Modelling bacterial behaviour close to a no-slip plane boundary: the influence of bacterial geometry

Shum, Henry; Gaffney, Eamonn A.; Smith, D. J.

doi:10.1098/rspa.2009.0520

Cited by 144 publications

(244 citation statements)

References 57 publications

(88 reference statements)

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“…With these considerations, combination of equation (45) with the constitutive relations (46) , (47) From expression (43) the explicit time dependence contribution to the mean square displacement, due to active motion, can be straightforwardly obtained, namely…”

Section: Resultsmentioning

confidence: 99%

“…The processes that lead to chiral motion of active articles may be diverse [46][47][48][49], the simplest situation in two dimensions corresponds to a geometric effect, that is to say, to the misaligning of the direction of the propelling force and the orientation of the particle axis [50,51]. A simple effective-force model, that leads to circular patterns of motion, is the inclusion of an effective constant "torque" in the Langevin equations that drive the orientation of the self-propulsive force [52].…”

Section: Introductionmentioning

confidence: 99%

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Diffusion of active chiral particles

Sevilla

2016

Phys. Rev. E

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The diffusion of chiral active Brownian particles in three-dimensional space is studied analytically, by consideration of the corresponding Fokker-Planck equation for the probability density of finding a particle at position x and moving along the directionv at time t, and numerically, by the use of Langevin dynamics simulations. The analysis is focused on the marginal probability density of finding a particle at a given location and at a given time (independently of its direction of motion), which is found from an infinite hierarchy of differential-recurrence relations for the coefficients that appear in the multipole expansion of the probability distribution which contains the whole kinematic information. This approach allows the explicit calculation of the time dependence of the mean squared displacement and the time dependence of the kurtosis of the marginal probability distribution, quantities from which the effective diffusion coefficient and the "shape" of the positions distribution are examined. Oscillations between two characteristic values were found in the time evolution of the kurtosis, namely, between the value that corresponds to a Gaussian and the one that corresponds to a distribution of spherical shell shape. In the case of an ensemble of particles, each one rotating around an uniformly-distributed random axis, it is found evidence of the so called effect "anomalous, yet Brownian, diffusion", for which particles follow a non-Gaussian distribution for the positions yet the mean squared displacement is a linear function of time.PACS numbers: 02.50.-r 05.40.-a 05.10.Gg

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Diffusion of active chiral particles

Sevilla

2016

Phys. Rev. E

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“…Principal points addressed by previous studies are the extent to which surface accumulation is a generic feature fluid dynamic effect associated with near-wall swimming, the role of specialized flagellar beat patterns, species-specific morphology, and the relative prevalence of swimming "near" as opposed to "against" walls; discussion of these questions can be found in recent editorials (12,13). There has also been a resurgence of interest recently in the fluid mechanics of motile bacteria (14)(15)(16)(17) and generic models for swimming cells (11,(18)(19)(20).…”

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confidence: 99%

Human spermatozoa migration in microchannels reveals boundary-following navigation

Denissenko

Kantsler²,

Smith³

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

256

241

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The migratory abilities of motile human spermatozoa in vivo are essential for natural fertility, but it remains a mystery what properties distinguish the tens of cells which find an egg from the millions of cells ejaculated. To reach the site of fertilization, sperm must traverse narrow and convoluted channels, filled with viscous fluids. To elucidate individual and group behaviors that may occur in the complex three-dimensional female tract environment, we examine the behavior of migrating sperm in assorted microchannel geometries. Cells rarely swim in the central part of the channel cross-section, instead traveling along the intersection of the channel walls ("channel corners"). When the channel turns sharply, cells leave the corner, continuing ahead until hitting the opposite wall of the channel, with a distribution of departure angles, the latter being modulated by fluid viscosity. If the channel bend is smooth, cells depart from the inner wall when the curvature radius is less than a threshold value close to 150 μm. Specific wall shapes are able to preferentially direct motile cells. As a consequence of swimming along the corners, the domain occupied by cells becomes essentially one-dimensional, leading to frequent collisions, and needs to be accounted for when modeling the behavior of populations of migratory cells and considering how sperm populate and navigate the female tract. The combined effect of viscosity and three-dimensional architecture should be accounted for in future in vitro studies of sperm chemoattraction.cell swimming | motility | reproduction | thigmotaxis S perm motility is influenced by surfaces; this is most simply and strikingly evident in the accumulation of cells on the surfaces of microscope slides and coverslips, a phenomenon known to every andrologist. The effect and its causes have been investigated extensively through a variety of approaches, including microscopy (1-4), computational fluid mechanics, (5-9), molecular dynamics (10), and mathematical analysis (11). Principal points addressed by previous studies are the extent to which surface accumulation is a generic feature fluid dynamic effect associated with near-wall swimming, the role of specialized flagellar beat patterns, species-specific morphology, and the relative prevalence of swimming "near" as opposed to "against" walls; discussion of these questions can be found in recent editorials (12, 13). There has also been a resurgence of interest recently in the fluid mechanics of motile bacteria (14-17) and generic models for swimming cells (11,(18)(19)(20).Previous studies have usually focused on the behavior of a cell near a single planar surface or between a pair of planar surfaces, modeling the interior of a haemocytometer or similar device; however, both the female reproductive tract and microfluidic in vitro fertilization (IVF) devices present sperm with a much more confined and potentially tortuous geometry. The fallopian tubes consist of ciliated epithelium (21), the distance between opposed epithelial surfaces bein...

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“…[7][8][9][10] In BEM, the Stokes flow equations are transformed into an integral of Green's functions over the domain boundaries. 6 These boundaries are discretised or "meshed" into typically triangular elements (Fig.…”

Section: Introductionmentioning

confidence: 99%

Microscale flow dynamics of ribbons and sheets

2017

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Numerical study of the hydrodynamics of thin sheets and ribbons presents difficulties associated with resolving multiple length scales. To circumvent these difficulties, asymptotic methods have been developed to describe the dynamics of slender fibres and ribbons. However, such theories entail restrictions on the shapes that can be studied, and often break down in regions where standard boundary element methods are still impractical. In this paper we develop a regularised stokeslet method for ribbons and sheets in order to bridge the gap between asymptotic and boundary element methods. The method is validated against the analytical solution for plate ellipsoids, as well as the dynamics of ribbon helices and an experimental microswimmer. We then demonstrate the versatility of this method by calculating the flow around a double helix, and the swimming dynamics of a microscale "magic carpet".

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Modelling bacterial behaviour close to a no-slip plane boundary: the influence of bacterial geometry

Cited by 144 publications

References 57 publications

Diffusion of active chiral particles

Diffusion of active chiral particles

Human spermatozoa migration in microchannels reveals boundary-following navigation

Microscale flow dynamics of ribbons and sheets

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