Bulletin of the American Physical Society
69th Annual Meeting of the APS Division of Fluid Dynamics
Volume 61, Number 20
Sunday–Tuesday, November 20–22, 2016; Portland, Oregon
Session L39: Bio: Modeling of Microswimmers |
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Chair: Enkeleida Lushi, Brown University Room: Portland Ballroom 256 |
Monday, November 21, 2016 4:30PM - 4:43PM |
L39.00001: On the interactions of micro-swimmers with surfaces Enkeleida Lushi Solid boundaries alter both motion and spatial distribution of microorganisms in ways that are currently not completely understood. We present novel micro-swimmer models and simulations able to display correct features seen in experiments such as bacteria circling near surfaces or micro-algae scattering from them. For pushers like bacteria we show that the correct flow singularity is more complex than a force dipole. For bi-flagellates like micro-algae we show that their behavior at surfaces results from a nuanced interplay of flagellar contact, hydrodynamics, noise and cell spinning, with the swimmer geometry being a crucial component. Our results compare well with the most recent experimental data and suggest ways of designing multi-swimmer simulations that capture the correct physics. [Preview Abstract] |
Monday, November 21, 2016 4:43PM - 4:56PM |
L39.00002: An elastic two-sphere swimmer in Stokes flow Babak Nasouri, Gwynn Elfring Swimming at low Reynolds number in Newtonian fluids is only possible through non-reciprocal body deformations due to the kinematic reversibility of the Stokes equations. We consider here a model swimmer consisting of two linked spheres, wherein one sphere is rigid and the other an incompressible neo-Hookean solid. The two spheres are connected by a rod which changes its length periodically. We show that the deformations of the body are non-reciprocal despite the reversible actuation and hence, the elastic two-sphere swimmer propels forward. Our results indicate that even weak elastic deformations of a body can qualitatively alter swimming dynamics and should not be neglected in analyzing swimming in Stokes flows. [Preview Abstract] |
Monday, November 21, 2016 4:56PM - 5:09PM |
L39.00003: Optimal control, optimization and asymptotic analysis of Purcell's microswimmer model Oren Wiezel, Yizhar Or Purcell's swimmer (1977) is a classic model of a three-link microswimmer that moves by performing periodic shape changes. Becker et al. (2003) showed that the swimmer's direction of net motion is reversed upon increasing the stroke amplitude of joint angles. Tam and Hosoi (2007) used numerical optimization in order to find optimal gaits for maximizing either net displacement or Lighthill's energetic efficiency. In our work, we analytically derive leading-order expressions as well as next-order corrections for both net displacement and energetic efficiency of Purcell's microswimmer. Using these expressions enables us to explicitly show the reversal in direction of motion, as well as obtaining an estimate for the optimal stroke amplitude. We also find the optimal swimmer's geometry for maximizing either displacement or energetic efficiency. Additionally, the gait optimization problem is revisited and analytically formulated as an optimal control system with only two state variables, which can be solved using Pontryagin's maximum principle. It can be shown that the optimal solution must follow a "singular arc''. Numerical solution of the boundary value problem is obtained, which exactly reproduces Tam and Hosoi's optimal gait. [Preview Abstract] |
Monday, November 21, 2016 5:09PM - 5:22PM |
L39.00004: The stresslet induced by active swimmers Sebastien Michelin, Eric Lauga Active particles such as self-propelled cells and catalytic swimmers disturb the fluid around them as stresslets, symmetric force dipoles whose flow field decays as the inverse distance squared. The characteristics of the stresslet govern their collective dynamics and their contribution to the suspension bulk stress. Unlike swimming speeds, the stresslets of active particles are rarely determined due to the lack of a suitable theoretical framework, since it combines information on both fluid velocity and forces at the surface of the active particle. We propose a new method, based on the reciprocal theorem of Stokes flows, to compute stresslets as integrals of the velocities on the particle's surface exclusively. This method can be efficiently used to determine the stresslet of spheroidal chemically-active particles. This approach will help tuning the stresslet of artificial swimmers and tailor their collective motion in complex environments. [Preview Abstract] |
Monday, November 21, 2016 5:22PM - 5:35PM |
L39.00005: Swimming in a suspension of rod-like molecules Juan Shi, Thomas Powers In nature, it is common for microorganisms to swim in fluids with microstructure, such as mucus. Motivated by this fact, there have been many recent theoretical, computational, and experimental studies of idealized swimmers in a dilute solution of flexible polymers. Here we study this problem from a different point of view by considering swimmers in a dilute solution of rigid rod-like polymers. We study the prescribed swimming problem of Taylor's sheet in a dilute suspension of non-Brownian rods. Using a simple continuum constitutive law for the suspension that describes the stress in terms of velocity gradient and local rod orientation, we calculate swimming speed to second order in the amplitude of the wave. Due to stresses induced by the presence of the rods, the first-order flow field differs from that of the Newtonian case. We find that the swimming speed increases linearly with rod concentration: the presence of the rods always makes the swimmer go faster. We also consider the problem of a finite swimmer by studying a two-dimensional circular squirmer. The squirmer is defined as a circle with a prescribed tangential slip velocity that leads to propulsion. By varying the prescribed slip boundary condition, we study both pushers and pullers. [Preview Abstract] |
Monday, November 21, 2016 5:35PM - 5:48PM |
L39.00006: Elastohydrodynamics of flagellated microorganisms Gaojin Li, arezoo ardekani The swimming motion of many microorganisms and cells are achieved by the waving deformation of their cilia and flagella. The typical structure of flagella and cilia contains nine doublets of parallel microtubules in a cylindrical arrangement surrounding one pair of microtubules in the center. The dynein molecular motors internally drive the sliding motion between the neighboring microtubules and cause the bending motion of the flagella and cilia and drive the microorganism swimming motion. In this work, we develop a numerical model for a microorganism swimming by an internally self-driven filament. Our numerical method captures the interaction between the elasticity of the flagellum and the surround fluid. The no-slip boundary conditions are satisfied by an iterative distributed Lagrangian multiplier method. We also investigate the effects of the non-Newtonian fluid rheology on the motion of an elastic flagellum near a wall. [Preview Abstract] |
Monday, November 21, 2016 5:48PM - 6:01PM |
L39.00007: What causes periodic beating in sperm flagella: synchronized internal forcing or fluid-structure interaction? Ranganathan Prabhakar, Ashwin Nandagiri, Sameer Jadhav Eucaryotic cells such as sperm propel themselves using internally driven flagella. Two different models for the origin of the whip-like beating observed in such flagella are compared. The first model assumes that internal protein motors actuate synchronously to cause a traveling active-force wave within the filament. The forcing wave is chosen such that its resultant and the total torque on the filament are zero. In contrast, the second model assumes that forces and torques exerted by the motors locally sum to zero across the scale of the filament diameter. The only effect of the motor activity is to give rise to a stresslet distribution across the filament length. In either model, the slender filament is modeled as a bead-spring chain with hydrodynamic interactions. Flagellar waveforms and trajectory patterns obtained are compared systematically while keeping the dissipation rates the same for the two models. Periodic beating emerges in freely swimming filaments with the second model without any imposed periodicity in the stresslet distribution. This suggests that periodic waveforms in eucaryotic flagella can emerge by fluid-structure interactions alone without significant internal synchronization of protein motor activity. [Preview Abstract] |
Monday, November 21, 2016 6:01PM - 6:14PM |
L39.00008: Vortex arrays and ciliary tangles underlie the feeding-swimming tradeoff in starfish larvae William Gilpin, Vivek N. Prakash, Manu Prakash Many marine invertebrates have larval stages covered in linear arrays of beating cilia, which propel the animal while simultaneously entraining planktonic prey. These bands are strongly conserved across taxa spanning four major superphyla, and they are responsible for the unusual morphologies of many invertebrates. However, few studies have investigated their underlying hydrodynamics. Here, we study the ciliary bands of starfish larvae, and discover a beautiful pattern of slowly-evolving vortices that surrounds the swimming animals. Closer inspection of the bands reveals unusual ciliary “tangles” analogous to topological defects that break-up and re-form as the animal adjusts its swimming stroke. Quantitative experiments and modeling demonstrate that these vortices create a physical tradeoff between feeding and swimming in heterogenous environments, which manifests as distinct flow patterns or "eigenstrokes" representing each behavior---potentially implicating neuronal control of cilia. This quantitative interplay between larval form and hydrodynamic function generalizes to other invertebrates, and illustrates the potential effects of active boundary conditions in other biological and synthetic systems. [Preview Abstract] |
Monday, November 21, 2016 6:14PM - 6:27PM |
L39.00009: Sorting of Sperm by Morphology James Koh, Marcos Marcos Many studies have proven that the percentage of morphologically normal sperm is a significant factor in determining the success of assisted reproduction. The velocity of sperm in a microchannel with shear flow subjected to an external field will be explored theoretically. The difference in response between morphologically normal and abnormal sperm will be computed from a statistical approach, to study the feasibility and effectiveness of sorting by an external field to remove abnormal sperm. [Preview Abstract] |
Monday, November 21, 2016 6:27PM - 6:40PM |
L39.00010: Stability transitions and directional flipping in a microswimmer with superparamagnetic links Yuval Harduf, Yizhar Or The famous work of Dreyfus et al (2005) introduced a microswimmer composed of a chain of superparamagnetic beads and actuated by a planar oscillating magnetic field. Further numerical simulations of the swimmer model by Gauger & Stark (2006) revealed that for large enough oscillation amplitude of the magnetic field's direction, the swimmer's mean orientation and net swimming direction both flip from the mean direction of the magnetic field to a direction perpendicular to it. This observation has been confirmed experimentally in Roper et al (2008). In our work, we analyze this phenomenon theoretically by studying the simplest possible microswimmer model: two slender links connected by an elastic joint, while one link is superparamagnetic. The dynamic equations of motion are formulated explicitly, and approximated by a second-order system which resembles the well-known Kapitza pendulum with an oscillating pivot. Conditions for stability transitions induced by the system's parametric excitation are obtained numerically and analytically by using Hill's equation and infinite determinant. Remarkably, it is also found that there exist intermediate parameter regions of dynamic bistability where the aligned and perpendicular directions are both stable under different initial conditions. [Preview Abstract] |
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