Abstract
Hydrodynamics and hydrodynamic interactions are fundamental for the motility of microswimmers. This includes the propulsion mechanism itself, the synchronized motion of flagella in flagellar bundles and beating cilia of cilia arrays, and even extends to collective behaviors. The general importance of hydrodynamics has stimulated the development of mesoscale simulation approaches to efficiently study dynamical properties of objects embedded in a fluid. In this minireview, the properties of flows at low Reynolds numbers are discussed, thereby the unsteady acceleration term is typically taken into account (Landau-Lifshitz Navier-Stokes equations). Specifically, the synchronization of microrotors by time-dependent hydrodynamic interactions is discussed and the propulsion of a rotating helix. Moreover, the multiparticle collisions dynamics method (MPC), a mesoscale simulation approach for fluids, is outlined. Simulation results for the flow field of a model E. Coli bacterium and its swimming behavior next to a surface are presented.
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References
J. Elgeti, R.G. Winkler, G. Gompper, Rep. Prog. Phys. 78, 056601 (2015)
J.M. Yeomans, D.O. Pushkin, H. Shum, Eur. Phys. J. Special Topics 223, 1771 (2014)
E. Lauga, T.R. Powers, Rep. Prog. Phys. 72, 096601 (2009)
D.B. Kearns, Nat. Rev. Microbiol. 8, 634 (2010)
M. Polin, I. Tuval, K. Drescher, J.P. Gollub, R.E. Goldstein, Science 325, 487 (2009)
R. Stocker, W.M. Durham, Science 325, 400 (2009)
B. Afzelius, Science 193, 317 (1976)
Q. Wang, J. Pan, W.J. Snell, Cell 125, 549 (2006)
J.H.E. Cartwright, O. Piro, I. Tuval, Proc. Natl. Acad. Sci. USA 101, 7234 (2004)
E.M. Purcell, Am. J. Phys. 45, 3 (1977)
J. Sivinski, in Sperm Competition and the Evolution of Animal Mating Systems, edited by R.L. Smith (Academic, Orlando, 1984), p. 174
H.H. Wensink, J. Dunkel, S. Heidenreich, K. Drescher, R.E. Goldstein, H. Löwen, J.M. Yeomans, Proc. Natl. Acad. Sci. USA 109, 14308 (2012)
N.C. Darnton, L. Turner, S. Rojevsky, H.C. Berg, Biophys. J. 98, 2082 (2010)
M.A. Sleigh, The Biology of Cilia and Flagella (Pergamon Press, Oxford, 1962)
P.J. Hoogerbrugge, J.M. V.A. Koelman, Europhys. Lett. 19, 155 (1992)
P. Español, Phys. Rev. E 52, 1734 (1995)
G.R. McNamara, G. Zanetti, Phys. Rev. Lett. 61, 2332 (1988)
X. Shan, H. Chen, Phys. Rev. E 47, 1815 (1993)
X. He, L.-S. Luo, Phys. Rev. E 56, 6811 (1997)
G.A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Oxford University Press, Oxford, 1994)
A. Malevanets, R. Kapral, J. Chem. Phys. 110, 8605 (1999)
R. Kapral, Adv. Chem. Phys. 140, 89 (2008)
G. Gompper, T. Ihle, D.M. Kroll, R.G. Winkler, Adv. Polym. Sci. 221, 1 (2009)
D. Marenduzzo, Eur. Phys. J. Special Topics 225, 2065 (2016)
L.D. Landau, E.M. Lifshitz, Fluid Mechanics (Pergamon Press, London, 1959)
J.P. Boon, S. Yip, Molecular Hydrodynamics (Dover, New York, 1980)
J.-P. Hansen, I.R. McDonald, Theory of Simple Liquids (Academic Press, London, 1986)
C.C. Huang, G. Gompper, R.G. Winkler, J. Chem. Phys. 138, 144902 (2013)
J.K. G. Dhont, An Introduction to Dynamics of Colloids (Elsevier, Amsterdam, 1996)
E. Lauga, Phys. Fluids 19, 061703 (2007)
M. Theers, R.G. Winkler, Soft Matter 10, 5894 (2014)
M. Doi, S.F. Edwards, The Theory of Polymer Dynamics (Clarendon Press, Oxford, 1986)
E. Lauga, Soft Matter 7, 3060 (2011)
B. Friedrich, Eur. Phys. J. Special Topics 225, 3053 (2016)
C.-C. Huang, G. Gompper, R.G. Winkler, Phys. Rev. E 86, 056711 (2012)
B.J. Alder, T.E. Wainwright, Phys. Rev. A 1, 18 (1970)
R. Zwanzig, M. Bixon, Phys. Rev. A 2, 2005 (1970)
A. Pikovsky, M. Rosenblum, J. Kurths, Synchronization: A Universal Concept in Nonlinear Science (Cambridge University Press, 2002)
S.H. Strogatz, Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life (Hyperion, 2004)
P. Lenz, A. Ryskin, Phys. Biol. 3, 285 (2006)
M. Theers, R.G. Winkler, Phys. Rev. E 88, 023012 (2013)
R.G. Winkler, J. Chem. Phys. 127, 054904 (2007)
E. Lauga, W.R. DiLuzio, G.M. Whitesides, H.A. Stone, Biophys. J. 90, 400 (2006)
B. Rodenborn, C.-H. Chen, H.L. Swinney, B. Liu, H.P. Zhang, Proc. Natl. Acad. Sci. USA 110, E338 (2013)
T. Ishikawa, J. R. Soc. Interface 6, 815 (2009)
K. Drescher, J. Dunkel, L.H. Cisneros, S. Ganguly, R.E. Goldstein, Proc. Natl. Acad. Sci. USA 108, 10940 (2011)
J. Hu, M. Yang, G. Gompper, R.G. Winkler, Soft Matter 11, 7843 (2015)
E. Allahyarov, G. Gompper, Phys. Rev. E 66, 036702 (2002)
H. Noguchi, G. Gompper, Phys. Rev. E 78, 016706 (2008)
A. Malevanets, R. Kapral, J. Chem. Phys. 112, 7260 (2000)
R.G. Winkler, in Hierarchical Methods for Dynamics in Complex Molecular Systems, edited by J. Grotendorst, G. Sutmann, G. Gompper, D. Marx (Forschungszentrum Jülich GmbH, Jülich, 2012), Vol. 10 of IAS Series
C.-C. Huang, A. Chatterji, G. Sutmann, G. Gompper, R.G. Winkler, J. Comput. Phys. 229, 168 (2010)
H. Noguchi, N. Kikuchi, G. Gompper, EPL 78, 10005 (2007)
T. Ihle, D.M. Kroll, Phys. Rev. E 63, 020201(R) (2001)
R.G. Winkler, C.-C. Huang, J. Chem. Phys. 130, 074907 (2009)
M. Ripoll, K. Mussawisade, R.G. Winkler, G. Gompper, Phys. Rev. E 72, 016701 (2005)
C.-C. Huang, A. Varghese, G. Gompper, R.G. Winkler, Phys. Rev. E 91, 013310 (2015)
A. Malevanets, J.M. Yeomans, Europhys. Lett. 52, 231 (2000)
M. Ripoll, K. Mussawisade, R.G. Winkler, G. Gompper, Europhys. Lett. 68, 106 (2004)
S. Poblete, A. Wysocki, G. Gompper, R.G. Winkler, Phys. Rev. E 90, 033314 (2014)
M.P. Allen, D.J. Tildesley, Computer Simulation of Liquids (Clarendon Press, Oxford, 1987)
S.H. Lee, R. Kapral, J. Chem. Phys. 121, 11163 (2004)
M. Theers, E. Westphal, G. Gompper, R.G. Winkler, Phys. Rev. E 93, 032604 (2016)
A. Lamura, G. Gompper, T. Ihle, D.M. Kroll, Europhys. Lett. 56, 319 (2001)
I.O. Götze, H. Noguchi, G. Gompper, Phys. Rev. E 76, 046705 (2007)
J.K. Whitmer, E. Luijten, J. Phys.: Condens. Matter 22, 104106 (2010)
M. Yang, M. Ripoll, Soft Matter 10, 1006 (2014)
J. Hu, A. Wysocki, R.G. Winkler, G. Gompper, Sci. Rep. 5, 9586 (2015)
H.C. Berg, E. Coli in Motion, Biological and Medical Physics Series (Springer, 2004)
S.Y. Reigh, R.G. Winkler, G. Gompper, Soft Matter 8, 4363 (2012)
J. Elgeti, G. Gompper, Eur. Phys. J. Special Topics 225, 3033 (2016)
R. Di Leonardo, D. Dell’Arciprete, L. Angelani, V. Iebba, Phys. Rev. Lett. 106, 038101 (2011)
H. Yamakawa, Helical Wormlike Chains in Polymer Solutions (Springer-Verlag, Berlin Heidelberg, 1997)
R. Vogel, H. Stark, Eur. Phys. J. E 33, 259 (2010)
L. Lemelle, J.-F. Palierne, E. Chatre, C. Vaillant, C. Place, Soft Matter 9, 9759 (2013)
E. Tüzel, G. Pan, T. Ihle, D.M. Kroll, EPL 80, 40010 (2007)
Y.-G. Tao, I.O. Götze, G. Gompper, J. Chem. Phys. 128, 144902 (2008)
B. Kowalik, R.G. Winkler, J. Chem. Phys. 138, 104903 (2013)
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Winkler, R.G. Low Reynolds number hydrodynamics and mesoscale simulations. Eur. Phys. J. Spec. Top. 225, 2079–2097 (2016). https://doi.org/10.1140/epjst/e2016-60087-9
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DOI: https://doi.org/10.1140/epjst/e2016-60087-9