scholarly journals Hydrodynamics of the double-wave structure of insect spermatozoa flagella

2012 ◽  
Vol 9 (73) ◽  
pp. 1908-1924 ◽  
Author(s):  
On Shun Pak ◽  
Saverio E. Spagnolie ◽  
Eric Lauga
Keyword(s):  
Wave Structure ◽  
Helical Structures ◽  
Slender Body Theory ◽  
Kinematic Data ◽  
Insect Sperm ◽  
Non Local ◽  
Body Theory ◽  
Swimming Kinematics ◽  
Insight Into ◽  
Opposite Chirality

In addition to conventional planar and helical flagellar waves, insect sperm flagella have also been observed to display a double-wave structure characterized by the presence of two superimposed helical waves. In this paper, we present a hydrodynamic investigation of the locomotion of insect spermatozoa exhibiting the double-wave structure, idealized here as superhelical waves. Resolving the hydrodynamic interactions with a non-local slender body theory, we predict the swimming kinematics of these superhelical swimmers based on experimentally collected geometric and kinematic data. Our consideration provides insight into the relative contributions of the major and minor helical waves to swimming; namely, propulsion is owing primarily to the minor wave, with negligible contribution from the major wave. We also explore the dependence of the propulsion speed on geometric and kinematic parameters, revealing counterintuitive results, particularly for the case when the minor and major helical structures are of opposite chirality.

THE SWIMMING OF UNIPOLAR CELLS OF SPIRILLUM VOLUTANS: THEORY AND OBSERVATIONS

1994 ◽  
Vol 187 (1) ◽  
pp. 75-100
Author(s):  
M Ramia ◽  
M Swan
Keyword(s):  
High Speed ◽  
Slender Body ◽  
Geometrical Parameters ◽  
Slender Body Theory ◽  
Typical Cell ◽  
Complete Set ◽  
The Mean ◽  
Resistive Force Theory ◽  
Body Theory ◽  
Swimming Kinematics

Bright-field high-speed cinemicrography was employed to record the swimming of six unipolar cells of Spirillum volutans. A complete set of geometrical parameters for each of these six cells, which are of typical but varying dimensions, was measured experimentally. For each cell, the mean swimming linear and angular speeds were measured for a period representing an exact number of flagellar cycles (at least four and up to 12 cycles). Two independent sets of measurements were carried out for each cell, one relating to the trailing and the other to the leading configuration of the flagellar bundle. The geometry of these cells was numerically modelled with curved isoparametric boundary elements (from the measured geometrical parameters), and an existing boundary element method (BEM) program was applied to predict the mean swimming linear and angular speeds. A direct comparison between the experimentally observed swimming speeds and those of the BEM predictions is made. For a typical cell, a direct comparison of the swimming trajectory, in each of the trailing and the leading flagellar configurations, was also included. Previous resistive force theory (RFT) as well as slender body theory (SBT) models are both restricted to somewhat non-realistic 'slender body' geometries, and they both fail to consider swimming kinematics. The present BEM model, however, is applicable to organisms with arbitrary geometry and correctly accounts for swimming kinematics; hence, it agrees better with experimental observations than do the previous models.

Kinematics of plaice,Pleuronectes platessa, and cod,Gadus morhua, swimming near the bottom

2002 ◽  
Vol 205 (14) ◽  
pp. 2125-2134 ◽  
Author(s):  
Paul W. Webb
Keyword(s):  
Swimming Speed ◽  
Power Output ◽  
Gadus Morhua ◽  
Fish Length ◽  
Slender Body Theory ◽  
Pleuronectes Platessa ◽  
Total Fish ◽  
Anterior Body ◽  
Body Theory ◽  
Swimming Kinematics

SUMMARYThe kinematics of plaice (Pleuronectes platessa, L=22.1 cm) and cod (Gadus morhua, L=25.0 cm, where L is total fish length)swimming at various speeds at the bottom and lifted to heights, h, of 10, 50 and 100 mm by a thin-wire grid were measured. For cod, tailbeat frequency, amplitude, body and fin span and propulsive wavelength were unaffected by h and varied with speed as described for fusiform pelagic species. In contrast, the kinematics of plaice was affected by h. Body and fin spans and propulsive wavelength were independent of swimming speed and h. Tailbeat amplitude was independent of swimming speed, but averaged 1.5 cm at h=0 and 2.5 cm at h≥10 mm. Plaice tailbeat frequency increased with swimming speed for fish at the bottom but was independent of swimming speed at h=10, 50 and 100 mm,averaging 4.6, 6.0 and 5.8 Hz respectively. Total mechanical power, P, produced by propulsive movements calculated from the bulk-momentum form of elongated slender-body theory was similar for cod and plaice swimming at the bottom but, at h≥10 mm, P for plaice was larger than that for cod. Plaice support their weight in water by swimming at a small tilt angle. The small changes in swimming kinematics with swimming speed are attributed to decreasing induced power costs to support the weight as speed increases. The contribution of the tail to power output increased monotonically with the tail gap/span ratio, z/B, for z/B=0.23 (h=0 mm) to z/B=1.1 (h=50 mm). The smaller tailbeat amplitude of the tail decreased both z/B and the power output for plaice swimming at the bottom. For the maximum body and fin span of plaice, the contribution to power output increased for local z/B values of 0.044 (h-0 mm) to 0.1 (h=10 mm) and declined somewhat at larger values of z/B. The smaller effect of the bottom on power output of the largespan anterior body sections may result from the resorption of much of the upstream wake at the re-entrant downstream tail.

Note on the swimming of slender fish

1960 ◽  
Vol 9 (2) ◽  
pp. 305-317 ◽  
Author(s):  
M. J. Lighthill
Keyword(s):  
Swimming Speed ◽  
Critical Value ◽  
Slender Body ◽  
Vortex Wake ◽  
Frictional Drag ◽  
Slender Body Theory ◽  
Propulsive Efficiency ◽  
Deformable Bodies ◽  
Work Done ◽  
Body Theory

The paper seeks to determine what transverse oscillatory movements a slender fish can make which will give it a high Froude propulsive efficiency, $\frac{\hbox{(forward velocity)} \times \hbox{(thrust available to overcome frictional drag)}} {\hbox {(work done to produce both thrust and vortex wake)}}.$ The recommended procedure is for the fish to pass a wave down its body at a speed of around $\frac {5} {4}$ of the desired swimming speed, the amplitude increasing from zero over the front portion to a maximum at the tail, whose span should exceed a certain critical value, and the waveform including both a positive and a negative phase so that angular recoil is minimized. The Appendix gives a review of slender-body theory for deformable bodies.

Slender-body theory for slow viscous flow

1976 ◽  
Vol 75 (4) ◽  
pp. 705-714 ◽  
Author(s):  
Joseph B. Keller ◽  
Sol I. Rubinow
Keyword(s):  
Integral Equation ◽  
Incompressible Fluid ◽  
Viscous Incompressible Fluid ◽  
Unit Length ◽  
The Body ◽  
Slender Body ◽  
Slow Flow ◽  
Slender Body Theory ◽  
Slow Viscous Flow ◽  
Body Theory

Slow flow of a viscous incompressible fluid past a slender body of circular crosssection is treated by the method of matched asymptotic expansions. The main result is an integral equation for the force per unit length exerted on the body by the fluid. The novelty is that the body is permitted to twist and dilate in addition to undergoing the translating, bending and stretching, which have been considered by others. The method of derivation is relatively simple, and the resulting integral equation does not involve the limiting processes which occur in the previous work.

Phoretic self-propulsion of helical active particles

2021 ◽  
Vol 927 ◽  
Author(s):  
Ruben Poehnl ◽  
William Uspal
Keyword(s):  
Particle Surface ◽  
Design Parameters ◽  
Strong Impact ◽  
Directed Motion ◽  
Concentration Gradients ◽  
Slender Body Theory ◽  
Active Particles ◽  
Straight Line ◽  
Judicious Choice ◽  
Body Theory

Chemically active colloids self-propel by catalysing the decomposition of molecular ‘fuel’ available in the surrounding solution. If the various molecular species involved in the reaction have distinct interactions with the colloid surface, and if the colloid has some intrinsic asymmetry in its surface chemistry or geometry, there will be phoretic flows in an interfacial layer surrounding the particle, leading to directed motion. Most studies of chemically active colloids have focused on spherical, axisymmetric ‘Janus’ particles, which (in the bulk, and in absence of fluctuations) simply move in a straight line. For particles with a complex (non-spherical and non-axisymmetric) geometry, the dynamics can be much richer. Here, we consider chemically active helices. Via numerical calculations and slender body theory, we study how the translational and rotational velocities of the particle depend on geometry and the distribution of catalytic activity over the particle surface. We confirm the recent finding of Katsamba et al. (J. Fluid Mech., vol. 898, 2020, p. A24) that both tangential and circumferential concentration gradients contribute to the particle velocity. The relative importance of these contributions has a strong impact on the motion of the particle. We show that, by a judicious choice of the particle design parameters, one can suppress components of angular velocity that are perpendicular to the screw axis, or even select for purely ‘sideways’ translation of the helix.

Rods falling near a vertical wall

1977 ◽  
Vol 83 (2) ◽  
pp. 273-287 ◽  
Author(s):  
W. B. Russel ◽  
E. J. Hinch ◽  
L. G. Leal ◽  
G. Tieffenbruck
Keyword(s):  
Integral Equation ◽  
Viscous Fluid ◽  
Numerical Solution ◽  
Vertical Wall ◽  
Numerical Results ◽  
Slender Body ◽  
Asymptotic Results ◽  
Slender Body Theory ◽  
Friction Coefficients ◽  
Body Theory

As an inclined rod sediments in an unbounded viscous fluid it will drift horizontally but will not rotate. When it approaches a vertical wall, the rod rotates and so turns away from the wall. Illustrative experiments and a slender-body theory of this phenomenon are presented. In an incidental study the friction coefficients for an isolated rod are found by numerical solution of the slender-body integral equation. These friction coefficients are compared with the asymptotic results of Batchelor (1970) and the numerical results of Youngren ' Acrivos (1975), who did not make a slender-body approximation.

Application of Slender-Body Theory

1957 ◽  
Vol 1 (04) ◽  
pp. 40-49
Author(s):  
Paul Kaplan
Keyword(s):  
Slender Body ◽  
Vertical Force ◽  
Regular Waves ◽  
Slender Body Theory ◽  
Surface Theory ◽  
Surface Ship ◽  
Submerged Body ◽  
Dynamic Forces ◽  
Body Theory

The vertical force and pitching moment acting on a slender submerged body and on a surface ship moving normal to the crests of regular waves are found by application of slender-body theory, which utilizes two-dimensional crossflow concepts. Application of the same techniques also results in the evaluation of the dynamic forces and moments resulting from the heaving and pitching motions of the ship, which corrected previous errors in other works, and agreed with the results of specialized calculations of Havelock and Has-kind. An outline of a rational theory, which unites slender-body theory and linearized free-surface theory, for the determination of the forces, moments and motions of surface ships, is also included.

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