Session MV: Swimming V: Micro-organisms II

The combined effect of gravity and stresslets on the instability of a uniform suspension of swimming micro-organisms

Uniform dilute suspensions of gyrotactic, swimming micro-organisms (bottom-heavy algae) become unstable because of the effect of gravity [1]; suspensions of head-heavy organisms are stable. In the absence of gravity, uniform suspensions of aligned swimmers become unstable because of the stresslet distribution generated by their swimming actions, whether they are pullers (algae) or pushers (bacteria) [2,3], but only pushers cause instability of an isotropic suspension [3]. Here we examine the effect of weak gravity on a suspension's instability, and find that even a small gravitational term leads to instability for bottom-heavy cells at small enough wavenumber, whatever the magnitude and sign of the stresslet term, but may not be enough to stabilise suspensions of head-heavy pushers at a high enough number density of cells. However, use of realistic parameter values suggests that gravity will normally be dominant. \\[4pt] [1] T J Pedley {\&} J O Kessler, Ann. Rev. Fluid Mech. \textbf{24},313 (1992) \\[0pt] [2] R A Simha {\&} S Ramaswamy, Phys. Rev. Lett. \textbf{89},058101 (2002) \\[0pt] [3] D Saintillan {\&} M J Shelley, Phys. Fluids \textbf{20},123304 (2008)   

The dilute rheology of swimming suspensions: A simple kinetic model

A simple kinetic model is presented for the shear rheology of a dilute suspension of particles swimming at low Reynolds number. If interparticle hydrodynamic interactions are neglected, the configuration of the suspension is characterized by the particle orientation distribution, which satisfies a Fokker-Planck equation including the effects of the external shear flow, rotary diffusion, and particle tumbling. The orientation distribution then determines the leading-order term in the particle extra stress in the suspension, which can be evaluated based on the classic theory of Hinch and Leal [J. Fluid. Mech. 52(4):683-712 (1972)], and involves an additional contribution arising from the permanent force dipole exerted by the particles as they propel themselves through the fluid. Numerical solutions of the steady-state Fokker-Planck equation were obtained using a spectral method, and results are reported for the shear viscosity and normal stress differences in terms of flow strength, rotary diffusivity, and correlation time for tumbling. It is found that the rheology is characterized by much stronger normal stress differences than for passive suspensions, and that tail-actuated swimmers result in a strong decrease in the effective shear viscosity of the fluid.   

Three-Dimensional Pattern Formation in Flowing Suspensions of Swimming Particles

Suspensions of self-propelled particles, such as swimming micro-organisms, are known to undergo complex dynamics as a result of hydrodynamic interactions. Using the kinetic theory recently developed by Saintillan and Shelley (``Instabilities, pattern formation, and mixing in active suspensions'', \textit{Physics of Fluids} \textbf{20}, 123304, 2008), we investigate the three-dimensional pattern formation occurring in suspensions of active particles. Our numerical simulations confirm the results of the linear stability analysis of Saintillan et al., and the long-time nonlinear behavior is shown to be characterized by the formation of strong density fluctuations, which merge and break up in time in a quasiperiodic fashion. These complex motions result in very efficient fluid mixing, which we quantify by means of a multiscale mixing norm. The effects of an external shear flow on the pattern formation are also investigated using both simulations and a stability analysis.   

Linear Stability for Models of Active Suspensions

Recent work by Saintillan \& Shelley has modeled the dynamics of active suspensions, such as swirling bacterial baths, through a modification of Doi rod theory. However, the sign of the dipolar extra stress can be of the opposite sign of Doi theory, and this leads to large-scale flow instability. We investigate the structure of this system linearized near a state of isotropy and uniformity. We show that concentration fluctuations generally decay, and that while long-wave instability depends upon the particular swimming mechanism, short-wave stability does not. This suggests that the model is well-posed, even in the absence of translational and rotational diffusion effects.   

Colloidal motility and patterning by physical chemotaxis

We developped a microfluidic setup to show the motility of colloids or biomolecules under a controlled salt gradient thanks to the diffusiophoresis phenomenon [1,2]. We can therefore mimic chemotaxis on simple physical basis with thrilling analogies with the biological chemotaxis of E. Coli bacteria: salt dependance of the velocity [3] and log-sensing behavior [4]. In addition with a temporally tunable gradient we show we can generate an effective osmotic potential to trap colloids or DNA. These experimental observations are supported by numerical simulations and an asymptotic ratchet model. Finally, we use these traps to generate various patterns and because concentration gradients are ubiquitous in nature, we question for the role of such a mecanism in morphogenesis [5] or positioning perspectives in cells [6]. \\[4pt] [1] B. Abecassis, C. Cottin-Bizonne, C. Ybert, A. Ajdari, and L. Bocquet, Nat. Mat., 7(10):785--789, 2008. [2] Anderson, Ann. Rev. Fluid Mech, 21, 1989. [3] Y. L. Qi and J. Adler, PNAS, 86(21):8358--8362, 1989. [4] Y. V. Kalinin, L. L. Jiang, Y. H. Tu, and M. M. Wu, Biophys. J., 96(6):2439--2448, 2009. [4] J. B. Moseley, A. Mayeux, A. Paoletti, and P. Nurse, Nat., 459(7248):857--U8, 2009. [6] L. Wolpert, Dev., 107:3--12, 1989   

Bacterial streamers in curved microchannels

Biofilms, generally identified as microbial communities embedded in a self-produced matrix of extracellular polymeric substances, are involved in a wide variety of health-related problems ranging from implant-associated infections to disease transmissions and dental plaque. The usual picture of these bacterial films is that they grow and develop on surfaces. However, suspended biofilm structures, or streamers, have been found in natural environments (e.g., rivers, acid mines, hydrothermal hot springs) and are always suggested to stem from a turbulent flow. We report the formation of bacterial streamers in curved microfluidic channels. By using confocal laser microscopy we are able to directly image and characterize the spatial and temporal evolution of these filamentous structures. Such streamers, which always connect the inner corners of opposite sides of the channel, are always located in the middle plane. Numerical simulations of the flow provide evidences for an underlying hydrodynamic mechanism behind the formation of the streamers.   

Swarming dynamics in bacterial colonies

Swarming is a widespread phenomenon observed in both biological and non-biological systems. Large mammal herds, fish schools, and bird flocks are among the most spectacular examples. Many theoretical and numerical efforts have been made to unveil the general principles of the phenomenon, but systematic experimental studies have been very limited. We determine the characteristic velocity, length, and time scales for bacterial motion in swarming colonies of \textit{Paenibacillus dendritiformis} growing on semi-solid agar substrates. The bacteria swim within a thin fluid layer, and they form long-lived jets and vortices. These coherent structures lead to anisotropy in velocity spatial correlations and to a two-step relaxation in velocity temporal correlations. The mean squared displacement of passive tracers exhibits a short-time regime with nearly ballistic transport and a diffusive long-time regime. We find that various definitions of the correlation length all lead to length scales that are, surprisingly, essentially independent of the mean bacterial speed, while the correlation time is linearly proportional to the ratio of the correlation length to the mean speed.   

Dynamics of Swimming Particles in Chaotic Fluid Flows

We numerically investigate the effect of swimming (modeled as an intrinsic velocity) on the transport of particles in chaotic two-dimensional, incompressible fluid flows. We consider spheroidal particles advected by an externally imposed flow, and show that even a small amount of swimming significantly changes the particle dynamics. The phase space is examined as the magnitude and direction of the swimming speed are varied.   

Turbulence and motility conspire to generate small-scale phytoplankton patchiness

Phytoplankton are heterogeneously distributed at nearly all scales in the Ocean. Small-scale patchiness is often thought to result from a passive ``top down'' process where large patches of phytoplankton are broken into subsequently smaller ones by turbulent motion. Here we demonstrate instead a ``bottom up'' process in which patchiness is generated {\em ex novo} by the coupling of turbulence and cell motility. We implemented an individual based model (IBM) for phytoplankton cells within a direct numerical simulation (DNS) of turbulence. The IBM describes the movement behavior of gyrotactic cells, for which the swimming direction is dictated by the interaction of cell morphology (e.g. bottom-heaviness) and fluid shear. Two dimensionless parameters govern the dynamics: the ratio of the Kolmogorov velocity to swimming velocity, and the ratio of Kolmogorov time scale to cell reorientation time. We find that this mechanism can indeed generate strong patchiness and discuss the parameter regime under which this occurs. An analytical single-vortex model helps to shed light on the fundamental physics at play. These findings strongly highlight the importance of microbial motility in the Ocean.   

Motility-enhanced bioflocculation

Bacteria often rely on their ability to aggregate to survive in nature. They can form clusters among themselves or with suspended colloids, leading to biologically-enhanced flocculation (bioflocculation). We investigate the role of cell motility on bioflocculation by comparing two strains of~\textit{Escherichia coli,~}a wild type and a non-motile mutant.~We quantify settling rates from a suspension of bacteria and 1 $\mu $m polystyrene beads, by independently varying the concentration of bacteria and colloids. We find that motility enhances settling rates up to 6-fold\textbf{. }We~rationalize our findings in terms of an increase in encounter rates between bacteria and colloids. These results could contribute to improve the performance of wastewater treatment processes and provide a possible explanation for why motile bacteria are more successful biofilm formers.