Mathematical Modelling of Flagellated Microswimmers

Zaitsev, M. Yu.; Karabasov, Sergey A.

doi:10.1134/s0965542518110167

Cited by 4 publications

(17 citation statements)

References 12 publications

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“…As a preliminary validation, we compare the results obtained by means of the regularized Stokeslet method with those attained through the FEM [21]: see the difference in the resistive matrix coefficients (table 1), and compare the blue solid line and the magenta circles in figure 5. The difference between the coefficients is within a few per cent, while the differences between the velocities, quantified in table 2, are barely distinguishable and of second order when compared with the effects of the head shape or the errors introduced by the simplified approaches (dashed-green curve).…”

Section: Numerical Results and Data Analysismentioning

confidence: 99%

“…According to the RFT, the viscous forces applied to the flagellum centreline depend on the flagellum velocities through f=false[KnormalNI−false(KnormalT−KnormalNfalse)tboldtnormalTfalse]⋅bolduBC,where K T and K N are the tangential and normal friction coefficients, t = (cos Ψ , sin Ψ ) the tangent to the flagellum centreline and I the identity matrix. Equation (3.2) can alternatively be expressed as [21] f=RKscriptR−1bolduBCwhere R is the rotation matrix [cosΨ−sinΨsinΨcosΨ]and K is a diagonal matrix with K T and K N on the diagonal. We proceed by (i) substituting the expressions for Ψ and u BC provided in §2.3 in (3.2) or (3.3), (ii) computing the coefficients of the propulsion matrix and (iii) solving the linear system (2.12)–(2.14).…”

Section: Numerical Results and Data Analysismentioning

confidence: 99%

“…We denote the mean flagellar curvature as K 0 , the flagellum frequency as ν , λ the wavelength and A 0 the amplitude of the wave [20]. Following [21], we first use the values: K 0 = 7735.5 rad m −1 , ν = 200 rad s −1 , λ = λ 0 = 52.19 µm, A 0 = 16828.83 rad m −1 , which give a similar flagellum waveshape compared with [12]. Additionally, we consider the flagellum radius to be F r = 0.25 µm, and the spherical swimmer head to have diameter of L head = 5 µm (figure 2).…”

Section: Mathematical Modelsmentioning

confidence: 99%

“…the frequency Reynolds number, is of the order of Re v ¼ L 2 v/n % 10 21 . Here L % 50 mm and U % 2 Â 10 À4 m s À1 are the characteristic length and velocity of the swimmer, v % 32 s 21 is the beating frequency of the flagellum and n ¼ 10 26 m 2 s 21 is the kinematic viscosity of water. For Re and Re v ( 1, the flow field is typically computed by integrating the Stokes equations in a time-independent zero-Reynolds number framework (e.g.…”

Section: Introductionmentioning

confidence: 99%

“…Recent experimental tests showed that either choices badly capture the behaviour of helical flagella for the range of shapes present in nature [18,19]. Other studies calibrated the parameters to match experimental observations [20] or the results obtained by integrating Stokes [21]. The necessity of calibrating the model versus experimental observations or the results of more sophisticated models highlights the unsuitability of the RFT approximation for applications outside the range of calibration.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

On the limitations of some popular numerical models of flagellated microswimmers: importance of long-range forces and flagellum waveform

2019

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For a sperm-cell-like flagellated swimmer in an unbounded domain, several numerical models of different fidelity are considered based on the Stokes flow approximation. The models include a regularized Stokeslet method and a three-dimensional finite-element method, which serve as the benchmark solutions for several approximate models considered. The latter include the resistive force theory versions of Lighthill, and Gray and Hancock, as well as a simplified approximation based on computing the hydrodynamic forces exerted on the head and the flagellum separately. It is shown how none of the simplified models is robust enough with regards to predicting the effect of the swimmer head shape change on the swimmer dynamics. For a range of swimmer motions considered, the resulting solutions for the swimmer force and velocities are analysed and the applicability of the Stokes model for the swimmers in question is probed.

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Section: Numerical Results and Data Analysismentioning

confidence: 99%

Section: Numerical Results and Data Analysismentioning

confidence: 99%

Section: Mathematical Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On the limitations of some popular numerical models of flagellated microswimmers: importance of long-range forces and flagellum waveform

2019

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The nut-and-bolt motion of a bacteriophage sliding along a bacterial flagellum: a complete hydrodynamics model

Karabasov

Zaitsev

Nerukh

2023

Sci Rep

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The ‘nut-and-bolt’ mechanism of a bacteriophage-bacteria flagellum translocation motion is modelled by numerically integrating the 3D Stokes equations using a Finite-Element Method (FEM). Following the works by Katsamba and Lauga (Phys Rev Fluids 4(1): 013101, 2019), two mechanical models of the flagellum-phage complex are considered. In the first model, the phage fiber wraps around the smooth flagellum surface separated by some distance. In the second model, the phage fiber is partly immersed in the flagellum volume via a helical groove imprinted in the flagellum and replicating the fiber shape. In both cases, the results of the Stokes solution for the translocation speed are compared with the Resistive Force Theory (RFT) solutions (obtained in Katsamba and Lauga Phys Rev Fluids 4(1): 013101, 2019) and the asymptotic theory in a limiting case. The previous RFT solutions of the same mechanical models of the flagellum-phage complex showed opposite trends for how the phage translocation speed depends on the phage tail length. The current work uses complete hydrodynamics solutions, which are free from the RFT assumptions to understand the divergence of the two mechanical models of the same biological system. A parametric investigation is performed by changing pertinent geometrical parameters of the flagellum-phage complex and computing the resulting phage translocation speed. The FEM solutions are compared with the RFT results using insights provided from the velocity field visualisation in the fluid domain.

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Experimental and theoretical studies of the fluid elasticity on the motion of macroscopic models of active helical swimmers

Irilan

Cunha

2022

Physics of Fluids

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This work presents experimental and theoretical studies on the locomotion of helical artificial swimmers at low Reynolds in both Newtonian and elastic ambient liquid. We examine the effect of fluid elasticity on the propulsive force and torque on the body and speed velocity of the swimmer in terms of two physical parameter: Deborah number and Strouhal number. For this end, some experiments with prototype microorganisms in creeping flow motion are conducted. In the experiments a macroscopic swimmer which propels itself by mimicking helical flagella are developed and tested. Three swimming models propelled by a helical tail with different wavelengths are investigated and their motions examined for both case: when ambient solvent is a pure Newtonian viscous fluid and when the base fluid is an elastic polymeric solution. In addition, we also apply the Slender Body Theory (SBT) and the method of regularized Stokeslet (RSM) in order to calculate theoretically the force and torque, as function of the Strouhal number, produced by the helical swimmer moving in a Newtonian fluid. The theoretical results are compared with experimental data and a very good agreement is observed specially for higher values of Strouhal within the error bars of the experimental data. In the case of a non-Newtonian ambient fluid, the flow problem of an Oldroyd-B elastic fluid is solved numerically using a computational code based on a finite element method (CFD).

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Mathematical Modelling of Flagellated Microswimmers

Cited by 4 publications

References 12 publications

On the limitations of some popular numerical models of flagellated microswimmers: importance of long-range forces and flagellum waveform

On the limitations of some popular numerical models of flagellated microswimmers: importance of long-range forces and flagellum waveform

The nut-and-bolt motion of a bacteriophage sliding along a bacterial flagellum: a complete hydrodynamics model

Experimental and theoretical studies of the fluid elasticity on the motion of macroscopic models of active helical swimmers

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