Bulletin of the American Physical Society
71st Annual Meeting of the APS Division of Fluid Dynamics
Volume 63, Number 13
Sunday–Tuesday, November 18–20, 2018; Atlanta, Georgia
Session Q20: Biological Fluid Dynamics: Microswimmers |
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Chair: Kevin Mitchell, University of California, Merced Room: Georgia World Congress Center B308 |
Tuesday, November 20, 2018 12:50PM - 1:03PM |
Q20.00001: Lattice model of bacterial turbulence Renato Assante, Alexander N Morozov One of the most striking difference between active and passive systems is the appearance of collective motion in self-propelled particles suspended in a fluid observed in recent experiments and simulations: at low densities particles move around in an uncorrelated fashion, while at higher densities they organise into jets and vortices comprising many |
Tuesday, November 20, 2018 1:03PM - 1:16PM |
Q20.00002: Flow-induced synchronization in large arrays of micro-rotors Anup V Kanale, Hanliang Guo, Sebastian Fürthauer, Michael John Shelley, Eva Kanso Motile cilia cover many eukaryotic cells, from single-celled protozoa to mammalian epithelial surfaces, and play important roles in fluid transport and mixing across the cell surface. They typically beat in coordinated patterns across length scales much greater than the length of the individual cilium. Existing literature attributes the origin of this large-scale coordination to hydrodynamic interaction. However, the stability of this collective synchrony is not yet quantitatively understood. Here, we model each cilium as a micro-rotor consisting of a rigid sphere moving along a circular trajectory in close proximity to a no-slip boundary. Using the modified Green-Oseen tensor to model the far-field interaction among rotors, we numerically investigate the long-time dynamics of over 20,000 rotors arranged in square and hexagonal lattices in doubly-periodic domains. Homogeneous and isotropic states are found to be unstable to small perturbations. More interestingly, this instability leads to robust large-scale metachronal coordination. |
Tuesday, November 20, 2018 1:16PM - 1:29PM |
Q20.00003: Gyrotactic trapping can by hydrodynamically unstable Smitha Maretvadakethope, Eric E. Keaveny, Yongyun Hwang Several meters below the coastal ocean surface there are areas of high ecological activity that contain thin layers of concentrated motile phytoplankton. Gyrotactic trapping has been proposed as a potential mechanism for layer formation of bottom-heavy swimming cells like Chlamydomonas, especially in flows where the shear stress varies linearly with depth. In this study, we use a continuum model for dilute swimmer suspensions to examine gyrotactic trapping in a pressure-driven channel flow. While we find that the parabolic base flow does generate a thin layer with high cell concentration, an analysis of its linear stability reveals that the layer is hydrodynamically unstable due to negative swimmer buoyancy over the relevant range of parameter values. Our results suggest that layers formed by gyrotaxis should be transient and the stability of such layers can instead be associated with perhaps a more complex biological mechanism. |
Tuesday, November 20, 2018 1:29PM - 1:42PM |
Q20.00004: Bifurcation and Stability of plumes in a downflowing gyrotactic microorganism suspensions in a vertical cylindrical pipe Lloyd Fung, Yongyun Hwang Experiments by Kessler (1986, J. Fluid Mech. 173:191–205) have shown that in a suspension of downflowing gyrotactic swimming microalgae, the cells form a beam-like structure (plumes). Such a structure is prone to an axisymmetric blip instability. To better understand the blip instability, a three-dimensional stability analysis is performed in a circular pipe flow by extending the previous analysis of two-dimensional channel flow (Hwang & Pedley, 2014, J. Fluid Mech. 749:750-777). It is found that under the axisymmetric and streamwise-invariant assumption, there can be multiple branches of steady solutions for the gyrotactic plume. Their respective stability is computed, and the unstable mode is consistent with the blips observed in gyrotactic plumes. |
Tuesday, November 20, 2018 1:42PM - 1:55PM |
Q20.00005: The loss of isotropy due to confinement in kinesin-driven active fluids. Yi Fan, Kun-Ta Wu, S. Ali Aghvami, Seth Fraden, Zvonimir Dogic, Kenneth S. Breuer Kinesin-driven microtubule systems demonstrate complex non-equilibrium dynamics. Here, we focus on the 3D behavior in systems measuring 2 or 4 mm in the horizontal direction, but with varying confinement - ranging from 0.1 to 4 mm - in the vertical direction. Our results reveal that the active systems maintain small-scale isotropy, independent of the system size or confining boundary location, but lose large-scale isotropy as confinement increases. Meanwhile, the flow observes a transition from sub-diffusion to super-diffusion, initially in the direction perpendicular to the confining boundary and eventually in all three directions. Temporal velocity correlations reflect these transitions, showing faster decay along the perpendicular direction. The size of the large-scale flow structures, characterized by integrating the spatial correlation function, increases with the system size. However, the integral scale saturates at a maximum size of approximately 400 microns - an order of magnitude smaller than the largest system size tested. Such saturation indicates an intrinsic length scale which, along with the small-scale isotropy, demonstrate the multi-scale nature of these kinesin-driven microtubule systems. |
Tuesday, November 20, 2018 1:55PM - 2:08PM |
Q20.00006: Dynamical phases in a model for active fluids Martin James, Michael Wilczek Active fluids such as dense bacterial and microtubule suspensions exhibit interesting dynamical phases, ranging from quasi-turbulence to well-ordered patterns. Motivated by recent attempts at modeling such flows, we study a class of equations which combine elements of pattern formation with an advective nonlinearity. Such a continuum description captures a rich variety of states such as polar phases, vortex lattices and turbulence. We explore its phase space, and investigate the stability as well as the transitions between the phases. In particular, we study the properties of a type of turbulent pattern formation leading to a quasi-stationary hexagonal vortex lattice after a long turbulent transient. Our results provide new insights into the dynamics of active fluids by combining tools from pattern formation and turbulence theory. |
Tuesday, November 20, 2018 2:08PM - 2:21PM |
Q20.00007: On the oscillatory behavior of living particles suspension under step strain Sara Malvar, Bruno Souza Carmo, Francisco Ricardo Cunha In the present work, we investigated the response of a C. elegans suspension under step strain. Most experimental measurements and theoretical models published so far have focused on the steady-flow rheology. However, under transient conditions, we expected to observe competition between flow alignment and orientational relaxation. Upon startup of rotation, an initial viscous stress jump occurred primarily due to the solvent viscosity. After this initial jump, particle orientations relaxed leading to a decrease in the measured viscosity as a result of the extensile stresslet. When rotation stopped, the negative active stress persisted for a certain time, leading to a negative undershoot in the stress response, which corresponds to a retrograde torque. These mechanics led to an oscillatory response. Based on these experimental findings, we postulate an expression for the equivalent relaxation function based on the Landau-de Gennes theory and physics of nematic liquid crystals. |
Tuesday, November 20, 2018 2:21PM - 2:34PM |
Q20.00008: Phase transition to large scale coherent structures in 2d active matter turbulence Moritz Linkmann, Guido Boffetta, M. Cristina Marchetti, Bruno Eckhardt The collective motion of microswimmers in suspensions induce patterns of vortices on scales that are much larger than the characteristic size of a microswimmer, attaining a state called bacterial turbulence. Hydrodynamic turbulence acts on even larger scales and is dominated by inertial transport of energy. Using an established modification of the Navier-Stokes equation that accounts for the small scale forcing of hydrodynamic flow by microswimmers, we study the properties of a dense supension of microswimmers in two dimensions, where the conservation of enstrophy can drive an inverse cascade through which energy is accumulated on the largest scales. We find that the dynamical and statistical properties of the flow show a sharp transition to the formation of vortices at the largest length scale. The results show that 2d bacterial and hydrodynamic turbulence are separated by a subcritical phase transition. |
Tuesday, November 20, 2018 2:34PM - 2:47PM |
Q20.00009: Transitions in synchronization states of model cilia through basal-connection coupling Yujie Liu, Rory Claydon, Marco Polin, Douglas Brumley Despite evidence for a hydrodynamic origin of flagellar synchronization between different eukaryotic cells, recent experiments have shown that in single multi-flagellated organisms, coordination hinges instead on direct basal body connections. The mechanism by which these connections leads to coordination, however, is currently not understood. Here we focus on the model biflagellate Chlamydomonas reinhardtii, and propose a minimal model for the synchronization of its two flagella as a result of both hydrodynamic and direct mechanical coupling. A spectrum of different types of coordination can be selected, depending on small changes in the stiffness of intracellular couplings. These include prolonged in-phase and anti-phase synchronization, as well as a range of multistable states induced by spontaneous symmetry breaking of the system. Linking synchrony to intracellular stiffness could lead to the use of flagellar dynamics as a probe for the mechanical state of the cell. |
Tuesday, November 20, 2018 2:47PM - 3:00PM |
Q20.00010: Driving Forces for Microtubule Transport in the Mitotic Spindle Bernardo Gouveia, Akanksha Thawani, Sabine Petry, Howard A Stone The mitotic spindle is an active polymeric suspension made up of polar microtubules, chemically-reactive proteins, and molecular motors self-assembled for the purpose of capturing and segregating chromosomes during cell division. This self-assembly is orchestrated by a signaling gradient of the small protein RanGTP that emanates from the chromosomes. We present a mesoscale continuum theory that coarsely describes the concentration field of microtubules in a RanGTP gradient, accounting for the dynamic polymerization of tubulin as well as the RanGTP-mediated autocatalytic branching nucleation of microtubules. The analytic results are compared to numerical simulations of the stochastic chemical kinetics as well as experiments conducted in Xenopus laevis meiotic extracts. These data motivate the hypothesis that microtubules are stabilized in the presence of RanGTP, biasing their transport up the RanGTP gradient towards chromosomes. This stabilization manifests itself as a phoretic drift velocity of the microtubules relative to the suspending fluid, which we explore analytically as well as present preliminary experimental findings. |
Tuesday, November 20, 2018 3:00PM - 3:13PM |
Q20.00011: Topological dynamics in active nematic liquid crystals Kevin A Mitchell, Amanda Tan, Eric J Roberts, Spencer A Smith, Linda Hirst Recent years have seen a surge of interest in active materials, in which energy injected at the microscale gives rise to larger-scale coherent motion. One prominent example is an active 2D liquid crystal composed of microtubules in the nematic phase. The activity is generated by molecular motors that consume ATP to generate local shearing between the microtubules. The resulting 2D fluid flow exhibits self-generated mesoscale chaotic dynamics with a characteristic folding and stretching pattern. We analyse this dynamics in the context of chaotic advection, in which the fluid can be viewed as "stirred" by the topological defects in the nematic order parameter. We compute the topological entropy from the braiding of these defects and show that all of the entropy arises from the positive one-half defects; the negative one-half defects, which are also present, contribute nothing to the entropy. We also show that the topological entropy generated by this stirring can be understood as a direct consequence of the micro-scale stretching quantified by the Lyapunov exponent. Our work is based on experimental studies of particle tracking in the liquid crystal as well as direct imaging of the microtubule structure. |
Tuesday, November 20, 2018 3:13PM - 3:26PM |
Q20.00012: Characterizing chaotic mixing in a biological active nematic Amanda J Tan, Kevin A Mitchell, Linda S Hirst Active fluids represent an emerging field of soft matter in which the fluid’s constituent particles are not in equilibrium, instead they consume energy and move collectively with unusual dynamics to produce spontaneous chaotic mixing. We study a biological active fluid composed of semi-flexible biopolymers (microtubules), and clusters of molecular motors (kinesin). In this system, the microtubules are bundled together and crosslinked by the kinesin clusters. As the kinesin motors walk along the filaments, the bundles extend from each other and will bend, buckle, and fracture. When confined in 2D at an oil-water interface, the active network behaves as an extensile active nematic. We use fluid dynamic concepts to quantify the mixing efficiency in this active fluid. Beads are directly coupled to the microtubule bundles and we track their motion during mixing. Bead trajectories are used to measure the local rate of stretching in the fluid and extract the (local) Lyapunov exponent. The rate of local extension can be varied by changing ATP concentration and observing the effect on the Lyapunov exponents. |
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