Hostname: page-component-6d856f89d9-5pczc Total loading time: 0 Render date: 2024-07-16T06:50:06.842Z Has data issue: false hasContentIssue false
  • English
  • Français

Flow-induced diffusion in a packed lattice of squirmers

Published online by Cambridge University Press:  18 September 2023

Yu Kogure Open the ORCID record for Yu Kogure [Opens in a new window] ,
Toshihiro Omori Open the ORCID record for Toshihiro Omori [Opens in a new window]  and
Takuji Ishikawa Open the ORCID record for Takuji Ishikawa [Opens in a new window]
Yu Kogure*
Affiliation:
Department of Biomedical Engineering, Tohoku University, Sendai 980-8579, Japan
Toshihiro Omori
Affiliation:
Department of Finemechanics, Tohoku University, Sendai 980-8579, Japan
Takuji Ishikawa
Affiliation:
Department of Biomedical Engineering, Tohoku University, Sendai 980-8579, Japan Department of Finemechanics, Tohoku University, Sendai 980-8579, Japan
*
†Email address for correspondence: yu.kogure.s1@dc.tohoku.ac.jp
Get access Rights & Permissions [Opens in a new window]

Abstract

Mass transport in suspensions of swimming microorganisms is one of the most important factors for the colonisation and growth of microorganisms. Hydrodynamic interactions among swimming microorganisms play an important role in mass transport, especially in highly concentrated suspensions. To elucidate the influence of highly concentrated cells on mass transport, we numerically simulated mass transport in lattices of squirmers that were fixed in space and oriented in the same direction. The effects of different volume fractions, Péclet numbers ($Pe$) and lattice configurations on mass transport were quantified by tracking Lagrangian material points that move with background flow with Brownian diffusivity. Although the flow field became periodic in space and each streamline basically extended in one direction, the motion of tracer particles became diffusive over long durations due to Brownian motion and cross-flows. Flow-induced diffusion was anisotropic and significantly enhanced over Brownian diffusion in the longitudinal direction. We also investigated mass transport in random configurations of squirmers to reproduce more general conditions. Similar enhanced diffusion was also observed in the random configurations, indicating that the flow-induced diffusion appears regardless of the configurations. The present flow-induced diffusion did not follow $Pe$ dependency of the conventional Taylor dispersion due to the cross-flows. The time and velocity scales were proposed, which enabled us to predict the flow-induced diffusivity from the data of the flow field and Brownian diffusivity without solving the mass conservation equation. The findings reported here improve our understanding of the transport phenomena in packed suspensions of swimming microorganisms.

JFM classification

Biological Fluid Dynamics: Micro-organism dynamics Low-Reynolds-number flows: Boundary integral methods Mass Transport: Coupled diffusion and flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 971 , 25 September 2023 , A17
Check for updates
Copyright
© The Author(s), 2023. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Beenakker, C.W.J. 1986 Ewald sum of the Rotne–Prager tensor. J. Chem. Phys. 85, 1581–1582.CrossRefGoogle Scholar
Berg, H.C. 1984 Diffusion: microscopic theory. In Random Walks in Biology, chap. 1. Princeton University Press.CrossRefGoogle Scholar
Bjarnsholt, T., Alhede, M., Alhede, M., Eickhardt-Sørensen, S.R., Moser, C., Kühl, M., Jensen, P.Ø. & Høiby, N. 2013 The in vivo biofilm. Trends Microbiol. 21, 466–474.CrossRefGoogle ScholarPubMed
Blake, J.R. 1971 A spherical envelope approach to ciliary propulsion. J. Fluid Mech. 46, 199–208.CrossRefGoogle Scholar
Blees, M.H. & Leyte, J.C. 1994 The effective translational self-diffusion coefficient of small molecules in colloidal crystals of spherical particles. J. Colloid Interface Sci. 166, 118–127.CrossRefGoogle Scholar
Box, G.E.P. & Muller, M.E. 1958 A note on the generation of random normal deviates. Ann. Math. Statist. 29, 610–611.CrossRefGoogle Scholar
Brady, J.F., Phillips, R.J., Lester, J.C. & Bossis, G. 1988 Dynamic simulation of hydrodynamically interacting suspensions. J. Fluid Mech. 195, 257–280.CrossRefGoogle Scholar
Brenner, H. 1980 Dispersion resulting from flow through spatially periodic porous media. Phil. Trans. R. Soc. Lond. A 297, 81–133.Google Scholar
Broeck, C.V.D. 1982 A stochastic description of longitudinal dispersion in uniaxial flows. Physica A 112, 343–352.CrossRefGoogle Scholar
Broeck, C.V.D. 1990 Taylor dispersion revisited. Physica A 168, 677–696.CrossRefGoogle Scholar
Burkholder, E.W. & Brady, J.F. 2017 Tracer diffusion in active suspensions. Phys. Rev. E 95, 052605.CrossRefGoogle ScholarPubMed
Delmotte, B., Keaveny, E.E., Climent, E. & Plouraboué, F. 2018 Simulation of Brownian tracer transport in squirmer suspensions. IMA J. Appl. Maths 83, 680–699.CrossRefGoogle Scholar
Dombrowski, C., Cisneros, L., Goldstein, R.E. & Kessler, J.O. 2004 Self-concentration and large-scale coherence in bacterial dynamics. Phys. Rev. Lett. 93, 098103.CrossRefGoogle ScholarPubMed
Drescher, K., Leptos, K.C., Tuval, I., Ishikawa, T., Pedley, T.J. & Goldstein, R.E. 2009 Dancing Volvox: hydrodynamic bound states of swimming algae. Phys. Rev. Lett. 102, 168101.CrossRefGoogle ScholarPubMed
Dunkel, J., Heidenreich, S., Drescher, K., Wensink, H.H., Bär, M. & Goldstein, R.E. 2013 Fluid dynamics of bacterial turbulence. Phys. Rev. Lett. 110, 228102.CrossRefGoogle ScholarPubMed
Ermak, D.L. & McCammon, J.A. 1978 Brownian dynamics with hydrodynamic interactions. J. Chem. Phys. 69, 1352–1360.CrossRefGoogle Scholar
Ferracci, J., Ueno, H., Numayama-Tsuruta, K., Imai, Y., Yamaguchi, T. & Ishikawa, T. 2013 Entrapment of ciliates at the water–air interface. PLoS ONE 8, e75238.CrossRefGoogle ScholarPubMed
Harding, J.L. & Reynolds, M.M. 2014 Combating medical device fouling. Trends Biotechnol. 32, 140–146.CrossRefGoogle ScholarPubMed
Ishikawa, T., Kajiki, S., Imai, Y. & Omori, T. 2016 Nutrient uptake in a suspension of squirmers. J. Fluid Mech. 789, 481–499.CrossRefGoogle Scholar
Ishikawa, T., Locsei, J.T. & Pedley, T.J. 2010 Fluid particle diffusion in a semidilute suspension of model micro-organisms. Phys. Rev. E 82, 021408.CrossRefGoogle Scholar
Ishikawa, T., Omori, T. & Kikuchi, K. 2020 Bacterial biomechanics – from individual behaviors to biofilm and the gut flora. APL Bioengng 4, 041504.CrossRefGoogle ScholarPubMed
Ishikawa, T., Pedley, T.J., Drescher, K. & Goldstein, R.E. 2020 Stability of dancing Volvox. J. Fluid Mech. 903, A11.CrossRefGoogle Scholar
Ishikawa, T., Yoshida, N., Ueno, H., Wiedeman, M., Imai, Y. & Yamaguchi, T. 2011 Energy transport in a concentrated suspension of bacteria. Phys. Rev. Lett. 107, 028102.CrossRefGoogle Scholar
Jang, H., Rusconi, R. & Stocker, R. 2017 Biofilm disruption by an air bubble reveals heterogeneous age-dependent detachment patterns dictated by initial extracellular matrix distribution. NPJ Biofilms Microbiomes 3, 6.CrossRefGoogle ScholarPubMed
Jansons, K.M. 2006 On Taylor dispersion in oscillatory channel flows. Proc. R. Soc. Lond. A 462, 3501–3509.Google Scholar
Jepson, A., Martinez, V.A., Schwarz-Linek, J., Morozov, A. & Poon, W.C.K. 2013 Enhanced diffusion of nonswimmers in a three-dimensional bath of motile bacteria. Phys. Rev. E 88, 041002.CrossRefGoogle Scholar
Jin, C., Chen, Y., Maass, C.C. & Mathijssen, A.J.T.M. 2021 Collective entrainment and confinement amplify transport by schooling microswimmers. Phys. Rev. Lett. 127, 088006.CrossRefGoogle ScholarPubMed
Kasyap, T.V., Koch, D.L. & Wu, M. 2014 Hydrodynamic tracer diffusion in suspensions of swimming bacteria. Phys. Fluids 26, 081901.CrossRefGoogle Scholar
Kitamura, H., Omori, T. & Ishikwa, T. 2021 Impact of rheological properties on bacterial streamer formation. J. R. Soc. Interface 18, 20210546.CrossRefGoogle ScholarPubMed
Koch, D.J., Cox, R.G., Brenner, H. & Brady, J.F. 1989 The effect of order on dispersion in porous media. J. Fluid Mech. 200, 173–188.CrossRefGoogle Scholar
Lambert, R.A., Picano, F., Breugem, W.-P. & Brandt, L. 2013 Active suspensions in thin films: nutrient uptake and swimmer. J. Fluid Mech. 733, 528–557.CrossRefGoogle Scholar
Leptos, K.C., Guasto, J.S., Gollub, J.P., Pesci, A.I. & Goldstein, R.E. 2009 Dynamics of enhanced tracer diffusion in suspensions of swimming eukaryotic microorganisms. Phys. Rev. Lett. 103, 198103.CrossRefGoogle ScholarPubMed
Levesque, M., Bénichou, O., Voituriez, R. & Rotenberg, B. 2012 Taylor dispersion with adsorption and desorption. Phys. Rev. E 86, 036316.CrossRefGoogle ScholarPubMed
Lighthill, M.J. 1952 On the squirming motion of nearly spherical deformable bodies through liquids at very small Reynolds numbers. Commun. Pure Appl. Maths 5, 109–118.CrossRefGoogle Scholar
Lin, T.Y. & Shaqfeh, E.S.G. 2019 Taylor dispersion in the presence of cross flow and interfacial mass transfer. Phys. Rev. Fluids 4, 034501.CrossRefGoogle Scholar
Lin, Z., Thiffeault, J.-L. & Childress, S. 2011 Stirring by squirmers. J. Fluid Mech. 669, 167–177.CrossRefGoogle Scholar
Magar, V., Goto, T. & Pedley, T.J. 2003 Nutrient uptake by a self-propelled steady squirmer. Q. J. Mech. Appl. Maths 56, 65–91.CrossRefGoogle Scholar
Magar, V. & Pedley, T.J. 2005 Average nutrient uptake by a self-propelled unsteady squirmer. J. Fluid Mech. 539, 93–112.CrossRefGoogle Scholar
Miño, G., Mallouk, T.E., Darnige, T., Hoyos, M., Dauchet, J., Dunstan, J., Soto, R., Wang, Y., Rousselet, A. & Clement, E. 2011 Enhanced diffusion due to active swimmers at a solid surface. Phys. Rev. Lett. 106, 048102.CrossRefGoogle Scholar
Miño, G.L., Dunstan, J., Rousselet, A., Clément, E. & Soto, R. 2013 Induced diffusion of tracers in a bacterial suspension: theory and experiments. J. Fluid Mech. 729, 423–444.CrossRefGoogle Scholar
Morozov, A. & Marenduzzo, D. 2014 Enhanced diffusion of tracer particles in dilute bacterial suspensions. Soft Matt. 10, 2748–2758.CrossRefGoogle ScholarPubMed
Patteson, A.E., Gopinath, A., Purohit, P.K. & Arratia, P. 2016 Particle diffusion in active fluids is non-monotonic in size. Soft Matt. 12, 2365–2372.CrossRefGoogle ScholarPubMed
Pedley, T.J. 2016 Spherical squirmers: models for swimming micro-organisms. IMA J. Appl. Maths 81, 488–521.CrossRefGoogle Scholar
Pozrikidis, C. 1992 Generalized boundary integral methods. In Boundary Integral and Singularity Methods for Linearized Viscous Flow, chap. 4. Cambridge University Press.CrossRefGoogle Scholar
Pushkin, D.O., Shum, H. & Yeomans, J.M. 2013 Fluid transport by individual microswimmers. J. Fluid Mech. 726, 5–25.CrossRefGoogle Scholar
Shapiro, M. & Brenner, H. 1986 Taylor dispersion of chemically reactive species: irreversible first-order reactions in bulk and on boundaries. Chem. Engng Sci. 41, 1417–1433.CrossRefGoogle Scholar
Sokolov, A., Goldstein, R.E., Feldchtein, F.I. & Aranson, I.S. 2009 Enhanced mixing and spatial instability in concentrated bacterial suspensions. Phys. Rev. E 80, 031903.CrossRefGoogle ScholarPubMed
Taylor, G.I. 1953 Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. R. Soc. Lond. A 219, 186–203.Google Scholar
Thiffeault, J.-L. & Childress, S. 2010 Stirring by swimming bodies. Phys. Lett. A 374, 3487–3490.CrossRefGoogle Scholar
Underhill, P.T., Hernandez-Ortiz, J.P. & Graham, M.D. 2008 Diffusion and spatial correlations in suspensions of swimming particles. Phys. Rev. Lett. 100, 248101.CrossRefGoogle ScholarPubMed
Wang, B., Jiang, W., Chen, G. & Tao, L. 2022 Transient dispersion in a channel with crossflow and wall adsorption. Phys. Rev. Fluids 7, 074501.CrossRefGoogle Scholar
Wensink, H.H., Dunkel, J., Heidenreich, S., Drescher, K., Goldstein, R.E., Löwen, H. & Yeomans, J.M. 2012 Meso-scale turbulence in living fluids. Proc. Natl Acad. Sci. USA 109, 14308–14313.CrossRefGoogle ScholarPubMed
Wu, X.-L. & Libchaber, A. 2000 Particle diffusion in a quasi-two-dimensional bacterial bath. Phys. Rev. Lett. 84, 3017–3020.CrossRefGoogle Scholar
Zhang, H.P., Be'er, A., Florin, E.-L. & Swinney, H.L. 2010 Collective motion and density fluctuation in bacterial colonies. Proc. Natl Acad. Sci. USA 107, 13626–13630.CrossRefGoogle ScholarPubMed