臺灣博碩士論文加值系統

本論論文主要探討二維的高濃度度大腸桿菌在可滑滑動邊界附近的運動行行為。在液體中高濃度度大腸桿菌,因大腸桿菌本身的自 我推進力力,棒狀狀結構強交互作用所造成的與相互排列列效應, 形成集體運動,以具不不同時空尺度度同調性的渦流流與噴流流型態 出現,又稱自發紊流流。自發紊流流之激發,在遠離離邊界的薄液 中,具有均向性。本研究首度度透過拉拉膜過程,在薄膜中心區形 成厚度度達奈奈米尺度度的尋常黑膜,讓微米尺度度的大腸桿菌無法 游入尋常黑膜區。換言之,此尋常黑膜周圍的可滑滑動邊界,壓 抑垂直與邊界的運動,破壞運動的均向性。我們透過實驗,利利 用粒粒子影像速度度量量測法,量量測流流場、旋度度場、細菌速度度分佈函 數數。首度度發現,邊界區附近細菌,平行行邊界方向運動會被增 強,邊界區細菌傾向沿邊界做往復復混沌振盪性運動,而遠離離 邊界區仍進行行均向運動。透過沿邊界非均向速度度的長距離離效 應所誘發的秩序性,往復復混沌振盪具長空間尺度度的同步性, 稱之搖擺振盪。當尋常黑膜尺寸變小時,搖擺振盪甚至可以 明顯地環繞整個尋常黑膜邊界。

The high concentration suspensions of bacteria in the liquid exhibit turbulent like behaviors in the form of multi-scale vortices and jets, through the interplay of self-propelling and nonlinear mutual interactions between cells. Regardless of the recent intensive studies on the bacterial turbulence, the effect of boundary on their collective motions and turbulence is still elusive. In this work, for the first time, the dynamical behaviors of the turbulence of dense E. coli suspensions nearby a slipping boundary of a thin liquid film is experimentally investigated. By carefully stretching a liquid film with E. coli suspensions, an ultra-thin film called “common black film (CBF)” is formed at the center of the thin liquid film. The small thickness of the CBF forms a slipping boundary which prevents the cells to move into the CBF.

The 2D velocity distribution functions of local cell velocities along two normal directions, and the velocity and the vorticity fields, are measured via particle image velocimetry (PIV). It is found that the slipping boundary suppresses transverse motion and enhance longitudinal motion of cells nearby the boundary. The cell motion gradually becomes more isotropic in the region with increasing distance from the boundary. The synchronized chaotic rocking jets with long range correlation in the region surrounding the CBF boundary, due to the long distance propagation of the information of flow alignment along the boundary, are observed for the first time. When the CBF becomes small, the synchronized chaotic rocking can be extended to the region surrounding the entire CBF boundary.

Abstract ……………………………………………………………………………..I
List of figures ……………………………………………………..……………..….V
1 Introduction ……………………………………………………………….… 1
2 Background and theory …..………………………………………….……....… 5
2.1 Bacterial motion ……...…………………………………………….…..….. 5
2.1.1 The structure of the E. coli cell and its basic dynamic behavior …... 5
2.1.2 Motion of E. coli cells at the high concentration …………..….….…7
2.2 Collective motion near the solid boundary …………………………………9
2.2.1 The boundary effect on the bacterial flow fields ………….……..….9
2.2.2 Anisotropic motion near the rigid boundary ………….……………10
2.3 Bacterial motion near the slipping boundary of the 2D film ………...…….11
2.4 The formation of the CBF and NBF ……………………………………….13
3 Experimental setup and data analysis ….…………..….…….…………….15
3.1 Experimental setup ……..……………………………………………………15
3.1.1 The preparation of the bacterial suspension ………………………..15
3.1.2 The preparation of the chamber ………………………………….16
3.2 Data analysis …………………………………………………………………… 17
3.2.1 Particle Image Velocimetry …………………………………….…..17
3.2.2 Cross-correlation and auto-correlation ……………………………..18
3.3.3 Temporal correlation ……………………………………………….19
4 Results and discussions …………………………………….……….…..20
4.1 The formation processes of the CBF ………………………………………20
4.1.1 Two formation processes of the CBF …………………………….21
4.1.2 The coalescence of the CBF ………………………………………..22
4.1.3 The formation of the CBF inside the bacterial suspension ………24
4.2 The variation of collective motion near the boundary …………………..25
4.2.1 The velocity field and the vorticity field …….……………………..25
4.2.2 The temporal evolution of the velocity fields at different distances
from the CBF boundary …………………………………………….26
4.2.3 The temporal evolution of the vorticity field .……………………28
4.2.4 The temporal correlation of the velocity …………………………30
4.2.5 The probability distribution function ………………………………31
4.3 Bacterial rocking motion around the CBF ………………………………34
4.3.1 The definition of rocking motion .. ………………………………34
4.3.2 The flow fields of rocking motion …………………………………34
4.3.3 The time evolution of rocking motion ……………………………..35
4.3.4 The cross-correlation of rocking motion …………………………..37
5 Conclusion …………………………..………………………………………….39
Bibliography …..……………………………………………………………………………………………42

[1] Peter P. Marra, Keith A. Hobson, Richard T. Holmes, Science 282, 1884
(1998).
[2] Tony J. Pitcher, Christopher J. Wyche, Development in environmental
biology of fishes 2, 193-204 (1983).
[3] Vijay Narayan, Sriram Ramaswamy, Narayanan Menon, Science 317, 105
(2007).
[4] Guillaume  Gre  ́goire, Hugues  Chate  ́,  and  Yuhai  Tu, Phys. Rev. E 64,
011902 (2001).
[5] T. Vicsek, A. Zafeiris, Physics Reports 517, 71–140 (2012).
[6] Howard C. Berg, E. Coli in Motion (2004).
[7] C. Dombrowski, L. Cisneros, S. Chatkaew, R. E. Goldstein, and J. O. Kessler,
Phys. Rev. Lett. 93, 098103 (2004).
[8] S. M. Fielding, D. Marenduzzo, and M. E. Cates, Phys. Rev. E 83, 041910
(2011).
[9] L. H. Cisneros, R. Cortez, C. Dombrowski, R. E. Goldstein, and J. O. Kessler,
Phys. Rev. E 83, 041910 (2011).
[10] H. P. Zhang, A. Beer, E. L. Florin, and H. L. Swinney, Proc. Natl. Acad. Sci.
USA 107, 13626 (2010).
[11] T. Ishikawa, N. Yoshida, H. Ueno, M. Wiedeman, Y. Imai, and T.
Yamaguchi, Phys. Rev. Lett. 107, 028102 (2011).
[12] Christopher Dombrowski, Luis Cisneros Sunita Chatkaew, Raymond
E.Goldstein, and John O. Kessler, Phys. Rev. Lett. 93, 098103 (2004).
[13] Guillaume Grégoire and Hugues Chaté, Phys. Rev. Lett. 86, 0031-9007
(2011).
[14] Xiao-Lun Wu and Albert Libchaber, Phys. Rev. Lett. 84, 0031-9007
(2011).
[15] Kuo-An Liu and Lin I, Phys. Rev. E. 84, 001900 (2012).
[16] Jo  ̈rn  Dunkel,  Sebastian  Heidenreich,  K. Drescher, Henricus H.
Wensink, Markus  Ba  ̈r,  and  R. E. Goldstein, Phys. Rev. Lett. 110, 228102
(2013).
[17] Willow R. DiLuzio, Linda Turner, Michael Mayer, Piotr Garstecki, Douglas
B. Weibel, Howard C. Berg, and George M. Whitesides, Nature Lett. 435
(2005).
[18] Pauld. Frymier, Roseanne M. Ford, Howard C Berg, and Peter T.
Cummings, Proc. Natl. Acad. Sci. 92 (1995).
[19] Eric Lauga, Willow R. DiLuzio, George M. Whitesides, and Howard A.
Stone, Biophysical Journal 90, 400-412 (2006).
[20] Vasily Kantsler, Jo  r̈ n  Dunkel, Marco Polin, Raymond E. Goldstein, PNAS
110, 1187-1192 (2013).
[21] Guillaume Lambert, David Liao, and Robert H. Austin, Phys. Rev. Lett 104,
168102 (2010).
[22] Laurence  Lemelle,  Jean-­Fran  ̧cois  Palierne,  Elodie  Chatre,  and  
Christophe  Place, Journal of Bacteriology 192, 6307–6308 (2010).
[23] Nikolai D. Denkov, Philip Cooper, and Jean-Yves Martin, Langmuir 15
(1999).
[24] H. P. Zhang, A. Beer, R. S. Smith, E. L. Florin and H. L. Swinney, Europhys.
Lett. 87, 48011 (2009).
[25] L. H. Cisneros, R. Cortez, C. Dombrowski, R. E. Gold- 
 stein, J. O. Kessler,
Exp. Fluids 43, 737 (2007).
[26] Supravat Dey, Dibyendu Das, and R. Rajesh, Phys. Rev. Lett. 108, 238001
(2012).
[27] A. Sokolov, R. E. Goldstein, F. I. Feldchtein, and I. S. Aranson, Phys. Rev.
E. 80, 031903 (2009).
[28] B. M. Haines, A. Sokolov, I. S. Aranson, L. Berlyand, and D. A. Karpeev,
Phys. Rev. E. 80, 041922 (2009).
[29] Xiao Chen, X. Dong,  Avraham  Be’er,  Harry  L.  Swinney,  and  H.  P.
Zhang, Phys. Rev. Lett. 108, 148101 (2012).
[30] M. A. S. Vigeant and R. M. Ford, Appl. Environ. Microbiol. 63, 3474
(1997).
[31] E. Lauga, W. R. DiLuzio, G. M. Whitesides, and H. Stone, Biophys. J. 90, 400 (2006).
[32] Guillaume Lambert, David Liao, and Robert H. Austin, Phys. Rev. Lett 104,
168102 (2010)
[33] A. Kaiser, H. H. Wensink, and H. Lowen, Phys. Rev. Lett. 108, 268307
(2012).
[34] Andrey Sokolova, Mario M. Apodaca, Bartosz A. Grzybowskic, and Igor S.
Aranson, PNAS 107, 969-974 (2010).
[35] R.  Di  Leonardo,  D.  Dell’Arciprete, L. Angelani, and V. Iebba, Phys. Rev.
Lett. 106, 038101 (2011).
[36] Regine v. Klitzinga and  Hans-­Joachim  M  ü ller, Current Opinion in
Colloid & Interface Science 7, 42-49 (2002).
[37] Seung Soon Jang and William A. Goddard, J. Phys. Chem. B 110, 7992-
8001 (2006).
[38] Dimiter N. Petsev, Langmuir 16, 2093-2100 (2000).
[39] Eli Ruckenstein and Marian Manciu, Langmuir 18, 2727-2736 (2002).
[40] Nikolov, A. D. Wasan, D. T.; Kralchevsky, P. A. Ivanov, I. B. J. Colloid
Interface Sci. 133 (1989).
[41] Bergeron, V. Radke, C. J. Langmuir 8, 3020 (1992).
[42] G. Sezonov, D. Joseleau-Petit,  and  R.  D’Ari,  J. Bacteriol. 189, 8746
(2007).
[43] L. G. Wilson, V. A. Martinez, J. Schwarz-Linek, J. Tailleur, P. N. Pusey, W.
C.K. Poon, and G. Bryant, Phys. Rev. Lett. 106, 018101 (2011).
[44] T. Ishikawa, N. Yoshida, H. Ueno, M. Wiedeman, Y. Imai, and T.
Yamaguchi, Phys. Rev. Lett. 107, 028102 (2011).
[45] Wiki (https://en.wikipedia.org/wiki/Autocorrelation)
[46] Dimiter N. Petsev, Langmuir 16, 2093-2100 (2000).