Bulletin of the American Physical Society
65th Annual Meeting of the APS Division of Fluid Dynamics
Volume 57, Number 17
Sunday–Tuesday, November 18–20, 2012; San Diego, California
Session R17: Biofluids: Micro-swimming Theory II |
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Chair: Jeffrey Guasto, Massachusetts Institute of Technology Room: 28C |
Tuesday, November 20, 2012 1:00PM - 1:13PM |
R17.00001: Studies of Ciliated Microorganism Swimming with and against a Magnetic Field Tuned Apparent Weight Force Ilyong Jung, Harry Mickalide, James M. Valles Jr. There is a class of microorganisms that are small enough to swim at low Reynolds number but large enough for gravity to influence their behavior. Remarkably, {\it Paramecia} exert a stronger (weaker) propulsion force when swimming against (with) their apparent weight force, $\vec W$. To investigate the source of the swimming speed response, we are examining how the trajectories of single swimmers change when they reverse their direction relative to $\vec W$. We characterize their helical trajectories with three parameters that we can relate to their beating of their cilia using a simple model. The latest results will be described. [Preview Abstract] |
Tuesday, November 20, 2012 1:13PM - 1:26PM |
R17.00002: Micropropulsion and microrheology in complex fluids via symmetry breaking On Shun Pak, Lailai Zhu, Luca Brandt, Eric Lauga Many biological fluids have polymeric microstructures and display non-Newtonian rheology. We take advantage of such nonlinear fluid behavior and combine it with geometrical symmetry-breaking to design a novel small-scale propeller able to move only in complex fluids. Its propulsion characteristics are explored numerically in an Oldroyd-B fluid for finite Deborah numbers while the small Deborah number limit is investigated analytically using a second-order fluid model. We then derive expressions relating the propulsion speed to the rheological properties of the complex fluid, allowing thus to infer the normal stress coefficients in the fluid from the locomotion of the propeller. Our simple mechanism can therefore be used either as a non-Newtonian micro-propeller or as a micro-rheometer. [Preview Abstract] |
Tuesday, November 20, 2012 1:26PM - 1:39PM |
R17.00003: A Numerical Study of Muco-Ciliary Transport under the condition of Primary Ciliary Dyskinesia Pahala Gedara Jayathilake, Wan Lung Lee, Duc Vinh Le, Heow Pueh Lee, Boo Cheong Khoo Primary ciliary dyskinesia (PCD) is a disease due to the defects in motile cilia. A two-dimensional numerical model based on the immersed boundary method coupled with the projection method is used for a preliminary study of the flow physics of muco-ciliary transport of human respiratory tract under PCD conditions. The effects of the cilia beating amplitude, cilia beat pattern (CBP), cilia beat frequency (CBF), immotile cilia, and uncoordinated beating of cilia on mucus transport are investigated. As expected, the mucus velocity decreases as the beating amplitude and CBF decrease. The windscreen wiper motion and rigid rod motion, which are two abnormal CBPs owing to PCD, would greatly reduce the mucus transport. The mucus velocity decreases rather linearly if the number of uniformly distributed immotile cilia increases. The results further show that the mucus velocity would be slightly reduced when the uniformly distributed immotile cilia are rearranged as a cluster of immotile cilia. Furthermore, if the half of the cilia are immotile and uniformly distributed, the incoordination between motile cilia would not significantly affect the mucus velocity. [Preview Abstract] |
Tuesday, November 20, 2012 1:39PM - 1:52PM |
R17.00004: Dynamics of artificial bacterial flagella Yi Man, Eric Lauga Artificial bacterial flagella (ABF) are small-scale rigid helices actuated by an external rotating magnetic field and therefore able to propel in a viscous fluid. In experiments, ABF are observed to display wobbling motion at low frequencies and a transition to directed swimming at higher frequencies. We use here a combination of numerics and asymptotics to provide a theoretical explanation for this dynamics. In particular we show that the wobbling angle - the angle between the direction of propulsion and the axis of the helix - is inversely proportional to the Mason number, a dimensionless number given by the ratio of the magnitudes of viscous torque to magnetic torque. Our theoretical predictions agree well with experimental results. [Preview Abstract] |
Tuesday, November 20, 2012 1:52PM - 2:05PM |
R17.00005: Analysis of the orbits of particles generating one-dimensional dynamic coherent structures Denis Melnikov, Dmitri Pushkin, Valentina Shevtsova The particle accumulation in time-periodic incompressible flows is studied experimentally and numerically. The geometry of interest is a cylindrical column of finite length where a liquid is suspended between two differentially heated horizontal flat disks. The increase of the temperature difference between disks beyond the critical values results in appearance of time periodic flows which are either standing or azimuthally travelling hydrothermal wave. In the case of travelling wave inertial particles have a tendency to spontaneously align in one-dimensional dynamic coherent structures called below as orbits. Three types of orbits are experimentally found in the system with polydisperse particles (differing in size, shape and density). Initial positions of different particles were close to each other. These orbits can be classified as periodic (loop PAS), quasi-periodic (toroidal PAS) and temporally synchronized orbits. Assuming the motion of particles is described by the simplified Maxey-Riley equation, the phenomenon of formation of particles accumulation structures was numerically analysed. The experimental observations are in a favourable agreement with the results of the computer simulations. [Preview Abstract] |
Tuesday, November 20, 2012 2:05PM - 2:18PM |
R17.00006: Optimal shapes of surface-slip driven self-propelled swimmers Andrej Vilfan, Natan Osterman If one defines the swimming efficiency of a microorganism as the power needed to move it against viscous drag, divided by the total dissipated power, one usually finds values no better than 1\%. In order to find out how close this is to the theoretically achievable optimum, we first introduced a new efficiency measure at the level of a single cilium or an infinite ciliated surface and numerically determined the optimal beating patterns according to this criterion [1]. In the following we also determined the optimal shape of a swimmer such that the total power is minimal while maintaining the volume and the swimming speed. The resulting shape depends strongly on the allowed maximum curvature. When sufficient curvature is allowed the optimal swimmer exhibits two protrusions along the symmetry axis. The results show that prolate swimmers such as Paramecium have an efficiency that is $\sim$ 20\% higher than that of a spherical body, whereas some microorganisms have shapes that allow even higher efficiency.\\[4pt] [1] N. Osterman and A. Vilfan, Finding the ciliary beating pattern with optimal efficiency, Proc. Natl. Acad. Sci. USA, 108 15727-15732 (2011) [Preview Abstract] |
Tuesday, November 20, 2012 2:18PM - 2:31PM |
R17.00007: Study of propulsion of microorganisms using viscous slender-body theory Srikanth Toppaladoddi, Neil Balmforth In this study, we investigate the swimming of a slender axisymmetrical body in a Newtonian fluid in the Stokes' regime. The slender body propels itself by generating surface travelling waves. The mathematical framework to study this problem has been built using the slender-body theory of Keller and Rubinow (J. Fluid Mech., vol. 75, part 4, pp. 705-714, 1976). The motion of the body and the dilation of its surface are incorporated by having Stokeslet and source distributions along the body's axis, and the propulsion speed is determined by solving the resulting integral equation using an asymptotic expansion. For high wavenumbers, the propulsion speed for a cylinder is found to agree with results presented by Setter et al. (Phys. Rev. E 85, 066304, 2012) in the limit of vanishing cylinder radius and wave amplitude. We quantify the efficiency of the swimmer and explore its internal mechanics when the body is treated as a fluid-filled cavity with elastic fibres driving surface deformation. [Preview Abstract] |
Tuesday, November 20, 2012 2:31PM - 2:44PM |
R17.00008: Hydrodynamic Contributions to Amoeboid Cell Motility Owen Lewis, Robert Guy Understanding the methods by which cells move is a fundamental problem in modern biology. Recent evidence has shown that the fluid dynamics of cytoplasm can play a vital role in cellular motility. The slime mold Physarum polycephalum provides an excellent model organism for the study of amoeboid motion. In this research, we use a simply analytic model in conjuction with computational experiments to investigate intracellular fluid flow in a simple model of Physarum. Of particlar interest are stresses generated by cytoplasmic flow which may be used to aid in cellular motility. In our numerical model, the Immersed Boundary Method is used to account for such stresses. We investigate the relationship between contraction waves, flow waves, adhesion, and locomotive forces in an attempt to characterize conditions necessary to generate directed motion. [Preview Abstract] |
Tuesday, November 20, 2012 2:44PM - 2:57PM |
R17.00009: Gyrotactic Bioconvection in Density-Stratified Fluids Alireza Karimi, Arezoo Ardekani Bioconvection is a complex phenomenon causing spontaneous pattern formation in some biological systems, for instance in bacterial, algal, and ciliate cultures. It occurs as a result of the collective behavior of up-swimming microorganisms in response to the certain types of physical stimuli. We are interested in the special case of gyrotaxis where the swimming is directed by the balance of the viscous torque arising from shear flow and the torque due to gravity acting on a bottom-heavy cell. We investigate gyrotactic bioconvection in the presence of a temperature or salinity stratification, using large-scale numerical simulations of a continuum model consisting of Navier-Stokes equations with Boussinesq approximation coupled with two conservation equations for the concentration of microorganisms and stratified agent. We explore different regimes of the flow by varying the corresponding dimensionless variables such as Rayleigh number and Lewis number, to shed light on the characteristics of double-diffusive convection engendered by active swimmers in a stratified environment. [Preview Abstract] |
Tuesday, November 20, 2012 2:57PM - 3:10PM |
R17.00010: Asymmetry and stability of shape kinematics in microswimmers' motion Yizhar Or Many swimming microorganisms governed by low-Reynolds-number hydrodynamics utilize flagellar undulations for self propulsion. Most of existing theoretical models assume that the shape kinematics is directly controlled, while in reality, eukaryotes actuate internal bending moments along their flagellum. Under control of the internal forces and torques, the swimmer's shape is dynamically evolving and periodic gaits may become unstable. In this work the problem is addressed by revisiting Purcell's three-link swimmer model where the joint torques are controlled. The swimmer's dynamic equations of motion are formulated and the underlying geometric symmetries are analyzed. It is found that certain symmetry properties of the input induce a reversing symmetry on the dynamics of the joint angles, under which periodic solutions are marginally stable. Moreover, it is proven that one has to break the front-back symmetry of the swimmer's structure and/or actuation profile in order to induce time-periodic solution for the shape kinematics which is asymptotically stable under perturbations. In particular, a swimmer with large drag resistance at its front enjoys a strongly stable shape kinematics. The results may explain why most of the flagellated eukaryotes swim with their head forward. [Preview Abstract] |
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