Bulletin of the American Physical Society
66th Annual Meeting of the APS Division of Fluid Dynamics
Volume 58, Number 18
Sunday–Tuesday, November 24–26, 2013; Pittsburgh, Pennsylvania
Session L17: Biofluids: Locomotion VII - Active Suspensions and Bacteria |
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Chair: Sung Kwon Cho, University of Pittsburgh Room: 305 |
Monday, November 25, 2013 3:35PM - 3:48PM |
L17.00001: Marangoni-driven chemotaxis, chemotactic collapse, and the Keller-Segel equation Michael Shelley, Hassan Masoud Almost by definition, chemotaxis involves the biased motion of \textit{motile} particles along gradients of a chemical concentration field. Perhaps the most famous model for collective chemotaxis in mathematical biology is the Keller-Segel model, conceived to describe collective aggregation of slime mold colonies in response to an intrinsically produced, and diffusing, chemo-attractant. Heavily studied, particularly in 2D where the system is ``super-critical'', it has been proved that the KS model can develop finite-time singularities -- so-called chemotactic collapse -- of delta-function type. Here, we study the collective dynamics of \textit{immotile} particles bound to a 2D interface above a 3D fluid. These particles are chemically active and produce a diffusing field that creates surface-tension gradients along the surface. The resultant Marangoni stresses create flows that carry the particles, possibly concentrating them. Remarkably, we show that this system involving 3D diffusion and fluid dynamics, exactly yields the 2D Keller-Segel model for the surface-flow of active particles. We discuss the consequences of collapse on the 3D fluid dynamics, and generalizations of the fluid-dynamical model. [Preview Abstract] |
Monday, November 25, 2013 3:48PM - 4:01PM |
L17.00002: Coherent structures, globally aligned states, and hydrodynamic traffic jams in confined active suspensions David Saintillan, Adrien Lefauve Strongly confined active liquids are subject to unique hydrodynamic interactions due to momentum screening and lubricated friction by the confining walls. Using numerical simulations based on a minimal model for swimmer dynamics and interactions, we demonstrate that two-dimensional dilute suspensions of fore-aft asymmetric polar swimmers in a Hele-Shaw geometry can exhibit a rich variety of collective behaviors depending on particle shape and density, including: coherent polarized density waves with global alignment, stationary aster-shaped clusters, persistent counter-rotating vortices, density shocks and rarefaction waves. We also substantiate these various phenomena using a linear stability analysis and a nonlinear traffic flow model, both derived from a mean-field kinetic theory. [Preview Abstract] |
Monday, November 25, 2013 4:01PM - 4:14PM |
L17.00003: A nonlocal kinetic theory for active suspensions in confined geometries Barath Ezhilan, David Saintillan We consider a suspension of biologically active particles confined by bounding walls separated by distances that are of the same-order as (or one order of magnitude higher than) the individual particle length. In such systems, the fluid velocity, particle concentration and orientation distribution vary on length scales that are comparable to that of the suspended active particles and a nonlocal theory is required to explain the dynamics. The theory presented here is based on our previous kinetic model for active suspensions, where nonlocal effects are taken into account by extending previous theories for passive fiber suspensions [Schiek and Shaqfeh (1995)]. Contacts between the active particles and the solid walls create sterically-excluded regions of particle configurations within a distance of a half particle length from the walls, and a rigorous no-flux boundary condition is imposed on the hypersurfaces separating the allowed and forbidden configurations. A pressure-driven flow is also imposed on this system and a numerical solution is utilized to study the concentration, orientation distributions, stress profiles, and effective viscosity. Comparisons are made to recent rheological measurements in confined bacterial suspensions [Gachelin et al (2013)]. [Preview Abstract] |
Monday, November 25, 2013 4:14PM - 4:27PM |
L17.00004: Rotors in low Re fluid: interactions and dynamics near a wall Enkeleida Lushi, Petia Vlahovska Active suspensions exhibit many interesting phenomena, e.g., self-organization and pattern formation. While collections of swimmers, which translate, have been extensively studied, rotors have received limited attention. We present a minimal model and numerical method to study the behaviour of externally or internally driven rotors in low Reynolds number flow. The rotors interact with each-other via the fluid as well as via excluded volumes. We discuss the coupled dynamics of two or more such particles, and their behaviour near a wall. Two same-spin rotors oscillate about their own center of mass with the oscillation time-scale depending on the particle aspect ratio, while their slow dynamics describes a large circular trajectory about the pair's center of mass. Two opposite-spin rotors perform, on average, co-operative self-propulsion in the direction perpendicular to their separation as well as oscillate about their centres of mass. A single rotor can move along a wall as it performs a co-operative self-propulsion with its own image. Last, we discuss the coupled dynamics and trajectories of many rotors. [Preview Abstract] |
Monday, November 25, 2013 4:27PM - 4:40PM |
L17.00005: Active clusters and swimming crystals: instabilities and nonlinear dynamics in aggregates of model microswimmers Arthur Evans Self-propelled particles, from synthetic Janus swimmers to living microorganisms, behave very differently when they are in isolation, near boundaries, or in the presence of their fellow swimmers. Although many systems studied involve dilute suspensions of these active particles, for large volume fractions near-field fluid mechanics and boundary effects can dominate the dynamics. In this talk I will use the ``squirmer'' model for self-propelled microswimmers to discuss the nonlinear dynamics of spherical particles that are nearly touching; in this limit the fluid mechanics are vastly simplified and predictions can be made for dynamical self-assembly and the overall motion of aggregates. For small clusters the behavior is analytically tractable, and results for the stability of paired swimmers can be recovered, while for aggregates of three or more particles chaotic behavior is predicted. In the limit of large numbers of nearly close-packed particles the lubrication analysis presented here can be used to predict instabilities in active colloidal crystals. [Preview Abstract] |
Monday, November 25, 2013 4:40PM - 4:53PM |
L17.00006: Orientational order in two-dimensional confined active suspensions Alan Cheng Hou Tsang, Eva Kanso Geometric confinement in physical space is important for the studies of the collective motion of active suspensions. The reasons are two-fold: motile biological micro-organisms or active collides are always subject to different types of confinement in their swimming environment; The existence of confinement can significantly affects hydrodynamic interactions between the swimmers and thus changes the nature of collective motion. We focus on the situation when the swimmers are confined between two parallel plates such that the motion of the particles are restricted to two dimensions. In this case, the far-field hydrodynamic effect of a swimmer is no longer given by a force-dipole, which has been used in numerous studies on discrete numerical simulations and continuum theories. Instead, the far-field effect of a confined swimmer is given by a potential-dipole. Using a potential-dipole model in doubly-periodic domain, we perform numerical simulations to probe into the collective dynamics of confined active suspensions. We show that isotropic suspensions of swimmers are unstable and develop long time polar orientation order. This results in coherent clusters swimming in the same direction, reminiscent to the collective behavior usually observed in phenomenological models. [Preview Abstract] |
Monday, November 25, 2013 4:53PM - 5:06PM |
L17.00007: Effects of bubble length and excitation frequency on micro propulsion by oscillating bubble Jian Feng, Sung Kwon Cho Previously, we have showed that an oscillating micro bubble column trapped in a one-end open channel can generate a propulsion force in the presence of an acoustic excitation [1]. The main mechanism for this propulsion is generation of asymmetric flows within the cyclic period of excitation. In particular, the amplitude of the bubble interface oscillation at the open end of the channel seems to be highly correlated to the propulsion strength. In addition, the oscillation amplitude highly depends on the excitation frequency as well as the bubble length. This means that the frequency and bubble length can be key parameters for controlling the propulsion strength. In this talk, we discuss how the bubble length and excitation frequency affect the micro propulsion. As the bubble length and the excitation frequency are varied, the oscillation amplitude, the strength of generated flows near the oscillating bubble and the propulsion speed are measured. Based on the measurements, the relation of these parameters with the propulsion strength is investigated. \\[4pt] [1] Jian Feng and Sung Kwon Cho, MEMS2013 Conference, pp. 63-66. [Preview Abstract] |
Monday, November 25, 2013 5:06PM - 5:19PM |
L17.00008: Stochastic dynamics of active Brownian spheres in linear flows Mario Sandoval, Eric Lauga Most classical work on the hydrodynamics of low-Reynolds swimming addresses deterministic locomotion in quiescent environments. Thermal fluctuations in fluids are known to lead to a Brownian loss of the swimming direction and to effective long-time diffusion. As most swimming cells or synthetic swimmers are surrounded by external flows, we consider theoretically the stochastic dynamics of a model active particle (a self-propelled sphere) in a steady general linear flow. We derive a general formulation for all components of the long-time mean-square displacement tensor and apply our general results analytically to the case of a steadily-swimming particle in three different external linear flows (pure rotation, shear, and extension). Self-propulsion leads to the same long-time temporal scalings as for passive particles but with increased coefficients. By comparing the active terms with those obtained for passive particles we see that swimming can lead to enhancement of the mean-square displacements by orders of magnitude, and could be relevant for biological organisms or synthetic swimming devices in fluctuating environmental or biological flows. [Preview Abstract] |
Monday, November 25, 2013 5:19PM - 5:32PM |
L17.00009: Swimming bacteria at complex interfaces Diego Lopez, Eric Lauga Swimming microorganisms such as bacteria often move in confined geometries. Such confinement can be caused by the presence of solid boundaries, free surfaces, or liquid interfaces. It is well established that confinement affects significantly locomotion, generating additional forces and torques on the bacteria. In the presence of a solid boundary (imposing a no-slip condition), microorganisms using helical propulsion undergo circular motion (clockwise in the case of E. coli). Conversely, close to a free (no-shear) surface the circular motion is reversed. However, realistic interfaces are complex, and experimental results do not always agree with theoretical predictions. In this work, we show, using analytical modeling, how different complex interfaces affect a nearby bacterium and modify its swimming kinematics. [Preview Abstract] |
Monday, November 25, 2013 5:32PM - 5:45PM |
L17.00010: Artificial Rheotaxis Jeremie Palacci, Stefano Sacanna, Anais Abramian, Kasey Hanson, David Pine, Paul Chaikin Self propelled colloids realize a controlled realization of an artificial bacterium. However living systems present a range of advanced properties such as the migration in gradients, or taxis, based on complex conformational change of proteins. For example, rheotaxis, the directed movement of an organism resulting from a fluid flow, has been reported notably for fish, e.g. salmon, or spermatozoa. Here, we present experimental observations of artificial rheotaxis, i.e. upstream migration of self propelled particles in the presence of a flow. We will present a simple model to account for this surprising effect. In the absence of biological component, this effect is intriguing and questions the ingredients at stake in the living matter. [Preview Abstract] |
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