Bulletin of the American Physical Society
64th Annual Meeting of the APS Division of Fluid Dynamics
Volume 56, Number 18
Sunday–Tuesday, November 20–22, 2011; Baltimore, Maryland
Session G8: Low Reynolds Number Swimming II |
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Chair: Lisa Fauci, Tulane University Room: 311 |
Monday, November 21, 2011 8:00AM - 8:13AM |
G8.00001: Stability of an array of bottom-heavy, upswimming, spherical squirmers Timothy Pedley, Douglas Brumley Numerical simulations by Ishikawa \& Pedley (Phys Rev Lett. 100:088103,2008; IP) of identical, bottom-heavy, spherical squirmers swimming in a vertical planar monolayer reveal a configuration in which many equally-spaced spheres swim upwards in a hexagonal array. This occurs for sufficiently large values of the bottom-heaviness parameter G. Here we perform an instability analysis in which the forces and torques on individual spheres are calculated using lubrication theory for the gaps between neighbouring squirmers. The results show that stability is impossible in the absence of the repulsive force which IP introduced to save computer time whenever two squirmers were less than 0.00001 radii apart. When the force is present, there is a critical value of G above which stability is assured. An unexpected finding is the existence of another equilibrium configuration in which the spheres' orientations are not vertical and columns of spheres are not equally spaced; in this case, however, perturbation leads to limit-cycle oscillations, not to static stability. The above results are qualitatively unaffected if the monolayer is confined between vertical walls. [Preview Abstract] |
Monday, November 21, 2011 8:13AM - 8:26AM |
G8.00002: Investigations of the Response of Swimming Paramecia to Variations in their Apparent Weight James Valles, Ilyong Jung, Karine Guevorkian, Harry Mickalide, Michael Wagman There is a set of micro-organisms that are small enough that they swim at low Reynolds number and large enough that gravity exerts an influence on their behavior Many protists, like paramecia, for example, exhibit negative gravi-taxis by orienting their swimming upward and negative gravi-kinesis by increasing their propulsion when swimming against their apparent weight. It is not clear whether these responses to a very weak force (about 100 pN) are active or passive. We have developed a technique, Magnetic Force Buoyancy Variation, which enables us to vary the apparent weight of the swimmers in situ. We will describe experiments on paramecia conducted at the National High Magnetic Field Laboratory. In particular, we will describe how increasing the apparent weight induces paramecia to accumulate at upper surfaces. A simple force model suggests that this accumulation is a passive response. [Preview Abstract] |
Monday, November 21, 2011 8:26AM - 8:39AM |
G8.00003: Locomotion of a Reciprocal Swimmer by Fluid Elasticity Nathan C. Keim, Mike Garcia, Paulo E. Arratia When fluid response is entirely viscous, a swimmer performing a reciprocal motion achieves no net displacement. This form of time-reversal symmetry is commonly broken by a non-reciprocal swimming stroke, but it may also break down if the fluidic environment has a nonlinear viscoelastic response, as found in many natural media such as mucus. In this talk, we present experiments on a rigid dimer that is ``wiggled'' in a reciprocal motion by a magnetic field, in the vicinity of a wall. When the dimer is immersed in a viscoelastic fluid, its motion produces a net translation. Surprisingly, the dimer can swim in a direction that is primarily parallel to the wall. No net translation is seen in a viscous Newtonian fluid under the same conditions. We report the effect's dependence on Deborah number, swimming stroke, and geometric parameters. The underlying mechanism is examined with particle tracking measurements. [Preview Abstract] |
Monday, November 21, 2011 8:39AM - 8:52AM |
G8.00004: Optimal ciliary beating patterns Andrej Vilfan, Natan Osterman We introduce a measure for energetic efficiency of single or collective biological cilia. We define the efficiency of a single cilium as $Q^2/P$, where $Q$ is the volume flow rate of the pumped fluid and $P$ is the dissipated power. For ciliary arrays, we define it as $(\rho Q)^2/(\rho P)$, with $\rho$ denoting the surface density of cilia. We then numerically determine the optimal beating patterns according to this criterion. For a single cilium optimization leads to curly, somewhat counterintuitive patterns. But when looking at a densely ciliated surface, the optimal patterns become remarkably similar to what is observed in microorganisms like \textit{Paramecium}. The optimal beating pattern then consists of a fast effective stroke and a slow sweeping recovery stroke. Metachronal waves lead to a significantly higher efficiency than synchronous beating. Efficiency also increases with an increasing density of cilia up to the point where crowding becomes a problem. We finally relate the pumping efficiency of cilia to the swimming efficiency of a spherical microorganism and show that the experimentally estimated efficiency of \textit{Paramecium} is surprisingly close to the theoretically possible optimum.\\[4pt] [1] N. Osterman and A. Vilfan, Finding the ciliary beating pattern with optimal efficiency, Proc. Natl. Acad. Sci. USA, in press (2011) [Preview Abstract] |
Monday, November 21, 2011 8:52AM - 9:05AM |
G8.00005: Optimal feeding vs. optimal swimming of model ciliates Sebastien Michelin, Eric Lauga To swim at low Reynolds numbers, micro-organisms create flow fields that modify the transport of nutrients around them, thereby impacting their feeding rate. When the nutrient is a passive scalar, the feeding rate of a given micro-swimmer greatly varies with the P\'eclet number (Pe) a relative measure of advection and diffusion in the nutrient transport, that strongly depends on the nutrient species considered. Using an axisymmetric envelope model for ciliary locomotion and adjoint-based optimization, we determine the swimming (or possibly non-swimming) strokes maximizing the nutrient uptake by the micro-swimmer for a given energy cost. We show that, unlike the feeding rate, this optimal feeding stroke is essentially independent of the P\'eclet number (and, therefore, of the nutrient considered) and is identical to the stroke with maximum swimming efficiency. [Preview Abstract] |
Monday, November 21, 2011 9:05AM - 9:18AM |
G8.00006: Sea Butterfly Swimming: Time-resolved Tomographic PIV measurements David Murphy, Lingxiao Zheng, Rajat Mittal, Donald Webster, Jeannette Yen The planktonic sea butterfly \textit{Limacina helicina} swims by flapping its flexible, wing-like parapodia. The appendage stroke kinematics of this shell-bearing pteropod are three-dimensional and likely contain elements of both drag-based (rowing) and lift-based (flapping) propulsion. Unsteady lift-generating mechanisms such as clap-and-fling may also be present. Upstroke and downstroke motions both propel the animal upward and roll it forwards and backwards, resulting in a sawtooth trajectory. We present time-resolved, tomographic PIV measurements of flow generated by free-swimming pteropods (\textit{Limacina helicina}) moving upwards with average swimming speeds of 5 -- 17 mm/s. The pteropods beat their appendages with a stroke frequency of 4 -- 5 Hz. With a size range of 1 -- 2 mm, the animals filmed in this study operate in a viscous environment with a Reynolds number of 5 to 20. The volumetric flow measurements provide insight into the three dimensional nature of the flow and into the relative importance of drag- and lift-based propulsion at this low Reynolds number. Preliminary results from Navier-Stokes simulations of the flow associated with the~swimming of this organism will also be presented. [Preview Abstract] |
Monday, November 21, 2011 9:18AM - 9:31AM |
G8.00007: Effect of phase delay on the pumping efficiency of a multi-plate gill array Mary Larson, Ken Kiger In nature, pumping by oscillating appendage arrays (used for respiration, feeding or locomotion) have been noted to exhibit distinct patterns of movement depending on their intended function and Reynolds number. One thing that is typically in common, however, is that a phase lag of 60 to 90 degrees between adjacent appendages is used for many low to intermediate Reynolds number conditions (10 to 10000). To understand why this trait is commonly exhibited, a robotic oscillating plate array modeled after a nymphal mayfly was constructed that permitted stroke, pitch and phase lag variation between adjacent plates. Stereoscopic PIV was used to obtain three-dimensional velocity data, allowing computation of the net pumping rate and flow induced dissipation for five cases, focusing on the role of the gill plate interactions and their dependence on the phase lag between adjacent gills. The results indicate that mayfly gills most likely use a phase lag of 90$^{\circ}$ because it produces the highest net mass flow rate while consuming the least amount of energy. Measurements indicate that this occurs as a balance between excessive dissipation during close-approach events while optimizing favorable hydrodynamic interactions between adjacent plates. [Preview Abstract] |
Monday, November 21, 2011 9:31AM - 9:44AM |
G8.00008: A numerical study on swimming micro-organisms inside a capillary tube Lailai Zhu, Eric Lauga, Luca Brandt The locomotivity of micro-organisms is highly dependent on the surrounding environments such as walls, free surface and neighbouring cells. In our current work, we perform simulations of swimming micro-organisms inside a capillary tube based on boundary element method. We focus on the swimming speed, power consumption and locomotive trajectory of swimming cells for different levels of confinement. For a cell propelling itself by tangential surface deformation, we show that it will swim along a helical trajectory with a specified swimming gait. Such a helical trajectory was observed before by experiments on swimming \textit{Paramecium} inside a capillary tube. [Preview Abstract] |
Monday, November 21, 2011 9:44AM - 9:57AM |
G8.00009: Swimming of Flexible Nanowire Motors On Shun Pak, Wei Gao, Joseph Wang, Eric Lauga In this talk, we report on a new nanowire motor which exploits the flexibility of nanowires for propulsion. The motor is made of nickel and silver nanowires, and it is fabricated using a common template-directed electrodeposition protocol. These readily prepared nanomotors display both high dimensional and dimensionless (in body lengths per revolution) propulsion velocities when compared with natural microorganisms and other artificial propellers. Their propulsion characteristics are studied theoretically using an elastohydrodynamic model which takes into account the elasticity of the nanowire and its hydrodynamic interaction with the fluid medium. The theoretical predictions by an asymptotic analysis for small-amplitude swimming are then compared with experimental measurements and we obtain good agreement. Finally, we demonstrate the operation of these nanomotors in a real biological environment (human serum), emphasizing the robustness of their propulsion performance and their promise for biomedical applications. [Preview Abstract] |
Monday, November 21, 2011 9:57AM - 10:10AM |
G8.00010: Electrokinetic self-Propulsion of a Catalytic Nanomotor; a Perturbation Analysis Amir Nourhani, Paul Lammert, Ali Borhan, Vincent Crespi The development of bimetallic catalytic nanomotors has been one of many attempts to mimic the behavior of bionanomotors and micro-organisms. Recent experimental analysis has shown that electrokinetic self-propulsion is the dominant mechanism for autonomous motion of these nanomotors in hydrogen peroxide. In this work, we propose a mathematical model for the steady state locomotion of an axisymmetric spherical nanomotor in a symmetric binary electrolyte. The asymmetric production and consumption of hydrogen ions on the surface of the particle is modeled by a general position-dependent flux. The flux of negative ions on the surface is zero. Using perturbation analysis and the method of matched asymptotic expansion, we solve the model for the velocity of the particle to the leading order in Debye length and to the first order in the intensity of hydrogen ions flux. The velocity depends linearly on the interfacial potential of the surface of the particle and the intensity of hydrogen ions flux. It also inversely depends on the viscosity of fluid, the ion concentration in electrolyte and the diffusion coefficient of the hydrogen ions. The predicted behavior is consistent with experimental results and numerical calculations. [Preview Abstract] |
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