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A perspective of Batchelor's research in micro-hydrodynamics

Published online by Cambridge University Press:  04 November 2010

JOHN HINCH
JOHN HINCH*
Affiliation:
DAMTP-CMS, Cambridge University, Wilberforce Road, Cambridge CB3 0WA, UK
*
†Email address for correspondence: E.J.Hinch@damtp.cam.ac.uk
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Abstract

Batchelor made his name with research in turbulence in the 1940s and 1950s. He became disillusioned with turbulence at the Marseille meeting in 1961. At the end of the 1960s, he started his second wave of research on low-Reynolds-number suspensions of particles. Ten years after he died, I will describe his key results, what was before and what followed. Eight of his 10 most cited papers are in micro-hydrodynamics.

JFM classification

Micro-/Nano-fluid dynamics: Micro-/Nano-fluid dynamics
Type
Batchelor and Crighton Commemorative Talks
Information
Journal of Fluid Mechanics , Volume 663 , 25 November 2010 , pp. 8 - 17
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.Google Scholar
Batchelor, G. K. 1970 a Stress system in a suspension of force-free particles. J. Fluid Mech. 41, 545–570.CrossRefGoogle Scholar
Batchelor, G. K. 1970 b Slender-body theory for particles of arbitrary cross-section in Stokes flow. J. Fluid Mech. 44, 419–440.CrossRefGoogle Scholar
Batchelor, G. K. 1971 Stress generated in a non-dilute suspension of elongated particles by pure straining motion. J. Fluid Mech. 46, 813–829.CrossRefGoogle Scholar
Batchelor, G. K. 1972 Sedimentation in a dilute suspension of spheres. J. Fluid Mech. 52, 245–268.CrossRefGoogle Scholar
Batchelor, G. K. & Green, J. T. 1972 a The hydrodynamic interaction of two small freely-moving spheres in a linear flow. J. Fluid Mech. 56, 375–400.CrossRefGoogle Scholar
Batchelor, G. K. & Green, J. T. 1972 b The determination of the bulk stress in a suspension of spherical particles to order c2. J. Fluid Mech. 56, 401–427.CrossRefGoogle Scholar
Batchelor, G. K. 1977 The effect of Brownian motion on the bulk stress in a suspension of spherical particles. J. Fluid Mech. 83, 97–117.CrossRefGoogle Scholar
Batchelor, G. K. 1982 Sedimentation in a dilute polydisperse system of interacting spheres. Part 1. General theory. J. Fluid Mech. 119, 379–408.CrossRefGoogle Scholar
Batchelor, G. K. & Wen, C.-S. 1982 Sedimentation in a dilute polydisperse system of interacting spheres. Part 2. Numerical results. J. Fluid Mech. 124, 495–528, with Corrigendum 137, 467–469.CrossRefGoogle Scholar
Batchelor, G. K. 1983 Diffusion in a dilute polydisperse system of interacting spheres. J. Fluid Mech. 131, 155–175.CrossRefGoogle Scholar
Batchelor, G. K. & van Rensburg, R. W. J. 1986 Structure formation in bidisperse sedimentation. J. Fluid Mech. 166, 379–407.CrossRefGoogle Scholar
Brady, J. F. & Bossis, G. 1988 Stokesian dynamics. Annu. Rev. Fluid Mech. 20, 111–157.CrossRefGoogle Scholar
Davis, R. H. & Acrivos, A. 1985 Sedimentation of non-colloidal particles at low Reynolds numbers. Annu. Rev. Fluid Mech. 17, 91–118.CrossRefGoogle Scholar
Frankel, N. A. & Acrivos, A. 1970 Constitutive equation for a dilute emulsion. J. Fluid Mech. 44, 65–78.CrossRefGoogle Scholar
Guazzelli, E. & Hinch, E. J. 2011 Fluctuations and instability in sedimentation. Annu. Rev. Fluid Mech. 43.CrossRefGoogle Scholar
Hinch, E. J. & Leal, L. G. 1972 The effect of Brownian motion on the rheological properties of a suspension of non-spherical particles. J. Fluid Mech. 52, 683–712.CrossRefGoogle Scholar
Hinch, E. J. 1977 An averaged-equation approach to particle interactions in a fluid suspension. J. Fluid Mech. 83, 695–720.CrossRefGoogle Scholar
Koch, D. L. & Shaqfeh, E. S. G. 1989 The instability of a dispersion of sedimenting spheroids. J. Fluid Mech. 209, 521–542.CrossRefGoogle Scholar
Ladd, A. J. C. 1996 Hydrodynamic screening in sedimenting suspensions of non-Brownian spheres. Phys. Rev. Lett. 76, 1392–1395.CrossRefGoogle ScholarPubMed
Landau, L. D. & Lifshitz, E. M. 1959 Course of Theoretical Physics, vol. 6, J. Fluid Mech. p. 74, Pergamon Press.Google Scholar
Loewenberg, M. & Hinch, E. J. 1996 Numerical simulations of concentrated emulsions. J. Fluid Mech. 321, 395–419.CrossRefGoogle Scholar
Metzger, B., Nicolas, M. & Guazzelli, E. 2007 Falling clouds of particles in viscous fluids. J. Fluid Mech. 580, 283–301.CrossRefGoogle Scholar
Moffatt, H. K. 2002 G. K. Batchelor and the homogenization of turbulence. Annu. Rev. Fluid Mech. 34, 19–35.CrossRefGoogle Scholar
Mongruel, A. & Cloître, M. 2003 Axisymmetric orifice flow for measuring the elongational viscosity of semi-rigid polymer solutions. J. Non-Newton. Fluid Mech. 110, 27–43.CrossRefGoogle Scholar
Nitsche, J. M. & Batchelor, G. K. 1997 Break-up of a drop containing dispersed particles. J. Fluid Mech. 340, 161–175.CrossRefGoogle Scholar
Rallison, J. M. 1984 The deformation of small viscous drops and bubbles in shear flows. Annu. Rev. Fluid Mech. 16, 45–66.CrossRefGoogle Scholar
Russel, W. B. 1978 Rheology of suspensions of charged rigid spheres. J. Fluid Mech. 85, 209–232.CrossRefGoogle Scholar
Russel, W. B., Saville, D. A. & Schowalter, W. R. 1989 Colloidal Dispersions. Cambridge University Press.CrossRefGoogle Scholar
Shaqfeh, E. S. G. 1988 A non-local theory for the heat-transport in composites containing highly conducting fibrous inclusions. Phys. Fluids 31, 2405–2425.CrossRefGoogle Scholar
Shaqfeh, E. S. G. & Fredrickson, G. H. 1990 Hydrodynamic stress in a suspension of rods. Phys. Fluids A2, 7–24.CrossRefGoogle Scholar
Smart, J. R. & Leighton, D. T. 1989 Measurement of the hydrodynamic surface-roughness of non-colloidal spheres. Phys. Fluids A1, 52–60.CrossRefGoogle Scholar