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Journal articles on the topic 'Low Reynolds number locomotion'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Zhu, L., E. Lauga, and L. Brandt. "Low-Reynolds-number swimming in a capillary tube." Journal of Fluid Mechanics 726 (May 31, 2013): 285–311. http://dx.doi.org/10.1017/jfm.2013.225.

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AbstractWe use the boundary element method to study the low-Reynolds-number locomotion of a spherical model microorganism in a circular tube. The swimmer propels itself by tangential or normal surface motion in a tube whose radius is of the order of the swimmer size. Hydrodynamic interactions with the tube walls significantly affect the average swimming speed and power consumption of the model microorganism. In the case of swimming parallel to the tube axis, the locomotion speed is always reduced (respectively, increased) for swimmers with tangential (respectively, normal) deformation. In all cases, the rate of work necessary for swimming is increased by confinement. Swimmers with no force dipoles in the far field generally follow helical trajectories, solely induced by hydrodynamic interactions with the tube walls, and in qualitative agreement with recent experimental observations for Paramecium. Swimmers of the puller type always display stable locomotion at a location which depends on the strength of their force dipoles: swimmers with weak dipoles (small $\alpha $) swim in the centre of the tube while those with strong dipoles (large $\alpha $) swim near the walls. In contrast, pusher swimmers and those employing normal deformation are unstable and end up crashing into the walls of the tube. Similar dynamics is observed for swimming into a curved tube. These results could be relevant for the future design of artificial microswimmers in confined geometries.

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2

Reigh, Shang Yik, Lailai Zhu, François Gallaire, and Eric Lauga. "Swimming with a cage: low-Reynolds-number locomotion inside a droplet." Soft Matter 13, no. 17 (2017): 3161–73. http://dx.doi.org/10.1039/c6sm01636g.

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Inspired by recent experiments using synthetic microswimmers to manipulate droplets, we investigate the low-Reynolds-number locomotion of a model swimmer (a spherical squirmer) encapsulated inside a droplet of a comparable size in another viscous fluid.

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3

Han, Endao, Lailai Zhu, Joshua W. Shaevitz, and Howard A. Stone. "Low-Reynolds-number, biflagellated Quincke swimmers with multiple forms of motion." Proceedings of the National Academy of Sciences 118, no. 29 (July 15, 2021): e2022000118. http://dx.doi.org/10.1073/pnas.2022000118.

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In the limit of zero Reynolds number (Re), swimmers propel themselves exploiting a series of nonreciprocal body motions. For an artificial swimmer, a proper selection of the power source is required to drive its motion, in cooperation with its geometric and mechanical properties. Although various external fields (magnetic, acoustic, optical, etc.) have been introduced, electric fields are rarely utilized to actuate such swimmers experimentally in unbounded space. Here we use uniform and static electric fields to demonstrate locomotion of a biflagellated sphere at low Re via Quincke rotation. These Quincke swimmers exhibit three different forms of motion, including a self-oscillatory state due to elastohydrodynamic–electrohydrodynamic interactions. Each form of motion follows a distinct trajectory in space. Our experiments and numerical results demonstrate a method to generate, and potentially control, the locomotion of artificial flagellated swimmers.

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4

Cohen, Netta, and Jordan H. Boyle. "Swimming at low Reynolds number: a beginners guide to undulatory locomotion." Contemporary Physics 51, no. 2 (March 2010): 103–23. http://dx.doi.org/10.1080/00107510903268381.

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5

CROWDY, DARREN, SUNGYON LEE, OPHIR SAMSON, ERIC LAUGA, and A. E. HOSOI. "A two-dimensional model of low-Reynolds number swimming beneath a free surface." Journal of Fluid Mechanics 681 (June 29, 2011): 24–47. http://dx.doi.org/10.1017/jfm.2011.223.

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Biological organisms swimming at low-Reynolds number are often influenced by the presence of rigid boundaries and soft interfaces. In this paper, we present an analysis of locomotion near a free surface with surface tension. Using a simplified two-dimensional singularity model and combining a complex variable approach with conformal mapping techniques, we demonstrate that the deformation of a free surface can be harnessed to produce steady locomotion parallel to the interface. The crucial physical ingredient lies in the nonlinear hydrodynamic coupling between the disturbance flow created by the swimmer and the free boundary problem at the fluid surface.

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6

Wang, Qixuan. "Optimal Strokes of Low Reynolds Number Linked-Sphere Swimmers." Applied Sciences 9, no. 19 (September 26, 2019): 4023. http://dx.doi.org/10.3390/app9194023.

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Optimal gait design is important for micro-organisms and micro-robots that propel themselves in a fluid environment in the absence of external force or torque. The simplest models of shape changes are those that comprise a series of linked-spheres that can change their separation and/or their sizes. We examine the dynamics of three existing linked-sphere types of modeling swimmers in low Reynolds number Newtonian fluids using asymptotic analysis, and obtain their optimal swimming strokes by solving the Euler–Lagrange equation using the shooting method. The numerical results reveal that (1) with the minimal 2 degrees of freedom in shape deformations, the model swimmer adopting the mixed shape deformation modes strategy is more efficient than those with a single-mode of shape deformation modes, and (2) the swimming efficiency mostly decreases as the number of spheres increases, indicating that more degrees of freedom in shape deformations might not be a good strategy in optimal gait design in low Reynolds number locomotion.

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7

Pak, On Shun, and Eric Lauga. "The transient swimming of a waving sheet." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466, no. 2113 (October 2, 2009): 107–26. http://dx.doi.org/10.1098/rspa.2009.0208.

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Small-scale locomotion plays an important role in biology. Different modelling approaches have been proposed in the past. The simplest model is an infinite inextensible two-dimensional waving sheet, originally introduced by Taylor, which serves as an idealized geometrical model for both spermatozoa locomotion and ciliary transport in Stokes flow. Here, we complement classic steady-state calculations by deriving the transient low-Reynolds number swimming speed of such a waving sheet when starting from rest (small-amplitude initial-value problem). We also determine the transient fluid flow in the ‘pumping’ setup where the sheet is not free to move but instead generates a net fluid flow around it. The time scales for these two problems, which in general govern transient effects in transport and locomotion at low Reynolds numbers, are also derived using physical arguments.

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8

Lohéac, Jérôme, and Takéo Takahashi. "Controllability of low Reynolds numbers swimmers of ciliate type." ESAIM: Control, Optimisation and Calculus of Variations 26 (2020): 31. http://dx.doi.org/10.1051/cocv/2019010.

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We study the locomotion of a ciliated microorganism in a viscous incompressible fluid. We use the Blake ciliated model: the swimmer is a rigid body with tangential displacements at its boundary that allow it to propel in a Stokes fluid. This can be seen as a control problem: using periodical displacements, is it possible to reach a given position and a given orientation? We are interested in the minimal dimension d of the space of controls that allows the microorganism to swim. Our main result states the exact controllability with d = 3 generically with respect to the shape of the swimmer and with respect to the vector fields generating the tangential displacements. The proof is based on analyticity results and on the study of the particular case of a spheroidal swimmer.

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9

Ji, Lingbo, and Wim M. van Rees. "Locomotion of a rotating cylinder pair with periodic gaits at low Reynolds numbers." Physics of Fluids 32, no. 10 (October 1, 2020): 103102. http://dx.doi.org/10.1063/5.0022681.

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10

Lenz, Petra H., Daisuke Takagi, and Daniel K. Hartline. "Choreographed swimming of copepod nauplii." Journal of The Royal Society Interface 12, no. 112 (November 2015): 20150776. http://dx.doi.org/10.1098/rsif.2015.0776.

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Small metazoan paddlers, such as crustacean larvae (nauplii), are abundant, ecologically important and active swimmers, which depend on exploiting viscous forces for locomotion. The physics of micropaddling at low Reynolds number was investigated using a model of swimming based on slender-body theory for Stokes flow. Locomotion of nauplii of the copepod Bestiolina similis was quantified from high-speed video images to obtain precise measurements of appendage movements and the resulting displacement of the body. The kinematic and morphological data served as inputs to the model, which predicted the displacement in good agreement with observations. The results of interest did not depend sensitively on the parameters within the error of measurement. Model tests revealed that the commonly attributed mechanism of ‘feathering’ appendages during return strokes accounts for only part of the displacement. As important for effective paddling at low Reynolds number is the ability to generate a metachronal sequence of power strokes in combination with synchronous return strokes of appendages. The effect of feathering together with a synchronous return stroke is greater than the sum of each factor individually. The model serves as a foundation for future exploration of micropaddlers swimming at intermediate Reynolds number where both viscous and inertial forces are important.

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11

Huang, H. W., F. E. Uslu, P. Katsamba, E. Lauga, M. S. Sakar, and B. J. Nelson. "Adaptive locomotion of artificial microswimmers." Science Advances 5, no. 1 (January 2019): eaau1532. http://dx.doi.org/10.1126/sciadv.aau1532.

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Bacteria can exploit mechanics to display remarkable plasticity in response to locally changing physical and chemical conditions. Compliant structures play a notable role in their taxis behavior, specifically for navigation inside complex and structured environments. Bioinspired mechanisms with rationally designed architectures capable of large, nonlinear deformation present opportunities for introducing autonomy into engineered small-scale devices. This work analyzes the effect of hydrodynamic forces and rheology of local surroundings on swimming at low Reynolds number, identifies the challenges and benefits of using elastohydrodynamic coupling in locomotion, and further develops a suite of machinery for building untethered microrobots with self-regulated mobility. We demonstrate that coupling the structural and magnetic properties of artificial microswimmers with the dynamic properties of the fluid leads to adaptive locomotion in the absence of on-board sensors.

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12

Shaik, Vaseem A., Vishwa Vasani, and Arezoo M. Ardekani. "Locomotion inside a surfactant-laden drop at low surface Péclet numbers." Journal of Fluid Mechanics 851 (July 19, 2018): 187–230. http://dx.doi.org/10.1017/jfm.2018.491.

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We investigate the dynamics of a swimming microorganism inside a surfactant-laden drop for axisymmetric configurations under the assumptions of small Reynolds number and small surface Péclet number $(Pe_{s})$. Expanding the variables in $Pe_{s}$, we solve the Stokes equations for the concentric configuration using Lamb’s general solution, while the dynamic equation for the stream function is solved in the bipolar coordinates for the eccentric configurations. For a two-mode squirmer inside a drop, the surfactant redistribution can either increase or decrease the magnitude of swimmer and drop velocities, depending on the value of the eccentricity. This was explained by analysing the influence of surfactant redistribution on the thrust and drag forces acting on the swimmer and the drop. The far-field representation of a surfactant-covered drop enclosing a pusher swimmer at its centre is a puller; the strength of this far field is reduced due to the surfactant redistribution. The advection of surfactant on the drop surface leads to a time-averaged propulsion of the drop and the time-reversible swimmer that it engulfs, thereby causing them to escape from the constraints of the scallop theorem. We quantified the range of parameters for which an eccentrically stable configuration can be achieved for a two-mode squirmer inside a clean drop. The surfactant redistribution shifts this eccentrically stable position towards the top surface of the drop, although this shift is small.

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13

Dandekar, Rajat, Vaseem A. Shaik, and Arezoo M. Ardekani. "Swimming sheet in a density-stratified fluid." Journal of Fluid Mechanics 874 (July 4, 2019): 210–34. http://dx.doi.org/10.1017/jfm.2019.445.

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In this work, we theoretically investigate the swimming velocity of a Taylor swimming sheet immersed in a linearly density-stratified fluid. We use a regular perturbation expansion approach to estimate the swimming velocity up to second order in wave amplitude. We divide our analysis into two regimes of low ($\ll O(1)$) and finite Reynolds numbers. We use our solution to understand the effect of stratification on the swimming behaviour of organisms. We find that stratification significantly influences motility characteristics of the swimmer such as the swimming speed, hydrodynamic power expenditure, swimming efficiency and the induced mixing, quantified by mixing efficiency and diapycnal eddy diffusivity. We explore this dependence in detail for both low and finite Reynolds number and elucidate the fundamental insights obtained. We expect our work to shed some light on the importance of stratification in the locomotion of organisms living in density-stratified aquatic environments.

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14

Fahad Anwer, Syed, Syed Mohammed Yahya, Mohammad Athar Khan, and Saif Masood. "On the Thrust Generation from an Elliptic Airfoil in Plunging and Translating Motion at Low Reynolds Numbers." Advanced Science, Engineering and Medicine 12, no. 10 (October 1, 2020): 1261–71. http://dx.doi.org/10.1166/asem.2020.2711.

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In this paper, numerical simulation elliptic airfoil model, which mimics the biological locomotion, is studied. Elliptic airfoil undergoes a combined plunging and translating at low Reynolds number is simulated by using body fitted coordinate system. The moving mesh in the physical domain is mapped to a regular fixed mesh in the computational domain through a time dependent transformation between the physical and computational co-ordinates. The governing equations of laminar incompressible flow are transformed in the computational plane by incorporating the time dependent transformation, which naturally accounts for the mesh velocities. The transformed equations are discretized on the structured, collocated, o-type elliptic grid using the finite difference methodology. The unsteady equations are marched in time by using a semi-implicit pressure correction (projection) scheme. Along with the time marching of the governing equations, utilizing the mesh velocities and the forward Eulertime integration also moves the mesh points. The effect of Reynolds number (Re) is investigated on the flapping flight propulsion is investigated. It is found that there exists a critical Reynolds number (Rec) for every frequency after which there exists a thrust force. The effect of Rec is related to transformation of neutral wake to thrust generating wake. It is also found that the optimal frequency corresponds to a reduced frequency parameter of 0.7 where a lock in exists. It is also found that this Stc is independent of Re and the mode of vortex shedding is same at Re = 100 and 200 for Stc = 0.7. Further, it is shown that the mode of vortex shedding present is always helpful in thrust generation.

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15

Liu, H. "Simulation-Based Biological Fluid Dynamics in Animal Locomotion." Applied Mechanics Reviews 58, no. 4 (July 1, 2005): 269–82. http://dx.doi.org/10.1115/1.1946047.

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This article presents a wide-ranging review of the simulation-based biological fluid dynamic models that have been developed and used in animal swimming and flying. The prominent feature of biological fluid dynamics is the relatively low Reynolds number, e.g. ranging from 100 to 104 for most insects; and, in general, the highly unsteady motion and the geometric variation of the object result in large-scale vortex flow structure. We start by reviewing literature in the areas of fish swimming and insect flight to address the usefulness and the difficulties of the conventional theoretical models, the experimental physical models, and the computational mechanical models. Then we give a detailed description of the methodology of the simulation-based biological fluid dynamics, with a specific focus on three kinds of modeling methods: (1) morphological modeling methods, (2) kinematic modeling methods, and (3) computational fluid dynamic methods. An extended discussion on the verification and validation problem is also presented. Next, we present an overall review on the most representative simulation-based studies in undulatory swimming and in flapping flight over the past decade. Then two case studies, of the tadpole swimming and the hawkmoth hovering analyses, are presented to demonstrate the context for and the feasibility of using simulation-based biological fluid dynamics to understanding swimming and flying mechanisms. Finally, we conclude with comments on the effectiveness of the simulation-based methods, and also on its constraints.

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16

Sun, Ho Cheung Michael, Pan Liao, Tanyong Wei, Li Zhang, and Dong Sun. "Magnetically Powered Biodegradable Microswimmers." Micromachines 11, no. 4 (April 13, 2020): 404. http://dx.doi.org/10.3390/mi11040404.

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The propulsive efficiency and biodegradability of wireless microrobots play a significant role in facilitating promising biomedical applications. Mimicking biological matters is a promising way to improve the performance of microrobots. Among diverse locomotion strategies, undulatory propulsion shows remarkable efficiency and agility. This work proposes a novel magnetically powered and hydrogel-based biodegradable microswimmer. The microswimmer is fabricated integrally by 3D laser lithography based on two-photon polymerization from a biodegradable material and has a total length of 200 μm and a diameter of 8 μm. The designed microswimmer incorporates a novel design utilizing four rigid segments, each of which is connected to the succeeding segment by spring to achieve undulation, improving structural integrity as well as simplifying the fabrication process. Under an external oscillating magnetic field, the microswimmer with multiple rigid segments connected by flexible spring can achieve undulatory locomotion and move forward along with the directions guided by the external magnetic field in the low Reynolds number (Re) regime. In addition, experiments demonstrated that the microswimmer can be degraded successfully, which allows it to be safely applied in real-time in vivo environments. This design has great potential in future in vivo applications such as precision medicine, drug delivery, and diagnosis.

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17

Jacobs, David K. "Shape, Drag, and Power in Ammonoid Swimming." Paleobiology 18, no. 2 (March 1992): 203–20. http://dx.doi.org/10.1017/s009483730001397x.

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This study assesses swimming potential in a variety of ammonoid shell shapes on the basis of coefficients of drag (Cd) and the power needed to maintain a constant velocity. Reynolds numbers (Re) relevant to swimming ammonoids, and lower than those previously studied, were examined. Power consumption was scaled to a range of sizes and swimming velocities. Estimates of power available derived from studies of oxygen consumption in modern cephalopods and fish were used to calculate maximum sustainable swimming velocities (MSV).Laterally compressed, small thickness ratio (t. r.) ammonoids, previously assumed to be the most efficient swimmers, do not experience the lowest drag or power consumption at all sizes and velocities. At low values of size and velocity associated with Reynolds numbers below 104, less compressed forms have smaller drag coefficients and reduced power requirements. At hatching a roughly spherical shell shape would have minimized drag in ammonoids; with increasing size, hydrodynamic optima shift toward compressed morphologies.The high energetic cost of ammonoid locomotion may have limited dispersal and excluded ammonoids from high current velocity environments.

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18

Velho Rodrigues, Marcos F., Maciej Lisicki, and Eric Lauga. "The bank of swimming organisms at the micron scale (BOSO-Micro)." PLOS ONE 16, no. 6 (June 10, 2021): e0252291. http://dx.doi.org/10.1371/journal.pone.0252291.

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Unicellular microscopic organisms living in aqueous environments outnumber all other creatures on Earth. A large proportion of them are able to self-propel in fluids with a vast diversity of swimming gaits and motility patterns. In this paper we present a biophysical survey of the available experimental data produced to date on the characteristics of motile behaviour in unicellular microswimmers. We assemble from the available literature empirical data on the motility of four broad categories of organisms: bacteria (and archaea), flagellated eukaryotes, spermatozoa and ciliates. Whenever possible, we gather the following biological, morphological, kinematic and dynamical parameters: species, geometry and size of the organisms, swimming speeds, actuation frequencies, actuation amplitudes, number of flagella and properties of the surrounding fluid. We then organise the data using the established fluid mechanics principles for propulsion at low Reynolds number. Specifically, we use theoretical biophysical models for the locomotion of cells within the same taxonomic groups of organisms as a means of rationalising the raw material we have assembled, while demonstrating the variability for organisms of different species within the same group. The material gathered in our work is an attempt to summarise the available experimental data in the field, providing a convenient and practical reference point for future studies.

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19

Bottom II, R. G., I. Borazjani, E. L. Blevins, and G. V. Lauder. "Hydrodynamics of swimming in stingrays: numerical simulations and the role of the leading-edge vortex." Journal of Fluid Mechanics 788 (January 5, 2016): 407–43. http://dx.doi.org/10.1017/jfm.2015.702.

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Stingrays, in contrast with many other aquatic animals, have flattened disk-shaped bodies with expanded pectoral ‘wings’, which are used for locomotion in water. To discover the key features of stingray locomotion, large-eddy simulations of a self-propelled stingray, modelled closely after the freshwater stingray, Potamotrygon orbignyi, are performed. The stingray’s body motion was prescribed based on three-dimensional experimental measurement of wing and body kinematics in live stingrays at two different swimming speeds of 1.5 and $2.5L~\text{s}^{-1}$ ($L$ is the disk length of the stingray). The swimming speeds predicted by the self-propelled simulations were within 12 % of the nominal swimming speeds in the experiments. It was found that the fast-swimming stingray (Reynolds number $Re=23\,000$ and Strouhal number $St=0.27$) is approximately 12 % more efficient than the slow-swimming one ($Re=13\,500$, $St=0.34$). This is related to the wake of the fast- and slow-swimming stingrays, which was visualized along with the pressure on the stingray’s body. A horseshoe vortex was discovered to be present at the anterior margin of the stingray, creating a low-pressure region that enhances thrust for both fast and slow swimming speeds. Furthermore, it was found that a leading-edge vortex (LEV) on the pectoral disk of swimming stingrays generates a low-pressure region in the fast-swimming stingray, whereas the low- and high-pressure regions in the slow-swimming one are in the back half of the wing and not close to any vortical structures. The undulatory motion creates thrust by accelerating the adjacent fluid (the added-mass mechanism), which is maximized in the back of the wing because of higher undulations and velocities in the back. However, the thrust enhancement by the LEV occurs in the front portion of the wing. By computing the forces on the front half and the back half of the wing, it was found that the contribution of the back half of the wing to thrust in a slow-swimming stingray is several-fold higher than in the fast-swimming one. This indicates that the LEV enhances thrust in fast-swimming stingrays and improves the efficiency of swimming.

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20

Lauga, Eric, and Anthony M. J. Davis. "Viscous Marangoni propulsion." Journal of Fluid Mechanics 705 (December 19, 2011): 120–33. http://dx.doi.org/10.1017/jfm.2011.484.

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AbstractMarangoni propulsion is a form of locomotion wherein an asymmetric release of surfactant by a body located at the surface of a liquid leads to its directed motion. We present in this paper a mathematical model for Marangoni propulsion in the viscous regime. We consider the case of a thin rigid circular disk placed at the surface of a viscous fluid and whose perimeter has a prescribed concentration of an insoluble surfactant, to which the rest of its surface is impenetrable. Assuming a linearized equation of state between surface tension and surfactant concentration, we derive analytically the surfactant, velocity and pressure fields in the asymptotic limit of low capillary, Péclet and Reynolds numbers. We then exploit these results to calculate the Marangoni propulsion speed of the disk. Neglecting the stress contribution from Marangoni flows is seen to over-predict the propulsion speed by 50 %.

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21

Digumarti, Krishna Manaswi, Andrew T. Conn, and Jonathan Rossiter. "EuMoBot: replicating euglenoid movement in a soft robot." Journal of The Royal Society Interface 15, no. 148 (November 2018): 20180301. http://dx.doi.org/10.1098/rsif.2018.0301.

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Swimming is employed as a form of locomotion by many organisms in nature across a wide range of scales. Varied strategies of shape change are employed to achieve fluidic propulsion at different scales due to changes in hydrodynamics. In the case of microorganisms, the small mass, low Reynolds number and dominance of viscous forces in the medium, requires a change in shape that is non-invariant under time reversal to achieve movement. The Euglena family of unicellular flagellates evolved a characteristic type of locomotion called euglenoid movement to overcome this challenge, wherein the body undergoes a giant change in shape. It is believed that these large deformations enable the organism to move through viscous fluids and tiny spaces. The ability to drastically change the shape of the body is particularly attractive in robots designed to move through constrained spaces and cluttered environments such as through the human body for invasive medical procedures or through collapsed rubble in search of survivors. Inspired by the euglenoids, we present the design of EuMoBot, a multi-segment soft robot that replicates large body deformations to achieve locomotion. Two robots have been fabricated at different sizes operating with a constant internal volume, which exploit hyperelasticity of fluid-filled elastomeric chambers to replicate the motion of euglenoids. The smaller robot moves at a speed of body lengths per cycle (20 mm min −1 or 2.2 cycles min −1 ) while the larger one attains a speed of body lengths per cycle (4.5 mm min −1 or 0.4 cycles min −1 ). We show the potential for biomimetic soft robots employing shape change to both replicate biological motion and act as a tool for studying it. In addition, we present a quantitative method based on elliptic Fourier descriptors to characterize and compare the shape of the robot with that of its biological counterpart. Our results show a similarity in shape of 85% and indicate that this method can be applied to understand the evolution of shape in other nonlinear, dynamic soft robots where a model for the shape does not exist.

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22

ALI, N., M. SAJID, Z. ABBAS, and O. ANWAR BÉG. "SWIMMING DYNAMICS OF A MICRO-ORGANISM IN A COUPLE STRESS FLUID: A RHEOLOGICAL MODEL OF EMBRYOLOGICAL HYDRODYNAMIC PROPULSION." Journal of Mechanics in Medicine and Biology 17, no. 03 (January 26, 2017): 1750054. http://dx.doi.org/10.1142/s0219519417500543.

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Mathematical simulations of embryological fluid dynamics are fundamental to improving clinical understanding of the intricate mechanisms underlying sperm locomotion. The strongly rheological nature of reproductive fluids has been established for a number of decades. Complimentary to clinical studies, mathematical models of reproductive hydrodynamics provide a deeper understanding of the intricate mechanisms involved in spermatozoa locomotion which can be of immense benefit in clarifying fertilization processes. Although numerous non-Newtonian studies of spermatozoa swimming dynamics in non-Newtonian media have been communicated, very few have addressed the micro-structural characteristics of embryological media. This family of micro-continuum models include Eringen’s micro-stretch theory, Eringen’s microfluid and micropolar constructs and V. K. Stokes’ couple stress fluid model, all developed in the 1960s. In the present paper we implement the last of these models to examine the problem of micro-organism (spermatozoa) swimming at low Reynolds number in a homogenous embryological fluid medium with couple stress effects. The micro-organism is modeled as with Taylor’s classical approach, as an infinite flexible sheet on whose surface waves of lateral displacement are propagated. The swimming speed of the sheet and rate of work done by it are determined as function of the parameters of orbit and the couple stress fluid parameter ([Formula: see text]). The perturbation solutions are validated with a Nakamura finite difference algorithm. The perturbation solutions reveal that the normal beat pattern is effective for both couple stress and Newtonian fluids only when the amplitude of stretching wave is small. The swimming speed is observed to decrease with couple stress fluid parameter tending to its Newtonian limit as alpha tends to infinity. However the rate of work done by the sheet decreases with [Formula: see text] and approaches asymptotically to its Newtonian value. The present solutions also provide a good benchmark for more advanced numerical simulations of micro-organism swimming in couple-stress rheological biofluids.

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23

Farisenkov, Sergey E., Nadejda A. Lapina, Pyotr N. Petrov, and Alexey A. Polilov. "Extraordinary flight performance of the smallest beetles." Proceedings of the National Academy of Sciences 117, no. 40 (September 21, 2020): 24643–45. http://dx.doi.org/10.1073/pnas.2012404117.

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Size is a key to locomotion. In insects, miniaturization leads to fundamental changes in wing structure and kinematics, making the study of flight in the smallest species important for basic biology and physics, and, potentially, for applied disciplines. However, the flight efficiency of miniature insects has never been studied, and their speed and maneuverability have remained unknown. We report a comparative study of speeds and accelerations in the smallest free-living insects, featherwing beetles (Coleoptera: Ptiliidae), and in larger representatives of related groups of Staphylinoidea. Our results show that the average and maximum flight speeds of larger ptiliids are extraordinarily high and comparable to those of staphylinids that have bodies 3 times as long. This is one of the few known exceptions to the “Great Flight Diagram,” according to which the flight speed of smaller organisms is generally lower than that of larger ones. The horizontal acceleration values recorded in Ptiliidae are almost twice as high as even in Silphidae, which are more than an order of magnitude larger. High absolute and record-breaking relative flight characteristics suggest that the unique morphology and kinematics of the ptiliid wings are effective adaptations to flight at low Reynolds numbers. These results are important for understanding the evolution of body size and flight in insects and pose a challenge to designers of miniature biomorphic aircraft.

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24

Sandoval, Mario, Navaneeth K. Marath, Ganesh Subramanian, and Eric Lauga. "Stochastic dynamics of active swimmers in linear flows." Journal of Fluid Mechanics 742 (February 21, 2014): 50–70. http://dx.doi.org/10.1017/jfm.2013.651.

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AbstractMost classical work on the hydrodynamics of low-Reynolds-number swimming addresses deterministic locomotion in quiescent environments. Thermal fluctuations in fluids are known to lead to a Brownian loss of the swimming direction, resulting in a transition from short-time ballistic dynamics to effective long-time diffusion. As most cells or synthetic swimmers are immersed in external flows, we consider theoretically in this paper the stochastic dynamics of a model active particle (a self-propelled sphere) in a steady general linear flow. The stochasticity arises both from translational diffusion in physical space, and from a combination of rotary diffusion and so-called run-and-tumble dynamics in orientation space. The latter process characterizes the manner in which the orientation of many bacteria decorrelates during their swimming motion. In contrast to rotary diffusion, the decorrelation occurs by means of large and impulsive jumps in orientation (tumbles) governed by a Poisson process. We begin by deriving a general formulation for all components of the long-time mean square displacement tensor for a swimmer with a time-dependent swimming velocity and whose orientation decorrelates due to rotary diffusion alone. This general framework is applied to obtain the convectively enhanced mean-squared displacements of a steadily swimming particle in three canonical linear flows (extension, simple shear and solid-body rotation). We then show how to extend our results to the case where the swimmer orientation also decorrelates on account of run-and-tumble dynamics. Self-propulsion in general leads to the same long-time temporal scalings as for passive particles in linear flows but with increased coefficients. In the particular case of solid-body rotation, the effective long-time diffusion is the same as that in a quiescent fluid, and we clarify the lack of flow dependence by briefly examining the dynamics in elliptic linear flows. By comparing the new active terms with those obtained for passive particles we see that swimming can lead to an 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.

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25

Traub, Lance W., and Cory Coffman. "Efficient Low-Reynolds-Number Airfoils." Journal of Aircraft 56, no. 5 (September 2019): 1987–2003. http://dx.doi.org/10.2514/1.c035515.

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26

Drela, Mark. "Transonic low-Reynolds number airfoils." Journal of Aircraft 29, no. 6 (November 1992): 1106–13. http://dx.doi.org/10.2514/3.46292.

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27

Berti, Luca, Laetitia Giraldi, and Christophe Prud’homme. "Swimming at low Reynolds number." ESAIM: Proceedings and Surveys 67 (2020): 46–60. http://dx.doi.org/10.1051/proc/202067004.

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We address the swimming problem at low Reynolds number. This regime, which is typically used for micro-swimmers, is described by Stokes equations. We couple a PDE solver of Stokes equations, derived from the Feel++ ﬁnite elements library, to a quaternion-based rigid-body solver. We validate our numerical results both on a 2D exact solution and on an exact solution for a rotating rigid body respectively. Finally, we apply them to simulate the motion of a one-hinged swimmer, which obeys to the scallop theorem.

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28

WILLIAMSON, N., N. SRINARAYANA, S. W. ARMFIELD, G. D. McBAIN, and W. LIN. "Low-Reynolds-number fountain behaviour." Journal of Fluid Mechanics 608 (July 11, 2008): 297–317. http://dx.doi.org/10.1017/s0022112008002310.

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Experimental evidence for previously unreported fountain behaviour is presented. It has been found that the first unstable mode of a three-dimensional round fountain is a laminar flapping motion that can grow to a circling or multimodal flapping motion. With increasing Froude and Reynolds numbers, fountain behaviour becomes more disorderly, exhibiting a laminar bobbing motion. The transition between steady behaviour, the initial flapping modes and the laminar bobbing flow can be approximately described by a function FrRe2/3=C. The transition to turbulence occurs at Re > 120, independent of Froude number, and the flow appears to be fully turbulent at Re≈2000. For Fr > 10 and Re≲120, sinuous shear-driven instabilities have been observed in the rising fluid column. For Re≳120 these instabilities cause the fountain to intermittently breakdown into turbulent jet-like flow. For Fr≲10 buoyancy forces begin to dominate the flow and pulsing behaviour is observed. A regime map of the fountain behaviour for 0.7≲Fr≲100 and 15≲Re≲1900 is presented and the underlying mechanisms for the observed behaviour are proposed. Movies are available with the online version of the paper.

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29

Golestanian, Ramin, and Armand Ajdari. "Stochastic low Reynolds number swimmers." Journal of Physics: Condensed Matter 21, no. 20 (April 21, 2009): 204104. http://dx.doi.org/10.1088/0953-8984/21/20/204104.

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30

Najafi, Ali, and Ramin Golestanian. "Propulsion at low Reynolds number." Journal of Physics: Condensed Matter 17, no. 14 (March 25, 2005): S1203—S1208. http://dx.doi.org/10.1088/0953-8984/17/14/009.

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31

Boucher, R. F., and C. Mazharoglu. "Low Reynolds number fluidic flowmetering." Journal of Physics E: Scientific Instruments 21, no. 10 (October 1988): 977–89. http://dx.doi.org/10.1088/0022-3735/21/10/015.

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32

Horiguchi, Hironori, Daisuke Yumiba, Yoshinobu Tsujimoto, Masaaki Sakagami, and Shigeo Tanaka. "Reynolds Number Effect on Regenerative Pump Performance in Low Reynolds Number Range." International Journal of Fluid Machinery and Systems 1, no. 1 (August 1, 2008): 101–8. http://dx.doi.org/10.5293/ijfms.2008.1.1.101.

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33

Marchman, J. F., Edward A. Robertson, and Howard T. Emsley. "Rain effects at low Reynolds number." Journal of Aircraft 24, no. 9 (September 1987): 638–44. http://dx.doi.org/10.2514/3.45489.

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34

Erm, Lincoln P., and Peter N. Joubert. "Low-Reynolds-number turbulent boundary layers." Journal of Fluid Mechanics 230 (September 1991): 1–44. http://dx.doi.org/10.1017/s0022112091000691.

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An investigation was undertaken to improve our understanding of low-Reynolds-number turbulent boundary layers flowing over a smooth flat surface in nominally zero pressure gradients. In practice, such flows generally occur in close proximity to a tripping device and, though it was known that the flows are affected by the actual low value of the Reynolds number, it was realized that they may also be affected by the type of tripping device used and variations in free-stream velocity for a given device. Consequently, the experimental programme was devised to investigate systematically the effects of each of these three factors independently. Three different types of device were chosen: a wire, distributed grit and cylindrical pins. Mean-flow, broadband-turbulence and spectral measurements were taken, mostly for values of Rθ varying between about 715 and about 2810. It was found that the mean-flow and broadband-turbulence data showed variations with Rθ, as expected. Spectra were plotted using scaling given by Perry, Henbest & Chong (1986) and were compared with their models which were developed for high-Reynolds-number flows. For the turbulent wall region, spectra showed reasonably good agreement with their model. For the fully turbulent region, spectra did show some appreciable deviations from their model, owing to low-Reynolds-number effects. Mean-flow profiles, broadband-turbulence profiles and spectra were found to be affected very little by the type of device used for Rθ ≈ 1020 and above, indicating an absence of dependence on flow history for this Rθ range. These types of measurements were also compared at both Rθ ≈ 1020 and Rθ ≈ 2175 to see if they were dependent on how Rθ was formed (i.e. the combination of velocity and momentum thickness used to determine Rθ). There were noticeable differences for Rθ ≈ 1020, but these differences were only convincing for the pins, and there was a general overall improvement in agreement for Rθ ≈ 2175.

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35

Shapere, Alfred, and Frank Wilczek. "Self-Propulsion at Low Reynolds Number." Physical Review Letters 58, no. 20 (May 18, 1987): 2051–54. http://dx.doi.org/10.1103/physrevlett.58.2051.

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36

Glazner, Allen F. "Magmatic life at low Reynolds number." Geology 42, no. 11 (November 2014): 935–38. http://dx.doi.org/10.1130/g36078.1.

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37

Alouges, F. "Low Reynolds number swimming and controllability." ESAIM: Proceedings 41 (December 2013): 1–14. http://dx.doi.org/10.1051/proc/201341001.

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38

Golestanian, Ramin, Julia M. Yeomans, and Nariya Uchida. "Hydrodynamic synchronization at low Reynolds number." Soft Matter 7, no. 7 (2011): 3074. http://dx.doi.org/10.1039/c0sm01121e.

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39

Katz, J. I. "Subsuns and Low Reynolds Number Flow." Journal of the Atmospheric Sciences 55, no. 22 (November 1998): 3358–62. http://dx.doi.org/10.1175/1520-0469(1998)055<3358:salrnf>2.0.co;2.

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40

Rehm, Thomas R. "Low Reynolds Number Flow Heat Exchangers." Nuclear Technology 73, no. 1 (April 1986): 129–30. http://dx.doi.org/10.13182/nt86-a16213.

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41

Peterson, Mark A. "Membrane hydrodynamics at low Reynolds number." Physical Review E 53, no. 1 (January 1, 1996): 731–38. http://dx.doi.org/10.1103/physreve.53.731.

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42

Fu, Henry C., Vivek B. Shenoy, and Thomas R. Powers. "Low-Reynolds-number swimming in gels." EPL (Europhysics Letters) 91, no. 2 (July 1, 2010): 24002. http://dx.doi.org/10.1209/0295-5075/91/24002.

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43

Dey, Krishna Kanti. "Dynamic Coupling at Low Reynolds Number." Angewandte Chemie International Edition 58, no. 8 (February 18, 2019): 2208–28. http://dx.doi.org/10.1002/anie.201804599.

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44

Shen, C., and J. M. Floryan. "Low Reynolds number flow over cavities." Physics of Fluids 28, no. 11 (1985): 3191. http://dx.doi.org/10.1063/1.865366.

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45

Zhou, Donghuo, and Cesar Mendoza. "Low-Reynolds-number turbulent channel flows." Journal of Hydraulic Research 32, no. 6 (November 1994): 911–34. http://dx.doi.org/10.1080/00221689409498698.

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46

Doostmohammadi, A., R. Stocker, and A. M. Ardekani. "Low-Reynolds-number swimming at pycnoclines." Proceedings of the National Academy of Sciences 109, no. 10 (February 21, 2012): 3856–61. http://dx.doi.org/10.1073/pnas.1116210109.

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47

Glass, O., and T. Horsin. "Lagrangian controllability at low Reynolds number." ESAIM: Control, Optimisation and Calculus of Variations 22, no. 4 (July 28, 2016): 1040–53. http://dx.doi.org/10.1051/cocv/2016032.

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48

KIDA, Teruhiko. "310 Unsteady Low Reynolds Number Flows." Proceedings of Conference of Kansai Branch 2001.76 (2001): _3–27_—_3–28_. http://dx.doi.org/10.1299/jsmekansai.2001.76._3-27_.

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49

Lyman, Edward R. "Stirring a Low Reynolds Number MARTINI." Biophysical Journal 110, no. 3 (February 2016): 36a. http://dx.doi.org/10.1016/j.bpj.2015.11.262.

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50

Alexander, G. P., and J. M. Yeomans. "Hydrodynamic Interactions at Low Reynolds Number." Experimental Mechanics 50, no. 9 (August 3, 2010): 1283–92. http://dx.doi.org/10.1007/s11340-010-9387-6.

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