scholarly journals Swimming mediated by ciliary beating: comparison with a squirmer model

2019 ◽  
Vol 874 ◽  
pp. 774-796 ◽  
Author(s):  
Hiroaki Ito ◽  
Toshihiro Omori ◽  
Takuji Ishikawa
Keyword(s):  
Cell Body ◽  
Hydrodynamic Interactions ◽  
Swimming Velocity ◽  
Energy Costs ◽  
Theoretical Studies ◽  
Free Swimming ◽  
Ciliary Beating ◽  
Aspect Ratios ◽  
Swimming Efficiency ◽  
Micro Organisms

The squirmer model of Lighthill and Blake has been widely used to analyse swimming ciliates. However, real ciliates are covered by hair-like organelles, called cilia; the differences between the squirmer model and real ciliates remain unclear. Here, we developed a ciliate model incorporating the distinct ciliary apparatus, and analysed motion using a boundary element–slender-body coupling method. This methodology allows us to accurately calculate hydrodynamic interactions between cilia and the cell body under free-swimming conditions. Results showed that an antiplectic metachronal wave was optimal in the swimming speed with various cell-body aspect ratios, which is consistent with former theoretical studies. Exploiting oblique wave propagation, we reproduced a helical trajectory, like Paramecium, although the cell body was spherical. We confirmed that the swimming velocity of model ciliates was well represented by the squirmer model. However, squirmer modelling outside the envelope failed to estimate the energy costs of swimming; over 90 % of energy was dissipated inside the ciliary envelope. The optimal swimming efficiency was given by the antiplectic wave; the value was 6.7 times larger than in-phase beating. Our findings provide a fundamental basis for modelling swimming micro-organisms.

A boundary-element analysis of flagellar propulsion

1987 ◽  
Vol 184 ◽  
pp. 533-549 ◽  
Author(s):  
N. Phan-Thien ◽  
T. Tran-Cong ◽  
M. Ramia
Keyword(s):  
Boundary Element ◽  
Cell Body ◽  
Quantitative Agreement ◽  
Optimum Number ◽  
Element Analysis ◽  
Slender Body Theory ◽  
Aspect Ratios ◽  
Optimal Value ◽  
Micro Organisms ◽  
Body Theory

The swimming of a flagellar micro-organism by the propagation of helical waves along its flagellum is analysed by a boundary-element method. The method is not restricted to any particular geometry of the organism nor does it assume a specific wave motion for the flagellum. However, only results for an organism with a spherical or ellipsoidal cell body and a helically beating flagellum are presented here.With regard to the flagellum, it is concluded that the optimum helical wave (amplitude α and wavenumber k) has αk ≈ 1 (pitch angle of 45°) and that for the optimum flagellar length L/A = 10 (L being the flagellar length, A being the radius of the assumed spherical cell body) the optimum number of wavelengths Nλ is about 1.5. Furthermore there appears to be no optimal value for the flagellar radius a, with the thinner flagella being favoured. These conclusions show excellent quantitative agreement with those of slender-body theory.For the case of an ellipsoidal cell body, the optimum aspect ratios B/A and C/A of the ellipsoid are about 0.7 and 0.3 respectively; A, B and C are the principal radii of the ellipsoid. These and all of the above conclusions show good qualitative agreement with experimental observations of efficiently swimming micro-organisms.

scholarly journals Theoretical Studies of Intracellular Concentration of Micro-organisms’ Metabolites

2017 ◽  
Vol 7 (1) ◽  
Author(s):  
Hai-Feng Yang ◽  
Xiao-Nan Zhang ◽  
Yan Li ◽  
Yong-Hong Zhang ◽  
Qin Xu ◽  
...  
Keyword(s):  
Intracellular Concentration ◽  
Theoretical Studies ◽  
Micro Organisms

scholarly journals Dynamics of Swimmers in Fluids with Resistance

Fluids ◽  
2020 ◽  
Vol 5 (1) ◽  
pp. 14 ◽  
Author(s):  
Cole Jeznach ◽  
Sarah D. Olson
Keyword(s):  
Fluid Dynamics ◽  
Fluid Flow ◽  
Cell Body ◽  
Complex Dynamics ◽  
Viscous Fluids ◽  
Hydrodynamic Interactions ◽  
Brinkman Equation ◽  
Resistance Parameter ◽  
Fluid Resistance ◽  
Stationary Obstacles

Micro-swimmers such as spermatozoa are able to efficiently navigate through viscous fluids that contain a sparse network of fibers or other macromolecules. We utilize the Brinkman equation to capture the fluid dynamics of sparse and stationary obstacles that are represented via a single resistance parameter. The method of regularized Brinkmanlets is utilized to solve for the fluid flow and motion of the swimmer in 2-dimensions when assuming the flagellum (tail) propagates a curvature wave. Extending previous studies, we investigate the dynamics of swimming when varying the resistance parameter, head or cell body radius, and preferred beat form parameters. For a single swimmer, we determine that increased swimming speed occurs for a smaller cell body radius and smaller fluid resistance. Progression of swimmers exhibits complex dynamics when considering hydrodynamic interactions; attraction of two swimmers is a robust phenomenon for smaller beat amplitude of the tail and smaller fluid resistance. Wall attraction is also observed, with a longer time scale of wall attraction with a larger resistance parameter.

scholarly journals A neutrally stable shell in a Stokes flow: a rotational Taylor's sheet

2019 ◽  
Vol 475 (2227) ◽  
pp. 20190178 ◽  
Author(s):  
G. Corsi ◽  
A. De Simone ◽  
C. Maurini ◽  
S. Vidoli
Keyword(s):  
Viscous Fluid ◽  
Phase Speed ◽  
Travelling Wave ◽  
Viscous Fluids ◽  
Swimming Velocity ◽  
Active Materials ◽  
Seminal Paper ◽  
Transversal Displacement ◽  
Stable Equilibria ◽  
Micro Organisms

In a seminal paper published in 1951, Taylor studied the interactions between a viscous fluid and an immersed flat sheet which is subjected to a travelling wave of transversal displacement. The net reaction of the fluid over the sheet turned out to be a force in the direction of the wave phase-speed. This effect is a key mechanism for the swimming of micro-organisms in viscous fluids. Here, we study the interaction between a viscous fluid and a special class of nonlinear morphing shells. We consider pre-stressed shells showing a one-dimensional set of neutrally stable equilibria with almost cylindrical configurations. Their shape can be effectively controlled through embedded active materials, generating a large-amplitude shape-wave associated with precession of the axis of maximal curvature. We show that this shape-wave constitutes the rotational analogue of a Taylor's sheet, where the translational swimming velocity is replaced by an angular velocity. Despite the net force acting on the shell vanishes, the resultant torque does not. A similar mechanism can be used to manoeuver in viscous fluids.

scholarly journals Microswimmer Propulsion by Two Steadily Rotating Helical Flagella

Micromachines ◽  
2019 ◽  
Vol 10 (1) ◽  
pp. 65 ◽  
Author(s):  
Henry Shum
Keyword(s):  
Simple Model ◽  
Cell Body ◽  
Solid Surface ◽  
The Body ◽  
Theoretical Studies ◽  
Bacterial Strains ◽  
Bulk Fluid ◽  
Similar Shape ◽  
Bacterial Morphology ◽  
Single Flagellum

Many theoretical studies of bacterial locomotion adopt a simple model for the organism consisting of a spheroidal cell body and a single corkscrew-shaped flagellum that rotates to propel the body forward. Motivated by experimental observations of a group of magnetotactic bacterial strains, we extended the model by considering two flagella attached to the cell body and rotating about their respective axes. Using numerical simulations, we analyzed the motion of such a microswimmer in bulk fluid and close to a solid surface. We show that positioning the two flagella far apart on the cell body reduces the rate of rotation of the body and increases the swimming speed. Near surfaces, we found that swimmers with two flagella can swim in relatively straight trajectories or circular orbits in either direction. It is also possible for the swimmer to escape from surfaces, unlike a model swimmer of similar shape but with only a single flagellum. Thus, we conclude that there are important implications of swimming with two flagella or flagellar bundles rather than one. These considerations are relevant not only for understanding differences in bacterial morphology but also for designing microrobotic swimmers.

scholarly journals Observations of Stably Stratified Flow through a Microscale Gap

2021 ◽  
Vol 78 (1) ◽  
pp. 189-208
Author(s):  
Daniel Vassallo ◽  
Raghavendra Krishnamurthy ◽  
Robert Menke ◽  
Harindra J. S. Fernando
Keyword(s):  
Field Investigation ◽  
Buoyancy Frequency ◽  
Theoretical Studies ◽  
Atmospheric Variability ◽  
Wave Regime ◽  
Aspect Ratios ◽  
Gap Flow ◽  
Neutral Flow ◽  
Flow Through ◽  
Double Ridge

AbstractThis paper reports the findings of a comprehensive field investigation on flow through a mountain gap subject to a range of stably stratified environmental conditions. This study was embedded within the Perdigão field campaign, which was conducted in a region of parallel double-ridge topography with ridge-normal wind climatology. One of the ridges has a well-defined gap (col) at the top, and an array of in situ and remote sensors, including a novel triple Doppler lidar system, was deployed around it. The experimental design was mostly guided by previous numerical and theoretical studies conducted with an idealized configuration where a flow (with characteristic velocity U0 and buoyancy frequency N) approaches normal to a mountain of height h with a gap at its crest, for which the governing parameters are the dimensionless mountain height G = Nh/U0 and various gap aspect ratios. Modified forms of G were proposed to account for real-world atmospheric variability, and the results are discussed in terms of a gap-averaged value Gc. The nature of gap flow was highly dependent on Gc, wherein a nearly neutral flow regime (Gc < 1), a transitional mountain wave regime [Gc ~ O(1)], and a gap-jetting regime [Gc > O(1)] were identified. The measurements were in broad agreement with previous numerical and theoretical studies on a single ridge with a gap or double-ridge topography, although details vary. This is the first-ever detailed field study reported on microscale [O(100) m] gap flows, and it provides useful data and insights for future theoretical and numerical studies.

scholarly journals Stokesian dynamics simulations of a magnetotactic bacterium

2021 ◽  
Vol 44 (3) ◽  
Author(s):  
Sarah Mohammadinejad ◽  
Damien Faivre ◽  
Stefan Klumpp
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Cell Body ◽  
Magnetic Moment ◽  
Magnetotactic Bacteria ◽  
Swimming Velocity ◽  
Stokesian Dynamics ◽  
Inclination Angles ◽  
Dynamics Simulations ◽  
The Magnetic Field

AbstractThe swimming of bacteria provides insight into propulsion and steering under the conditions of low-Reynolds number hydrodynamics. Here we address the magnetically steered swimming of magnetotactic bacteria. We use Stokesian dynamics simulations to study the swimming of single-flagellated magnetotactic bacteria (MTB) in an external magnetic field. Our model MTB consists of a spherical cell body equipped with a magnetic dipole moment and a helical flagellum rotated by a rotary motor. The elasticity of the flagellum as well as magnetic and hydrodynamic interactions is taken into account in this model. We characterized how the swimming velocity is dependent on parameters of the model. We then studied the U-turn motion after a field reversal and found two regimes for weak and strong fields and, correspondingly, two characteristic time scales. In the two regimes, the U-turn time is dominated by the turning of the cell body and its magnetic moment or the turning of the flagellum, respectively. In the regime for weak fields, where turning is dominated by the magnetic relaxation, the U-turn time is approximately in agreement with a theoretical model based on torque balance. In the strong-field regime, strong deformations of the flagellum are observed. We further simulated the swimming of a bacterium with a magnetic moment that is inclined relative to the flagellar axis. This scenario leads to intriguing double helical trajectories that we characterize as functions of the magnetic moment inclination and the magnetic field. For small inclination angles ($$\lesssim {20^{\circ }}$$≲20∘) and typical field strengths, the inclination of the magnetic moment has only a minor effect on the swimming of MTB in an external magnetic field. Large inclination angles result in a strong reduction in the velocity in direction of the magnetic field, consistent with recent observations that bacteria with large inclination angles use a different propulsion mechanism.Graphic abstract

Distribution of gyrotactic micro-organisms in complex three-dimensional flows. Part 1. Horizontal shear flow past a vertical circular cylinder

2018 ◽  
Vol 852 ◽  
pp. 358-397 ◽  
Author(s):  
L. Zeng ◽  
T. J. Pedley
Keyword(s):  
Circular Cylinder ◽  
Shear Flow ◽  
Vortex Shedding ◽  
Water Surface ◽  
Concentration Distribution ◽  
Three Dimensional ◽  
Swimming Velocity ◽  
Horizontal Shear ◽  
Active Particles ◽  
Micro Organisms

As a first step towards understanding the distribution of swimming micro-organisms in flowing shallow water containing vegetation, we formulate a continuum model for dilute suspensions in horizontal shear flow, with a maximum Reynolds number of 100, past a single, rigid, vertical, circular cylinder that extends from a flat horizontal bed and penetrates the free water surface. A numerical platform was developed to solve this problem, in four stages: first, a scheme for computation of the flow field; second, a solver for the Fokker–Planck equation governing the probability distribution of the swimming direction of gyrotactic cells under the combined action of gravity, ambient vorticity and rotational diffusion; third, the construction of a database for the mean swimming velocity and the translational diffusivity tensor as functions of the three vorticity components, using parameters appropriate for the swimming alga, Chlamydomonas nivalis; fourth, a solver for the three-dimensional concentration distribution of the gyrotactic micro-organisms. Upstream of the cylinder, the cells are confined to a vertical strip of width equal to the cylinder diameter, which enables us to visualise mixing in the wake. The flow downstream of the cylinder is divided into three zones: parallel vortex shedding in the top zone near the water surface, oblique vortex shedding in the middle zone and quasi-steady flow in the bottom zone. Secondary (vertical) flow occurs just upstream and downstream of the cylinder. Frequency spectra of the velocity components in the wake of the cylinder show two dominant frequencies of vortex shedding, in the parallel- and oblique-shedding zones respectively, together with a low frequency, equal to the difference between those two frequencies, that corresponds to a beating modulation. The concentration distribution is calculated for both active particles and passive, non-swimming, particles for comparison. The concentration distribution is very similar for both active and passive particles, except near the top surface, where upswimming causes the concentration of active particles to reach values greater than in the upstream strip, and in a thin boundary layer on the downstream surface of the cylinder, where a high concentration of active particles occurs as a result of radial swimming.

Intracyclic Variation of Force and Swimming Performance

2018 ◽  
Vol 13 (7) ◽  
pp. 897-902 ◽  
Author(s):  
Pedro G. Morouço ◽  
Tiago M. Barbosa ◽  
Raul Arellano ◽  
João P. Vilas-Boas
Keyword(s):  
Swimming Performance ◽  
Time Trial ◽  
Velocity Variation ◽  
Swimming Velocity ◽  
Stroke Rate ◽  
Free Swimming ◽  
Front Crawl ◽  
Continuous Application ◽  
High Level ◽  
Maximal Effort

Context: In front-crawl swimming, the upper limbs perform alternating movements with the aim of achieving a continuous application of force in the water, leading to lower intracyclic velocity variation (dv). This parameter has been identified as a crucial criterion for swimmers’ evaluation. Purpose: To examine the assessment of intracyclic force variation (dF) and to analyze its relationship with dv and swimming performance. Methods: A total of 22 high-level male swimmers performed a maximal-effort 50-m front-crawl time trial and a 30-s maximal-effort fully tethered swimming test, which were randomly assigned. Instantaneous velocity was obtained by a speedometer and force by a strain-gauge system. Results: Similarity was observed between the tests, with dF attaining much higher magnitudes than dv (P < .001; d = 8.89). There were no differences in stroke rate or in physiological responses between tethered and free swimming, with a high level of agreement for the stroke rate and blood lactate increase. Swimming velocity presented a strong negative linear relationship with dF (r = −.826, P < .001) and a moderate negative nonlinear relationship with dv (r = .734, P < .01). With the addition of the maximum impulse to dF, multiple-regression analysis explained 83% of the free-swimming performance. Conclusions: Assessing dF is a promising approach for evaluating a swimmer’s performance. From the experiments, this new parameter showed that swimmers with higher dF also present higher dv, leading to a decrease in performance.

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