Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-24T18:39:02.881Z Has data issue: false hasContentIssue false
  • English
  • Français

BIOLOGICAL FLUID MECHANICS UNDER THE MICROSCOPE: A TRIBUTE TO JOHN BLAKE

Part of: Biological fluid mechanics

Published online by Cambridge University Press:  28 March 2018

DAVID J. SMITH Open the ORCID record for DAVID J. SMITH [Opens in a new window]
DAVID J. SMITH*
Affiliation:
School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK email D.J.Smith@bham.ac.uk
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

John Blake (1947–2016) was a leader in fluid mechanics, his two principal areas of expertise being biological fluid mechanics on microscopic scales and bubble dynamics. He produced leading research and mentored others in both Australia, his home country, and the UK, his adopted home. This article reviews John Blake’s contributions in biological fluid mechanics, as well as gives the author’s personal viewpoint as one of the many graduate students and researchers who benefitted from his supervision, guidance and inspiration. The key topics from biological mechanics discussed are: “squirmer” models of protozoa, the method of images in Stokes flow and the “blakelet” solution, discrete cilia modelling via slender body theory, physiological flows in respiration and reproduction, blinking stokeslets in microorganism feeding, human sperm motility and embryonic nodal cilia.

Keywords

ciliaflagellaStokes flowslender bodystokesletswimmingpropulsionfeedingchaotic advectionmucus

MSC classification

Primary: 76Z10: Biopropulsion in water and in air
Secondary: 76Z05: Physiological flows
Type
Research Article
Information
The ANZIAM Journal , Volume 59 , Issue 4 , April 2018 , pp. 416 - 442
Copyright
© 2018 Australian Mathematical Society 

References

Aderogba, K. and Blake, J. R., “Action of a force near the planar surface between two semi-infinite immiscible liquids at very low Reynolds numbers”, Bull. Aust. Math. Soc. 18 (1978) 345–356; doi:10.1017/S0004972700008224.Google Scholar
Aderogba, K. and Blake, J. R., “Action of a force near the planar surface between semi-infinite immiscible liquids at very low Reynolds numbers: addendum”, Bull. Aust. Math. Soc. 19 (1978) 309–318; doi:10.1017/S0004972700008819.CrossRefGoogle Scholar
Aref, H., “Stirring by chaotic advection”, J. Fluid Mech. 143 (1984) 1–21;doi:10.1017/S0022112084001233.CrossRefGoogle Scholar
Aref, H., Blake, J. R., Budišić, M., Cardoso, S. S. S., Cartwright, J. H. E., Clercx, H. J. H., El Omari, K., Feudel, U., Golestanian, R. and Gouillart, E. et al. , “Frontiers of chaotic advection”, Rev. Mod. Phys. 89 (2017) 025007; doi:10.1103/RevModPhys.89.025007.Google Scholar
Berdon, W. E., McManus, C. and Afzelius, B., “More on Kartagener’s syndrome and the contributions of Afzelius and A. K. Siewert”, Ped. Radiol. 34 (2004) 585–586;doi:10.1007/s00247-004-1203-y.CrossRefGoogle Scholar
Berdon, W. E. and Willi, U., “Situs inversus, bronchiectasis, and sinusitis and its relation to immotile cilia: history of the diseases and their discoverers–Manes Kartagener and Bjorn Afzelius”, Ped. Radiol. 34 (2004) 38–42; doi:10.1007/s00247-003-1072-9.Google Scholar
Blake, J. R., “A spherical envelope approach to ciliary propulsion”, J. Fluid Mech. 46 (1971) 199–208; doi:10.1017/S002211207100048X.CrossRefGoogle Scholar
Blake, J. R., “Infinite models for ciliary propulsion”, J. Fluid Mech. 49 (1971) 209–222;doi:10.1017/S0022112071002027.Google Scholar
Blake, J. R., “A note on the image system for a stokeslet in a no-slip boundary”, Proc. Cambridge Philos. Soc. 70 (1971) 303–310; doi:10.1017/S0305004100049902.Google Scholar
Blake, J. R., “Self propulsion due to oscillations on the surface of a cylinder at low Reynolds number”, Bull. Aust. Math. Soc. 5 (1971) 255–264; doi:10.1017/S0004972700047134.CrossRefGoogle Scholar
Blake, J., “A model for the micro-structure in ciliated organisms”, J. Fluid Mech. 55 (1972) 1–23; doi:10.1017/S0022112072001612.Google Scholar
Blake, J., “Flow in tubules due to ciliary activity”, Bull. Math. Biol. 35 (1973) 513–523;doi:10.1007/BF02575194.Google Scholar
Blake, J., “On the movement of mucus in the lung”, J. Biomech. 8 (1975) 179–190;doi:10.1016/0021-9290(75)90023-8.Google Scholar
Blake, J. R., “An active porous medium model for ciliary propulsion”, J. Theoret. Biol. 64 (1977) 697–701; doi:10.1016/0022-5193(77)90268-5.CrossRefGoogle ScholarPubMed
Blake, J. R., “On the fluid mechanics of the foetal lung”, Math. Sci. 2 (1977) 95–110; http://www.appliedprobability.org/data/files/TMS%20articles/2_2_2.pdf.Google Scholar
Blake, J. R. and Chwang, A. T., “Fundamental singularities of viscous flow”, J. Engrg. Math. 8 (1974) 23–29; doi:10.1007/BF02353701.CrossRefGoogle Scholar
Blake, J. R. and Fulford, G. R., “Mechanics of muco-ciliary transport”, PCH Physicochem. Hydrodyn. 5 (1984) 401–411.Google Scholar
Blake, J. R. and Fulford, G. R., “Hydrodynamics of filter feeding”, Sympos. Soc. Exp. Biol. 49 (1994) 183–197; PMID:8571223.Google Scholar
Blake, J. R. and Gaffney, E. A., “Modeling aspects of tracer transport in mucociliary flows”, in: Cilia and mucus: from development to respiratory defense (ed. Salathe, M.), (CRC Press, Boca Raton, 2001) 291–302; ora.ox.ac.uk.Google Scholar
Blake, J. R. and Otto, S. R., “Ciliary propulsion, chaotic filtration and a ‘blinking’ stokeslet”, J. Engrg. Math. 30 (1996) 151–168; doi:10.1007/BF00118828.CrossRefGoogle Scholar
Blake, J. R., Otto, S. R. and Blake, D. A., “Filter feeding, chaotic filtration, and a blinking stokeslet”, Theor. Comput. Fluid Dyn. 10 (1998) 23–36; doi:10.1007/s001620050049.Google Scholar
Blake, J. R., Tuck, E. O. and Wakeley, P. W., “A note on the S-transform and slender body theory in Stokes flow”, IMA J. Appl. Math. 75 (2010) 343–355; doi:10.1093/imamat/hxq005.CrossRefGoogle Scholar
Blake, J. R., Vann, P. G. and Winet, H., “A model of ovum transport”, J. Theoret. Biol. 102 (1983) 145–166; doi:10.1016/0022-5193(83)90267-9.Google Scholar
Chilvers, M. A. and O’Callaghan, C., “Analysis of ciliary beat pattern and beat frequency using digital high speed imaging: comparison with the photomultiplier and photodiode methods”, Thorax 55 (2000) 314–317; doi:10.1136/thorax.55.4.314.Google Scholar
Chwang, A. T. and Wu, T. Y.-T., “Hydromechanics of low-Reynolds-number flow. Part 2. Singularity method for Stokes flows”, J. Fluid Mech. 67 (1975) 787–815;doi:10.1017/S0022112075000614.CrossRefGoogle Scholar
Cortez, R. and Varela, D., “A general system of images for regularized stokeslets and other elements near a plane wall”, J. Comput. Phys. 285 (2015) 41–54; doi:10.1016/j.jcp.2015.01.019.CrossRefGoogle Scholar
Fulford, G. R. and Blake, J. R., “Force distribution along a slender body straddling an interface”, J. Austral. Math. Soc. (Series B) 27 (1986) 295–315; doi:10.1017/S033427000000494X.Google Scholar
Fulford, G. R. and Blake, J. R., “Muco-ciliary transport in the lung”, J. Theoret. Biol. 121 (1986) 381–402; doi:10.1016/S0022-5193(86)80098-4.Google Scholar
Gaffney, E. A., Gadêlha, H., Smith, D. J., Blake, J. R. and Kirkman-Brown, J. C., “Mammalian sperm motility: observation and theory”, Annu. Rev. Fluid Mech. 43 (2011) 501–528;doi:10.1146/annurev-fluid-121108-145442.Google Scholar
Gray, J. and Hancock, G. J., “The propulsion of sea-urchin spermatozoa”, J. Exp. Biol. 32(4) (1955) 802–814; jeb.biologists.org.Google Scholar
Hancock, G. J., “The self-propulsion of microscopic organisms through liquids”, Proc. R. Soc. Lond. A 217(1128) (1953) 96–121; doi:10.1098/rspa.1953.0048.Google Scholar
Higdon, J. J. L., “The generation of feeding currents by flagellar motions”, J. Fluid Mech. 94 (1979) 305–330; doi:10.1017/S002211207900104X.Google Scholar
Hoffmann, F. and Cortez, R., “Numerical computation of doubly-periodic Stokes flow bounded by a plane with applications to nodal cilia”, Commun. Comput. Phys. 22(3) (2017) 620–642; doi:10.4208/cicp.OA-2016-0151.Google Scholar
Ishimoto, K., “A spherical squirming swimmer in unsteady Stokes flow”, J. Fluid Mech. 723 (2013) 163–189; doi:10.1017/jfm.2013.131.CrossRefGoogle Scholar
Jaffrin, M. Y. and Shapiro, A. H., “Peristaltic pumping”, Annu. Rev. Fluid Mech. 3 (1971) 13–37; doi:10.1146/annurev.fl.03.010171.000305.Google Scholar
Kennewell, P. J. and Blake, J. R., “Fluid flow in the human foetal lung: a theoretical model”, Respir. Physiol. 27 (1976) 131–145; doi:10.1016/0034-5687(76)90023-2.CrossRefGoogle ScholarPubMed
Lighthill, M. J., “On the squirming motion of nearly spherical deformable bodies through liquids at very small Reynolds numbers”, Comm. Pure Appl. Math. 5 (1952) 109–118; doi:10.1002/cpa.3160050201.Google Scholar
Liron, N., “Fluid transport by cilia between parallel plates”, J. Fluid Mech. 86 (1978) 705–726; doi:10.1017/S0022112078001354.Google Scholar
Liron, N. and Blake, J. R., “Existence of viscous eddies near boundaries”, J. Fluid Mech. 107 (1981) 109–129; doi:10.1017/S0022112081001699.Google Scholar
Liron, N. and Mochon, S., “Stokes flow for a stokeslet between two parallel flat plates”, J. Engrg. Math. 10 (1976) 287–303; doi:10.1007/BF01535565.Google Scholar
Machemer, H., “Ciliary activity and the origin of metachrony in Paramecium: effects of increased viscosity”, J. Exp. Biol. 57 (1972) 239–259; http://jeb.biologists.org/content/57/1/239.long.Google Scholar
Mathijssen, A. J. T. M., Doostmohammadi, A., Yeomans, J. M. and Shendruk, T. N., “Hydrodynamics of micro-swimmers in films”, J. Fluid Mech. 806 (2016) 35–70;doi:10.1017/jfm.2016.479.Google Scholar
Matsui, H., Grubb, B. R., Tarran, R., Randell, S. H., Gatzy, J. T., Davis, C. W. and Boucher, R. C., “Evidence for periciliary liquid layer depletion, not abnormal ion composition, in the pathogenesis of cystic fibrosis airways disease”, Cell 95 (1998) 1005–1015;doi:10.1016/S0092-8674(00)81724-9.Google Scholar
Montenegro-Johnson, T. D., Baker, D. I., Smith, D. J. and Lopes, S. S., “Three-dimensional flow in Kupffer’s vesicle”, J. Math. Biol. 73 (2016) 705–725; doi:10.1007/s00285-016-0967-7.CrossRefGoogle ScholarPubMed
Nonaka, S., Shiratori, H., Saijoh, Y. and Hamada, H., “Determination of left–right patterning of the mouse embryo by artificial nodal flow”, Nature 418(6893) (2002) 96–99;doi:10.1038/nature00849.Google Scholar
Nonaka, S., Tanaka, Y., Okada, Y., Takeda, S., Harada, A., Kanai, Y., Kido, M. and Hirokawa, N., “Randomization of left–right asymmetry due to loss of nodal cilia generating leftward flow of extraembryonic fluid in mice lacking KIF3B motor protein”, Cell 95 (1998) 829–837; doi:10.1016/S0092-8674(00)81705-5.Google Scholar
Nonaka, S., Yoshiba, S., Watanabe, D., Ikeuchi, S., Goto, T., Marshall, W. F. and Hamada, H., “De novo formation of left–right asymmetry by posterior tilt of nodal cilia”, PLoS Biol. 3 (2005) e268; doi:10.1371/journal.pbio.0030268.Google Scholar
Okada, Y., Takeda, S., Tanaka, Y., Belmonte, J.-C. I. and Hirokawa, N., “Mechanism of nodal flow: a conserved symmetry breaking event in left–right axis determination”, Cell 121(4) (2005) 633–644; doi:10.1016/j.cell.2005.04.008.Google Scholar
Orme, B. A. A., Otto, S. R. and Blake, J. R., “Chaos and mixing in micro-biological fluid dynamics: blinking stokeslets”, Math. Methods Appl. Sci. 24 (2001) 1337–1349; doi:10.1002/mma.183.Google Scholar
Otto, S. R., Yannacopoulos, A. N. and Blake, J. R., “Transport and mixing in Stokes flow: the effect of chaotic dynamics on the blinking stokeslet”, J. Fluid Mech. 430 (2001) 1–26; doi:10.1017/S0022112000002494.Google Scholar
Pedley, T. J., Brumley, D. R. and Goldstein, R. E., “Squirmers with swirl: a model for volvox swimming”, J. Fluid Mech. 798 (2016) 165–186; doi:10.1017/jfm.2016.306.CrossRefGoogle Scholar
Pintado, P., Sampaio, P., Tavares, B., Montenegro-Johnson, T. D., Smith, D. J. and Lopes, S. S., “Dynamics of cilia length in left–right development”, R. Soc. Open Sci. 4(3) (2017) 161102; doi:10.1098/rsos.161102.Google Scholar
Purcell, E. M., “Life at low Reynolds number”, Amer. J. Phys. 45 (1977) 3–11;doi:10.1119/1.10903.Google Scholar
Sanderson, M. J. and Sleigh, M. A., “Ciliary activity of cultured rabbit tracheal epithelium: beat pattern and metachrony”, J. Cell Sci. 47 (1981) 331–347; jcs.biologists.org.Google Scholar
Sleigh, M. A., Blake, J. R. and Liron, N., “State of art: the propulsion of mucus by cilia”, Amer. Rev. Respir. Dis. 137 (1988) 726–741; doi:10.1164/ajrccm/137.3.726.Google Scholar
Smith, A. A., Johnson, T. D., Smith, D. J. and Blake, J. R., “Symmetry breaking cilia-driven flow in the zebrafish embryo”, J. Fluid Mech. 705 (2012) 26–45; doi:10.1017/jfm.2012.117.CrossRefGoogle Scholar
Smith, D. J. and Blake, J. R., “Surface accumulation of spermatozoa: a fluid dynamic phenomenon”, Math. Sci. 34(2) (2009) 74–87;http://www.appliedprobability.org/data/files/TMS%20articles/34_2_3.pdf.Google Scholar
Smith, D. J., Gaffney, E. A. and Blake, J. R., “Discrete cilia modelling with singularity distributions: application to the embryonic node and the airway surface liquid”, Bull. Math. Biol. 69 (2007) 1477–1510; doi:10.1007/s11538-006-9172-y.Google Scholar
Smith, D. J., Gaffney, E. A. and Blake, J. R., “A model of tracer transport in airway surface liquid”, Bull. Math. Biol. 69 (2007) 817–836; doi:10.1007/s11538-006-9163-z.Google Scholar
Smith, D. J., Gaffney, E. A. and Blake, J. R., “A viscoelastic traction layer model of muco-ciliary transport”, Bull. Math. Biol. 69 (2007) 289–327; doi:10.1007/s11538-005-9036-x.Google Scholar
Smith, D. J., Gaffney, E. A. and Blake, J. R., “Modelling mucociliary clearance”, Respir. Physiol. Neurobiol. 163 (2008) 178–188; doi:10.1016/j.resp.2008.03.006.CrossRefGoogle ScholarPubMed
Smith, D. J., Gaffney, E. A., Blake, J. R. and Kirkman-Brown, J. C., “Human sperm accumulation near surfaces: a simulation study”, J. Fluid Mech. 621 (2009) 289–320; doi:10.1017/S0022112008004953.Google Scholar
Smith, D. J., Smith, A. A. and Blake, J. R., “Mathematical embryology: the fluid mechanics of nodal cilia”, J. Engrg. Math. 70 (2011) 255–279; doi:10.1007/s10665-010-9383-y.Google Scholar
Staben, M. E., Zinchenko, A. Z. and Davis, R. H., “Motion of a particle between two parallel plane walls in low-Reynolds-number Poiseuille flow”, Phys. Fluids 15 (2003) 1711–1733; doi:10.1063/1.1568341.CrossRefGoogle Scholar
Sulik, K., Dehart, D. B., Inagaki, T., Carson, J. L., Vrablic, T., Gesteland, K. and Schoenwolf, G. C., “Morphogenesis of the murine node and notochordal plate”, Dev. Dyn. 201 (1994) 260–278; doi:10.1002/aja.1002010309.Google Scholar
Supatto, W., Fraser, S. E. and Vermot, J., “An all-optical approach for probing microscopic flows in living embryos”, Biophys. J. 95 (2008) L29–L31; doi:10.1529/biophysj.108.137786.CrossRefGoogle ScholarPubMed
Taylor, G., “Analysis of the swimming of microscopic organisms”, Proc. R. Soc. Lond. A 209(1099) (1951) 447–461; doi:10.1098/rspa.1951.0218.Google Scholar
Tuck, E. O., “Some methods for flows past blunt slender bodies”, J. Fluid Mech. 18 (1964) 619–635; doi:10.1017/S0022112064000453.Google Scholar
Vilfan, A., “Generic flow profiles induced by a beating cilium”, Eur. Phys. J. E 35 (2012) 1–11; doi:10.1140/epje/i2012-12072-3.Google Scholar
Zöttl, A. and Stark, H., “Nonlinear dynamics of a microswimmer in Poiseuille flow”, Phys. Rev. Lett. 108(21) (2012) 218104; doi:10.1103/PhysRevLett.108.218104.Google Scholar