$350 Journal o f Biomechanics 2006, Vol. 39 (Suppl 1) Oral Presentations

squirming. However, in two-dimensional suspensions, or in three-dimensional suspensions of bottom-heavy cells, they show strong aggregation into clumps or bands.

5505 Mo, 12:00-12:15 (P9) Flagel la-driven f lows enhance long-range t ranspor t o f molecular nutrients M.B. Short 1 , C. Solari 2, S. Ganguly 1 , T.R. Powers 5, J.O. Kessler 1 , R.E. Goldstein 1,3,4. 1Department of Physics, University of Adzona, Tucson, AZ, USA, 2Department of Ecology and Evolutionary Biology, University of Arizona, Tucson, AZ, USA, 3program in Applied Mathematics, University of Arizona, Tucson, AZ, USA, 4B105 Institute, University of Arizona, Tucson, AZ, USA, 5 Division of Engineering, Brown University, Providence, RI, USA

Evolution from unicellular organisms to large, multicellular ones requires matching their needs to the rate of exchange of molecular nutrients with the environment. This logistic problem poses a severe constraint on development. For organisms whose body plan is a spherical shell, such as the volvocine green algae, the current of needed nutrients grows quadratically with radius, whereas the rate at which diffusion alone exchanges molecules grows linearly, leading to a bottleneck radius beyond which the diffusive current cannot meet metabolic demands. Using Volvox carted, we examine the role that advection of fluid by the coordinated beating of surface-mounted flagella plays in enhancing nutrient uptake, and show that it generates a boundary layer of concentration of the diffusing solute. That concentration gradient produces an exchange rate which is quadratic in the radius, as required, thus circumventing the bottleneck and allowing increase in size and evolutionary transitions featuring germ-soma differentiation.

7545 Mo, 12:15-12:30 (P9) Flow field for a microorganism swimming in a porous medium N.A. Hill. Department of Mathematics, University of Glasgow, Glasgow, Scotland, UK

Concentrated suspensions of swimming microorganisms are found in biofilms, in swarming bacterial cultures [Bees et al. 2000], and in laboratory experiments on bioconvection [Tuval et al. 2005]. Much progress has been made in constructing continuum theories to describe the bulk motion of the suspension but it is a major challenge to develop even ad hec models to describe the swimming and the streaming of the bacterium Bacillus subtilis that has been described by Kessler & Hill (1997). One possible way to develop an appropriate description is to regard the bulk suspension as a porous medium through which the individual cell swims. Long & Ajdari (2001) derived the fundamental solution (a 'porous medium stokeslet') for the flow induced by a point force in a porous medium in which the flow is governed by incompressibility V • u = 0 and Brinkman's equation [ IV2f . / - [l~:2f./- V p = -F , where u(x,t) and p(x,t) are the fluid velocity and pressure, respectively, and depend on position x and time t. f~ is the fluid viscosity, I, --1 is the pore size, and F is the force. Here we extend their results to derive the flow field due to a force dipole and show that in the limit that Ixl ~:> I, ~-1 , when the flow is governed by Darcy's Law, the fluid velocity decays as 14x31. This 'Darcy stresslet' flow is the leading order component of the far-field flow induced by a swimming cell and it is used to construct and study the flow fields due distributions of swimmers within the porous medium.

References Bees M.A., et al. (2000). The interaction of thin-film flow, bacterial swarming and

cell differentiation in colonies of Serratia liquefaciens. J Math Biol 40: 27-63. Kessler J.O., Hill N.A. (1997). Complementarity in the dynamics of swimming micro-

organisms. In: The Physics of Biological Systems, eds H. Flyvberg et al. Springer Lecture Notes in Physics 480: 324-340.

Long D., Ajdari A. (2001). A note on the screening of hydrodynamic interactions, in electrophoresis, and in porous media. Eur Phys J E 4: 29-32.

Tuval I., et al. (2005). Bacterial swarming and oxygen transport near contact lines. Proc Natl Acad Sci USA 102: 2277-2282.

4925 Mo, 14:00-14:15 (P11) Circular mot ion o f a bacter ium swimming close to a r igid boundary

T. Goto 1 , '~ Magariyama 2. 1 Department of Mechanical Engineering, Totted University, Totted, Japan, 2Food Engineering Division, National Food Research Institute, Tsukuba, Japan

Circular bacterium motions have been observed when the bacterium swims close to a solid boundary. For example, Eschedchia cell cells swimming above a glass-slide in a solution trace out clockwise circular trajectories when viewed from above, and Vibdo alginelyticus cells counter-clockwise trajectories. Several studies have shown that these circular motions are due to a natural consequence of fluid-dynamic interaction between the relative rotation of the cell-body and flagella, and the boundary [1-3]. These results are consistent with each other on the direction of circular motion. However, it is still inconclu- sive whether the swimming speed close to a boundary increases or decreases.

Also, the radii of the circular motion (i.e. the ratio of the swimming speed and yaw angle rate), and the pitch angle rates are considerably different. They seem to depend on the size of the cell-body and the flagella, the orientation of the cell relative to the boundary, and the distance from it. In this study, boundary element simulations are carried out for various sizes of bacterial models to elucidate the fluid-dynamic effect of the rigid wall on the swimming motion of bacteria. The bacterial model consists of a single flagellum and a cylindrical cell-body of which both ends are capped by hemispheres. Especially, the dependence of the cell-body size on the swimming speed and the angular velocities in yaw and pitch directions are investigated by changing the orientations of the bacterial model. They depend on the strength of the interactions between the boundary and the cell-body and between the boundary and the flagella. If the size of the cell-body is small, the swimming speed tends to increase at the presence of a boundary. If the cell-body size is big, the yaw angular velocity tends to increase, which results in circular trajectories.

References [1] Ramia M., et al. Biophys. J. 1993; 65: 755-778. [2] Lauga E., et al. Biophys. J. 2006; 90: 400-412. [3] Goto T., et al. Biophys. J. 2005; 89: 3771-3779.

4389 Mo, 14:15-14:30 ( P l l ) Model l ing a suspens ion of rod-l ike swimmers

R.J. Clarke 1,2. 1School of Mathematical Sciences, University of Adelaide, Adelaide, SA, Australia, 2Work primarily conducted as a David Cdghton fellow in DAMTR Cambridge, UK

The rod-like geometries which characterise many micro-organisms and their swimming apparatus (e.g. flagella, cilia) have acted as a strong stimulus for the development of slender-body theory (SBT), a popular technique which approximates the low-Reynolds-number flows about elongated bodies. Some notable successes in this field include descriptions of the thrust generated by beating flagella [1], as well as the feeding currents generated by sessile organisms [2]. In this study we incorporate the deterministic mechanics of rod-like swimmers, as described by SBT, into a collective description for a dilute suspension of micro-organisms as given by Pedley & Kessler [4], which accounts for inherent randomness in the swimming behaviour. Results pay particular attention to the effects of a background shear flow, as well as the presence of a nearby solid surface (which can be readily incorporated into the SBT formulation [3]), and these will be shown to be important factors when deciding whether a swimmer reaches the wall, or is returned back into the bulk flow. This, in turn, clearly has implications for the formation of wall-adhered collective bacterial states, such as biofilms.

References [1] Higdon J.J.L.J. Fluid Mech. 1979; 90, 685-711. [2] Orme B.A.A., et al. J. Fluid Mech. 2003; 475: 333-355. [3] Blake J.R.J. Eng. Math. 1974; 8: 113-124. [4] Pedley T.J., Kessler K.O.J. Fluid Mech. 1990; 212: 155-182.

6463 Mo, 14:45-15:00 ( P l l ) Object manipulat ion by mot ion control led Euglena group as bio-micromachines A. Itoh 1 , W. Tamura 2, ]7 Mishima 2. 1Department efMechanical Engineering, Tokyo Denki University, Tokyo, Japan, 2Tokyo Denki University, Tokyo, Japan

The authors have studied how to use microorganisms as bio-micromachines. This study investigates how to use a motion controlled Euglena group as a huge group of bio-micromachines. Motion control is done by using the positive orientation phototaxis of Euglena. A weak blue laser scanning system is made for this study. Its construction is that a blue laser is used and it passed through the mirrors of two galvano- scanners to make the two dimensional positioning of laser beam possible. After that, the laser beam is concentrated by a convex lens, and then irradiate into the experimental pool. After passing the experimental pool area, the blue laser is attenuated by high cut filter. The behaviors of the Euglena and the transportation object were recorded by CCD camera with macro lens. Since Euglena do not respond to the red light, red LED light is used for background illumination. First, the basic response properties of Euglena to the blue laser light were investigated. The intensity of the center of the laser beam is too strong and Euglena showed negative response at this area. Therefore, Euglena gather around the laser irradiation area. The population density of the Euglena accelerate the gathering speed of Euglena, therefore, the initial population density of the culture medium is very important to make object transportation by Euglena group possible. The results showed that this system can make any shape of Euglena group by drawing the laser irradiation area by the laser beam. The Euglena group can also be moved and deformed by the moving of the laser irradiation area.