Flow Induced by Bacterial Carpets and Transport of Microscale Loads

Abstract

In this paper we utilize the method of regularized Stokeslets to explore flow fields induced by 'carpets' of rotating flagella. We model each flagellum as a rigid, rotating helix attached to a wall, and study flows around both a single helix and a small patch of multiple helices. To test our numerical method and gain intuition about flows induced by a single rotating helix, we first perform a numerical timereversibility experiment. Next, we investigate the hypothesis put forth in (Darnton et al., Biophys J 86, 1863-1870) that a small number of rotating flagella could produce "whirlpools" and "rivers" a small distance above them. Using our model system, we are able to produce "whirlpools" and "rivers" when the helices are rotating out of phase. Finally, to better understand the transport of microscale loads by flagellated microorganisms, we model a fully coupled helix-vesicle system by placing a finite-sized vesicle held together by elastic springs in fluid near one or two rotating helices. We compare the trajectories of the vesicle and a tracer particle initially placed at the centroid of vesicle and find that the two trajectories can diverge significantly within a short amount of time. Interestingly, the divergent behavior is extremely sensitive to the initial position within the fluid.

Modeling Fluid Flow Induced by C. elegans Swimming at Low Reynolds Number

“…2b indicates the theoretically predicted exponential decay rate, e −2πr/λ , as the solid blue line [12]. This method is consistent with the computations of [5] and the experimental observations of [18] with rotating metal helices.…”

“…Adjacent forces positioned too far apart would result in our worm having holes, allowing fluid flow through the centerline. Conversely, the blobs cannot be too close together because overlapping blobs would create a total force much greater than the actual force induced by the worm [5].…”

“…The parameter controls where the majority of the force is concentrated and is generally chosen to represent a physical quantity such as the radius of the filamentary object, here the radius of the worm, 40μm. With the forcing given by this smooth function, (4) has an exact solution given by the regularized stokeslet [5]. A typical blob function is of the form φ (r) =…”

“…Fluid movement is potentially important for a number of reasons including mixing of either passive or active chemicals in the fluid [10,7,5], transport of nonzero volume particles [5], and swarm interactions of large numbers of organisms [9] all at low Reynolds number where viscosity, rather than inertia, dominates. In a viscosity dominated regime, where forcing is proportional to velocity rather than acceleration, mixing and flows are often counter intuitive due the reversibility.…”

Selective particle capture by asynchronously beating cilia

“…This is consistent with recent findings on a similar configuration which show that even for the particle sizes comparable to cilia movement, the difference between the motion of the fully resolved particles and that of passive tracers is small. 31 When the particles get in contact with cilia, based on recent observations that particles are captured by cilia moving in the flow direction, 10,32 we distinguish between two events: if a given particle is touched by the "front side" of the cilia, it gets captured. In biological systems, complex particle-organism interactions occur after downstream interception and the particle gets eventually removed from the capture region either directly or by other cilia and/or mouth-induced flows.…”