scholarly journals Stirring by periodic arrays of microswimmers

2016 ◽  
Vol 811 ◽  
pp. 487-498 ◽  
Author(s):  
Joost de Graaf ◽  
Joakim Stenhammar
Keyword(s):  
Theoretical Work ◽  
Difficult Problem ◽  
Hydrodynamic Interactions ◽  
Bulk Fluid ◽  
Enhanced Diffusion ◽  
Periodic Arrays ◽  
Ewald Sum ◽  
Tracer Particles ◽  
Micro Organisms ◽  
New Strategies

The interaction between swimming micro-organisms or artificial self-propelled colloids and passive (tracer) particles in a fluid leads to enhanced diffusion of the tracers. This enhancement has attracted strong interest, as it could lead to new strategies to tackle the difficult problem of mixing on a microfluidic scale. Most of the theoretical work on this topic has focused on hydrodynamic interactions between the tracers and swimmers in a bulk fluid. However, in simulations, periodic boundary conditions (PBCs) are often imposed on the sample and the fluid. Here, we theoretically analyse the effect of PBCs on the hydrodynamic interactions between tracer particles and microswimmers. We formulate an Ewald sum for the leading-order stresslet singularity produced by a swimmer to probe the effect of PBCs on tracer trajectories. We find that introducing periodicity into the system has a surprisingly significant effect, even for relatively small swimmer–tracer separations. We also find that the bulk limit is only reached for very large system sizes, which are challenging to simulate with most hydrodynamic solvers.

scholarly journals Enhanced diffusion of tracer particles in dilute bacterial suspensions

Soft Matter ◽  
2014 ◽  
Vol 10 (16) ◽  
pp. 2748 ◽  
Author(s):  
Alexander Morozov ◽  
Davide Marenduzzo
Keyword(s):  
Enhanced Diffusion ◽  
Tracer Particles

Tracer trajectories and displacement due to a micro-swimmer near a surface

2015 ◽  
Vol 773 ◽  
pp. 498-519 ◽  
Author(s):  
A. J. T. M. Mathijssen ◽  
D. O. Pushkin ◽  
J. M. Yeomans
Keyword(s):  
Particle Transport ◽  
Numerical Study ◽  
Tracer Particle ◽  
Persistence Length ◽  
Theoretical Work ◽  
Solid Boundary ◽  
Tracer Transport ◽  
Tracer Particles ◽  
Recent Theoretical Work ◽  
Run And Tumble

We study tracer particle transport due to flows created by a self-propelled micro-swimmer, such as a swimming bacterium, alga or a microscopic artificial swimmer. Recent theoretical work has shown that as a swimmer moves in the fluid bulk along an infinite straight path, tracer particles far from its path perform closed loops, whereas those close to the swimmer are entrained by its motion. However, in biologically and technologically important cases tracer transport is significantly altered for swimmers that move in a run-and-tumble fashion with a finite persistence length, and/or in the presence of a free surface or a solid boundary. Here we present a systematic analytical and numerical study exploring the resultant regimes and their crossovers. Our focus is on describing qualitative features of the tracer particle transport and developing quantitative tools for its analysis. Our work is a step towards understanding the ecological effects of flows created by swimming organisms, such as enhanced fluid mixing and biofilm formation.

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.

scholarly journals Lévy fluctuations and mixing in dilute suspensions of algae and bacteria

2011 ◽  
Vol 8 (62) ◽  
pp. 1314-1331 ◽  
Author(s):  
Irwin M. Zaid ◽  
Jörn Dunkel ◽  
Julia M. Yeomans
Keyword(s):  
Graphics Processing Units ◽  
Interaction Model ◽  
Tracer Diffusion ◽  
Theoretical Description ◽  
Active Suspensions ◽  
Tracer Particles ◽  
Dilute Suspensions ◽  
Nutrient Influx ◽  
Non Gaussian ◽  
Micro Organisms

Swimming micro-organisms rely on effective mixing strategies to achieve efficient nutrient influx. Recent experiments, probing the mixing capability of unicellular biflagellates, revealed that passive tracer particles exhibit anomalous non-Gaussian diffusion when immersed in a dilute suspension of self-motile Chlamydomonas reinhardtii algae. Qualitatively, this observation can be explained by the fact that the algae induce a fluid flow that may occasionally accelerate the colloidal tracers to relatively large velocities. A satisfactory quantitative theory of enhanced mixing in dilute active suspensions, however, is lacking at present. In particular, it is unclear how non-Gaussian signatures in the tracers' position distribution are linked to the self-propulsion mechanism of a micro-organism. Here, we develop a systematic theoretical description of anomalous tracer diffusion in active suspensions, based on a simplified tracer-swimmer interaction model that captures the typical distance scaling of a microswimmer's flow field. We show that the experimentally observed non-Gaussian tails are generic and arise owing to a combination of truncated Lévy statistics for the velocity field and algebraically decaying time correlations in the fluid. Our analytical considerations are illustrated through extensive simulations, implemented on graphics processing units to achieve the large sample sizes required for analysing the tails of the tracer distributions.

Directional locking and deterministic separation in periodic arrays

2009 ◽  
Vol 627 ◽  
pp. 379-401 ◽  
Author(s):  
JOELLE FRECHETTE ◽  
GERMAN DRAZER
Keyword(s):  
External Force ◽  
Hydrodynamic Interactions ◽  
Square Lattice ◽  
Stokesian Dynamics ◽  
Particle Mobility ◽  
Periodic Arrays ◽  
Moving Particle ◽  
Dynamics Simulations ◽  
Solid Obstacles ◽  
Vector Separation

We investigate the dynamics of a non-Brownian sphere suspended in a quiescent fluid and moving through a periodic array of solid obstacles under the action of a constant external force by means of Stokesian dynamics simulations. We show that in the presence of non-hydrodynamic, short-range interactions between the solid obstacles and the suspended sphere, the moving particle becomes locked into periodic trajectories with an average orientation that coincides with one of the lattice directions and is, in general, different from the direction of the driving force. The locking angle depends on the details of the non-hydrodynamic interactions and could lead to vector separation of different species for certain orientations of the external force. We explicitly show the presence of separation for a mixture of suspended particles with different roughness, moving through a square lattice of spherical obstacles. We also present a dilute model based on the two-particle mobility and resistance functions for the collision between spheres of different sizes. This simple model predicts the separation of particles of different size and also suggests that microdevices that maximize the differences in interaction area between the different particles and the solid obstacles would be more sensitive for size separation based on non-hydrodynamic interactions.

Ewald sum for hydrodynamic interactions of rigid spherical microswimmers

2018 ◽  
Vol 149 (14) ◽  
pp. 144110 ◽  
Author(s):  
Tapan Chandra Adhyapak ◽  
Sara Jabbari-Farouji
Keyword(s):  
Hydrodynamic Interactions ◽  
Ewald Sum

Nutrient uptake in a suspension of squirmers

2016 ◽  
Vol 789 ◽  
pp. 481-499 ◽  
Author(s):  
Takuji Ishikawa ◽  
Shunsuke Kajiki ◽  
Yohsuke Imai ◽  
Toshihiro Omori
Keyword(s):  
Nutrient Uptake ◽  
Sherwood Number ◽  
Volume Fraction ◽  
Industrial Applications ◽  
Hydrodynamic Interactions ◽  
Energetic Cost ◽  
Unit Energy ◽  
Micro Organisms ◽  
Dilute Limit ◽  
Good Agreement

Nutrient uptake is one of the most important factors in cell growth. Despite the biological importance, little is known about the effect of cell–cell hydrodynamic interactions on nutrient uptake in a suspension of swimming micro-organisms. In this study, we numerically investigate the nutrient uptake in an infinite suspension of squirmers. In the dilute limit, our results are in good agreement with a previous study by Magar et al. (Q. J. Mech. Appl. Maths, vol. 56, 2003, pp. 65–91). When we increased the volume fraction of squirmers, the nutrient uptake of individual cells was enhanced by the hydrodynamic interactions. The average nutrient concentration in the suspension decayed exponentially as a function of time, and the relaxation time could be scaled using the Sherwood number, the Péclet number and the volume fraction of cells. We propose a fitting function for the Sherwood number, which is useful in predicting nutrient uptake in the non-dilute regime. Furthermore, we analyse the swimming energy consumed by individual cells. The results indicate that both the energetic cost and the nutrient uptake increased as the volume fraction of cells was increased, and that the uptake per unit energy was not significantly affected by the volume fraction. These findings are important in understanding the mass transport and metabolism of swimming micro-organisms in nature and for industrial applications.

scholarly journals A combination of cis-2-decenoic acid and antibiotics eradicates pre-established catheter-associated biofilms

2014 ◽  
Vol 63 (11) ◽  
pp. 1509-1516 ◽  
Author(s):  
Azadeh Rahmani-Badi ◽  
Shayesteh Sepehr ◽  
Parisa Mohammadi ◽  
Mohammad Reza Soudi ◽  
Hamta Babaie-Naiej ◽  
...  
Keyword(s):  
Pseudomonas Aeruginosa ◽  
Urinary Tract ◽  
Surface Area ◽  
Biofilm Formation ◽  
Mixed Cultures ◽  
Decenoic Acid ◽  
Tract Infections ◽  
Micro Organisms ◽  
Antimicrobial Treatments ◽  
New Strategies

The catheterized urinary tract provides ideal conditions for the development of biofilm populations. Catheter-associated urinary tract infections (CAUTIs) are recalcitrant to existing antimicrobial treatments; therefore, established biofilms are not eradicated completely after treatment and surviving biofilm cells will carry on the infection. Cis-2-decenoic acid (CDA), an unsaturated fatty acid, is capable of inhibiting biofilm formation by Pseudomonas aeruginosa and of inducing the dispersion of established biofilms by multiple types of micro-organisms. Here, the ability of CDA to induce dispersal in pre-established single- and dual-species biofilms formed by Escherichia coli and Klebsiella pneumoniae was measured by using both semi-batch and continuous cultures bioassays. Removal of the biofilms by combined CDA and antibiotics (ciprofloxacin or ampicillin) was evaluated using microtitre plate assays (crystal violet staining). The c.f.u. counts were determined to assess the potential of combined CDA treatments to kill and eradicate pre-established biofilms formed on catheters. The effects of combined CDA treatments on biofilm surface area and bacteria viability were evaluated using fluorescence microscopy, digital image analysis and live/dead staining. To investigate the ability of CDA to prevent biofilm formation, single and mixed cultures were grown in the presence and absence of CDA. Treatment of pre-established biofilms with only 310 nM CDA resulted in at least threefold increase in the number of planktonic cells in all cultures tested. Whilst none of the antibiotics alone exerted a significant effect on c.f.u. counts and percentage of surface area covered by the biofilms, combined CDA treatments led to at least a 78 % reduction in biofilm biomass in all cases. Moreover, most of the biofilm cells remaining on the surface were killed by antibiotics. The addition of 310 nM CDA significantly prevented biofilm formation by the tested micro-organisms, even within mixed cultures, indicating the ability of CDA to inhibit biofilm formation by other types of bacteria in addition to Pseudomonas aeruginosa. These findings suggested that the biofilm-preventive characteristics of CDA make it a noble candidate for inhibition of biofilm-associated infections such as CAUTIs, which paves the way toward developing new strategies to control biofilms in clinical as well as industrial settings.

scholarly journals Growth of bioconvection patterns in a suspension of gyrotactic micro-organisms in a layer of finite depth

1989 ◽  
Vol 208 ◽  
pp. 509-543 ◽  
Author(s):  
N. A. Hill ◽  
T. J. Pedley ◽  
J. O. Kessler
Keyword(s):  
Schmidt Number ◽  
Fluid Motion ◽  
Finite Depth ◽  
Layer Depth ◽  
Bulk Fluid ◽  
Parameter Measuring ◽  
Micro Organisms ◽  
Parameter Values ◽  
Negatively Buoyant ◽  
The Continuum

The effect of gyrotaxis on the linear stability of a suspension of swimming, negatively buoyant micro-organisms is examined for a layer of finite depth. In the steady basic state there is no bulk fluid motion, and the upwards swimming of the cells is balanced by diffusion resulting from randomness in their shape, orientation and swimming behaviour. This leads to a bulk density stratification with denser fluid on top. The theory is based on the continuum model of Pedley, Hill & Kessler (1988), and employs both asymptotic and numerical analysis. The suspension is characterized by five dimensionless parameters: a Rayleigh number, a Schmidt number, a layer-depth parameter, a gyrotaxis number G, and a geometrical parameter measuring the ellipticity of the micro-organisms. For small values of G, the most unstable mode has a vanishing wavenumber, but for sufficiently large values of G, the predicted initial wavelength is finite, in agreement with experiments. The suspension becomes less stable as the layer depth is increased. Indeed, if the layer is sufficiently deep an initially homogeneous suspension is unstable, and the equilibrium state does not form. The theory of Pedley, Hill & Kessler (1988) for infinite depth is shown to be appropriate in that case. An unusual feature of the model is the existence of overstable or oscillatory modes which are driven by the gyrotactic response of the micro-organisms to the shear at the rigid boundaries of the layer. These modes occur at parameter values which could be realized in experiments.

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