||We investigate the collective dynamics in array formed by self-propelling particle (SPP) under low Reynolds number (Re) condition. This system is an interesting non-equilibrium issue to be explored. In microfluidic devices, Re is low due to small characteristic length scale and low inertial effect. The above constraints lead to non-rotational flow in microfluidics devices. Bacteria, as a kind of self-propelling particles, possess molecular motors that are able to perform highly efficient flagellum rotation even under low Re condition. |
In this work, we form self-propelling particle array by depositing bacteria on treated surface in a microfluidic device. The formed high density bacterial carpet renders high density ensemble of freely rotating flagella that are able to exert thrust in the surrounding fluid. The microﬂuidic channel is composed of single polarly-ﬂagellated Vibrio alginolyticus (VIO5 or NMB136) deposited glass substrates. The individual ﬂagellum swimming speed is tuned by varying buffer sodium concentration. Hydrodynamic coupling strength is tuned by varying buffer viscosity. Particle tracking statistics shows high ﬂagellum rotational rate and strong hydrodynamic coupling strength lead to collective sub-diffusive dynamics in VIO5 case, while not the case for NMB136.
The flick motions of the VIO5 could generate a thrust that propagates back to the original bacteria and exert a counteraction in the flow in between. In bacterial carpet condition, the suspended particle could experience an effectively confining action by the counteractions from all directions through hydrodynamic coupling. The NMB136 counterpart, however, could not generate strong thrust by rotational motion that could lead to strong anti-persistent motions in particle, thus no sub-diffusive dynamics.
According to the experiment observation, we find out a vertical force generated by bacterial carpet. It can be measured by optical tweezers. Interactions between neighboring ﬂagella and force measurement show the forces may come from the collective ﬂagella motion. At the low Reynolds number system, Saffman force pushes the tracer particles to the region of higher ﬂuid velocity in the non-uniform flow. This is a physically probable mechanism to explain the sub-diffusive behavior.
||. N. Darnton, L. Turner, K. Breuer, and H. C. Berg, Biophys. J. 86, 1963 (2004).|
. N. Uchida and R. Golestanian, Phys. Rev. Lett. 104, 178103 (2010).
. Rob Phillips, Jane Kondev, Julie Theriot, Physical Biology of the Cell
. E. M. Purcell, Am. J. Phys. 45, 3 (1977)
. Tamás Vicsek, and Anna Zafeiris, Physics Reports 517 71–140 (2012)
. Yi-Teng Hsiao, Jing-Hui Wang, Yi-Chun Hsu, Chien-Chun Chiu, Chien-Jung Lo, Chia-Wen Tsao, and Wei Yen Woon Appl. Phys. Lett. 100, 203702 (2012)
. Howard C. Berg, E. coli in Motion
. Howard C. Berg, Phys. Today 53(1), 24 (2000)
. Y Sowa, H Hotta, M Homma and A IshijimaJ. Mol. Biol. 327, 1043–1051 (2003)
. Faber, T.E, Fluid Dynamics for Physicists
. Daniel Goldfarb, Biophysics Demystified
. Eric Lauga and Thomas R Powers, Rep. Prog. Phys. 72 (2009)
. Tamás Vicsek, András Czirók, Eshel Ben-Jacob, Inon Cohen, and Ofer Shochet Physical Review Letters 75, 1226 (1995)
. John Toner, and Yuhai Tu, Physical Review Letters 75, 4326 (1995)
. Ramin Golestanian, Julia M. Yeomans and Nariya Uchida, Soft Matter, 7, 3074–3082 (2011)
. N. Li, S. Kojima, and M. Homma, Genes Cells 16, 985 (2011).
. M. J. Kim and K. S. Breuer, Small 4, 111 (2008).
. J. B. Segur and H. E. Oberstar, Ind. Eng. Chem. 43, 2117 (1951).
. N. Uchida, Phys. Rev. Lett. 106, 064101 (2011).
. Philip Nelson, Biological Physics
. Jing-Hui Wang’s thesis
. P. G. Saffman, ‘‘The lift force on a small sphere in a slow shear ﬂow,’’ J. Fluid Mech. 22, 385 (1965); Corrigendum, ibid. 31, 624 (1968).
. J. L. M. Poiseuille, Ann. Sci. Nat., vol. 5, pp. 111–, 1836.