 248101 (2008)
E.J. Hinch, L.G. Leal, J. Fluid Mech. 76, 187 (1976)
J.H. Irving, J.G. Kirkwood, J. Chem. Phys. 18, 817 (1950)
G.K. Batchelor, J. Fluid Mech. 41, 545 (1970)
C. Hohenegger, M. Shelley, in New Trends in the Physics and Mechanics of Biological Systems, ed. by M. Ben-Amar, A. Goriely, M. Muller, L. Cugliandolo (Oxford University Press, Oxford, 2011)
M. Doi, S.F. Edwards, J. Chem. Soc. Faraday Trans. II 74, 560 (1978)
X. Chen, J.G. Liu, J. Differ. Equat. 254, 2764 (2013)
A. Baskaran, M.C. Marchetti, Proc. Natl. Acad. Sci. USA 106, 15567 (2009)
C. Hohenegger, M. Shelley, Phys. Rev. E 81, 046311 (2010)
M. Betterton, A.S. Jhang, M. Shelley, In preparation (2014)
J.E. Butler, E.S.G. Shaqfeh, J. Fluid Mech. 468, 205 (2002)
A. Baskaran, M.C. Marchetti, J. Stat. Mech.: Theor. Exp. 2010, 04019 (2010)
L. Onsager, Ann. N. Y. Acad. Sci. 51, 627 (1949)
W. Maier, A. Saupe, Z. Naturforsch. 13, 564 (1958)
P.D. Cobb, J.E. Butler, J. Chem. Phys. 123, 054908 (2005)
E.S.G. Shaqfeh, G.H. Fredrickson, Phys. Fluids A 2, 7 (1990)
P.R. Nott, E. Guazzelli, O. Pouliquen, Phys. Fluids 23, 043304 (2011)
A.P. Berke, L. Turner, H.C. Berg, E. Lauga, Phys. Rev. Lett. 101, 038102 (2008)
G. Li, J.X. Tang, Phys. Rev. Lett. 103, 078101 (2009)
J. Hill, O. Kalkanci, J.L. McMurry, H. Koser, Phys. Rev. Lett. 98, 068101 (2007)
V. Kantsler, J. Dunkel, M. Polin, R.E. Goldstein, Proc. Natl. Acad. Sci. USA 110, 1187 (2013)
E. Altshuler, G. Miño, C. Perez-Penichet, L. del Rio, A. Lindner, A. Rousselet, E. Clément, Soft Matter 9, 1864 (2013)
G. Miño, T.E. Mallouk, T. Darnige, M. Hoyos, J. Dauchet, J. Dunstan, R. Soto, Y. Wang, A. Rousselet, E. Clément, Phys. Rev. Lett. 106, 048102 (2011)
E. Lauga, W.R. DiLuzio, G.M. Whitesides, H.A. Stone, J. Biophys. 90, 400 (2006)
F.G. Woodhouse, R.E. Goldstein, Phys. Rev. Lett. 109, 168105 (2012)
H. Wioland, F.G. Woodhouse, J. Dunkel, J.O. Kessler, R.E. Goldstein, Phys. Rev. Lett. 110, 268102 (2013)
A. Costanzo, R. Di Leonardo, G. Ruocco, L. Angelani, J. Phys.: Condens. Matter 24, 065101 (2012)
S. Chilukuri, C.H. Collins, P.T. Underhill, J. Phys.: Condens. Matter 26, 115101 (2014)
S.E. Spagnolie, E. Lauga, J. Fluid Mech. 700, 105 (2012)
R. Voituriez, J.F. Joanny, J. Prost, Europhys. Lett. 70, 404 (2005)
S.A. Edwards, J.M. Yeomans, Europhys. Lett. 85, 18008 (2009)
M. Ravnik, J.M. Yeomans, Phys. Rev. Lett. 110, 026001 (2013)
D. Takagi, J. Palacci, A. Braunschweig, M. Shelley, J. Zhang, Soft Matter 10, 1784 (2014)
R.L. Schiek, E.S.G. Shaqfeh, J. Fluid Mech. 296, 271 (1995)
B. Ezhilan, D. Saintillan, Submitted (2014)
T. Kaya, H. Koser, Biophys. J. 102, 1514 (2012)
Y. Shen, A. Siryapon, S. Lecuyer, Z. Gitai, H.A. Stone, Biophys. J. 103, 146 (2012)
R.W. Nash, R. Adhikari, J. Tailleur, M.E. Cates, Phys. Rev. Lett. 104, 258101 (2010)
A. Jhang, M. Shelley, In preparation (2014)
T. Brotto, J.B. Caussin, E. Lauga, D. Bartolo, Phys. Rev. Lett. 110, 038101 (2013)
N. Liron, S. Mochon, J. Eng. Math. 10, 287 (1976)
S. Bhattacharya, J. BÅ‚awzdziewicz, E. Wajnryb, J. Comp. Phys. 212, 718 (2006)
A. Lefauve, D. Saintillan, Phys. Rev. E 89, 021002 (2014)
A.C.H. Tsang, E. Kanso, Flagella-induced transitions in the collective behavior of confined microswimmers. Phys. Rev. E 90, 021001(R) (2014)
H.C. Berg, D.A. Brown, Nature 239, 500 (1972)
G. Subramanian, D.L. Koch, S.R. Fitzgibbon, Phys. Fluids 23, 041901 (2011)
T. Kasyap, D. Koch, Phys. Rev. Lett. 108, 038101 (2012)
T. Kasyap, D. Koch, J. Fluid Mech. 741, 619 (2014)
E.O. Budrene, H.C. Berg, Nature 349, 630 (1991)
B.L. Bassler, Cell 109, 421 (2002)
S. Park, P.M. Wolanin, E.A. Yuzbashyan, P. Silberzan, J.B. Stock, R.H. Austin, Science 301, 188 (2003)
E.F. Keller, L.A. Segel, J. Theor. Biol. 30, 225 (1971)
J.R. Vélez-Cordero, E. Lauga, J Non-Newtonian Fluid Mech 199, 37 (2013)
Y. Bozorgi, P. Underhill, Phys. Rev. E 84, 061901 (2011)
Y. Bozorgi, P. Underhill, J. Rheo. 57, 511 (2013)
R.B. Bird, R.C. Armstrong, O. Hassager, Dynamics of Polymeric Liquids (Wiley-Interscience, 1987)
K.J. Helmke, R. Heald, J.D. Wilbur, Int Rev Cell Mol Biol 306, 83 (2013)
A. Kimura, S. Onami, Dev Cell 8, 765 (2005)
C.S. Peskin, Acta numerica 11, 479 (2002)
K. Kimura, A. Kimura, Proc. Natl. Acad. Sci. USA 108, 137 (2011)
T. Gao, R. Blackwell, M. Glaser, M. Betterton, M. Shelley, Submitted (2014)
T. Surrey, F. Nédélec, S. Leibler, E. Karsenti, Science 292, 1167 (2001)
L. Giomi, M. Bowick, X. Ma, M. Marchetti, Phys. Rev. Lett. 110, 228101 (2013)
S. Thampi, R. Golestanian, J. Yeomans, Phys. Rev. Lett. 111, 118101 (2013)
H. Masoud, M. Shelley, Phys. Rev. Lett. 112, 128304 (2014)
J. Wang, Nanomachines: Fundamentals and Applications (Wiley, NewYork, 2013)
J.L. Moran, P.M. Wheat, J.D. Posner, Phys. Rev. E 81, 065302 (2010)
Y. Hong, N.M. Blackman, N.D. Kopp, A. Sen, D. Velegol, Phys. Rev. Lett. 99, 178103 (2007)
Y. Hong, D. Velegol, N. Chaturvedi, A. Sen, Phys. Chem. Chem. Phys. 12, 1423 (2010)
H. Masoud, H.A. Stone, J. Fluid Mech. 741, R4 (2014)
T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen, O. Shochet, Phys. Rev. Lett. 74, 1226 (1995)
D. Horstmann, From 1970 until present: The Keller-Segel model in chemotaxis and its consequences. Jahresber. Deutsch. Math.-Verein. 105, 103–165 (2003)
Acknowledgment
We thank our many students and postdocs that have worked with us on the topic of active suspensions and materials. We also much appreciate the editorial patience extended to us during the preparation of this chapter. DS acknowledges the support of NSF grants DMS-0920931 and CBET-1150590 (CAREER). MJS acknowledges the support of NSF grants DMR-0820341 (NYU MRSEC), DMS-0920930, DOE grant DE-FG02-88ER25053, and NIH grant R01 GM104976-03.
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Saintillan, D., Shelley, M.J. (2015). Theory of Active Suspensions. In: Spagnolie, S. (eds) Complex Fluids in Biological Systems. Biological and Medical Physics, Biomedical Engineering. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2065-5_9
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