Hydrodynamic interactions in squirmer motion: swimming with a neighbour and close to a wall. (English) Zbl 1425.76329
Summary: We analyze the hydrodynamic coupling of pairs of squirmers and the impact it has on their short and long-time behavior. The study combines an analytic analysis of the hydrodynamic interactions between pairs of squirmers with computer simulations to elucidate the quantitative capabilities of the theoretical approach. The numerical study allows us to address the motion of simple geometries of squirmers on long times and perform a complete discussion of the effective repulsive interactions in squirmer ensembles. The contrast between analytic and numerical results identifies the features of active motion responsible for such effective interactions. The framework developed also allows for an analysis of the hydrodynamic coupling between a squirmer and a solid wall and shows the possibility of bounded motion next to a solid wall.
MSC:
| 76Z10 | Biopropulsion in water and in air |
References:
| [1] | Toner, J.; Tu, Y. H.; Ramaswamy, S.: Ann. phys. Rev. lett., Ann. phys. Rev. lett. 318, 170 (2005) |
| [2] | Wu, X. L.; Libchaber, A.: Phys. rev. Lett., Phys. rev. Lett. 84, 3017 (2000) |
| [3] | Hernandez-Ortiz, J. P.; Stoltz, C. P.; Graham, M. D.: Phys. rev. Lett., Phys. rev. Lett. 95, 204501 (2005) |
| [4] | Najafi, A.; Golestanian, R.: Phys. rev. E, Phys. rev. E 69, 062901 (2004) |
| [5] | Pooley, C. M.; Alexander, G. P.; Yeomans, J. M.: Phys. rev. Lett., Phys. rev. Lett. 99, 229103 (2007) |
| [6] | Llopis, I.; Pagonabarraga, I.: Europhys. lett., Europhys. lett. 75, 999 (2006) |
| [7] | Llopis, I.; Pagonabarraga, I.: Eur. phys. J. E, Eur. phys. J. E 26, 103 (2008) |
| [8] | Tuval, I.; Cisneros, L.; Dombrowski, C.; Wolgemuth, C. W.; Kessler, J. O.; Goldstein, R. E.: Proc. natl. Acad. sci. USA, Proc. natl. Acad. sci. USA 102, 2277 (2005) |
| [9] | Kessler, J. O.; Pedley, T. J.: Annu. rev. Fluid mech., Annu. rev. Fluid mech. 24, 313 (1994) |
| [10] | Ishikawa, T.; Simmonds, M. P.; Pedley, T. J.: J. fluid mech., J. fluid mech. 568, 119 (2006) |
| [11] | Lighthill, M. J.: Comm. pure appl. Math., Comm. pure appl. Math. 46, 109 (1952) |
| [12] | Blake, J. R.: J. fluid mech., J. fluid mech. 46, 199 (1971) |
| [13] | Gueron, S.; Levit-Gurevich, L.: Proc. natl. Acad. sci. USA, Proc. natl. Acad. sci. USA 96, 12240 (1999) |
| [14] | The set of functions {Pn(x)} correspond to the Legendre polynomials, obtained from the Rodrigues’ formula: Pn(x)=1/2nn!dn/dxn(x2 - - 1)n, while the functions {Vn(x)} are derivaties of the Legendre polynomials, defined by the expression, Vn(x)=2/n(n+1)Pn\(^{\prime}\)(x). |
| [15] | Batchelor, G. J.; Green, J. T.: J. fluid mech., J. fluid mech. 56, 375 (1972) |
| [16] | Ramachandran, S.; Kumar, P. B. Sunil; Pagonabarraga, I.: Eur. phys. J. E, Eur. phys. J. E 20, 151 (2006) |
| [17] | Pagonabarraga, I.; Llopis, I.: Lect. notes phys., Lect. notes phys. 752, 133 (2008) |
| [18] | Russel, W. B.; Saville, D. A.; Schowalter, W. R.: Colloidal dispersions, (1992) · Zbl 0789.76003 |
| [19] | Hatwalne, Y.; Ramaswamy, S.; Rao, M.; Simha, R. A.: Phys. rev. Lett., Phys. rev. Lett. 92, 118101 (2004) |
| [20] | Cates, M. E.; Fielding, S. M.; Marenduzzo, D.; Orlandini, E.; Yeomans, J. M.: Phys. rev. Lett., Phys. rev. Lett. 101, 068102 (2008) |
| [21] | Cates, M. E.; Stratford, K.; Adhikari, R.; Stansell, P.; Desplat, J. -C.; Pagonabarraga, I.; Wagner, A. J.: J. phys. Condens. mater., J. phys. Condens. mater. 16, S3903 (2004) |
| [22] | Stratford, K.; Adhikari, R.; Pagonabarraga, I.; Desplat, J. -C.: J. stat. Phys., J. stat. Phys. 121, 163 (2005) |
| [23] | Dunweg, B.; Ladd, A. J. C.: Adv. polym. Sci., Adv. polym. Sci. 221, 89 (2009) |
| [24] | Pagonabarraga, I.; Hagen, M. H. J.; Lowe, C. P.; Frenkel, D.: Phys. rev. E, Phys. rev. E 58, 7288 (1998) |
| [25] | Berke, A. P.; Turner, L.; Berg, H. C.; Lauga, E.: Phys. rev. Lett., Phys. rev. Lett. 101, 038102 (2008) |
| [26] | Alexander, G. P.; Pooley, C. M.; Yeomans, J. M.: Phys. rev. E, Phys. rev. E 78, 046308 (2008) |
| [27] | Zargar, R.; Najafi, A.; Miri, M.: Phys. rev. E, Phys. rev. E 80, 026308 (2009) |
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