Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-19T16:49:59.490Z Has data issue: false hasContentIssue false
  • English
  • Français

Interfaces: in fluid mechanics and across disciplines

Published online by Cambridge University Press:  22 February 2010

HOWARD A. STONE
HOWARD A. STONE*
Affiliation:
School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
*
†Present address: Department of Mechanical & Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA. Email address for correspondence: [email protected]
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.

The dynamics of fluid–fluid interfaces are important in diverse problems that span many disciplines in science and engineering. A series of snapshots is used to illustrate the breadth of applications that can occur in viscous low-Reynolds-number flows and I highlight theoretical and modelling ideas that are broadly useful for these, as well as other, problems. By way of illustration of unifying quantitative ideas we discuss briefly (i) the use of the Reciprocal Theorem in low-Reynolds-number flows, (ii) the use of the lubrication approximation for characterizing thin-film coating flows sometimes referred to as Landau–Levich–Derjaguin–Bretherton problems and (iii) nearly two-dimensional viscously dominated flows.

Type
Batchelor Prize Lecture
Information
Journal of Fluid Mechanics , Volume 645 , 25 February 2010 , pp. 1 - 25
Copyright
Copyright © Cambridge University Press 2010

References

REFERENCES

Abkarian, M., Faivre, M. & Stone, H. A. 2006 High-speed microfluidic differential manometer for cellular-scale hydrodynamics. Proc. Natl Acad. Sci. USA 103, 538–542.CrossRefGoogle ScholarPubMed
Abkarian, M., Nunes, J. & Stone, H. A. 2004 Colloidal crystallization and banding in a cylindrical geometry. J. Am. Chem. Soc. 126, 5978–5979.CrossRefGoogle Scholar
Acrivos, A., Jeffrey, D. J. & Saville, D. A. 1990 Particle migration in suspensions by thermocapillary or electrophoretic motion. J. Fluid Mech. 212, 95–110.CrossRefGoogle Scholar
Ajdari, A. & Bocquet, L. 2006 Giant amplification of interfacially driven transport by hydrodynamic slip: diffusio-osmosis and beyond. Phys. Rev. Lett. 96, 186102.CrossRefGoogle ScholarPubMed
Anna, S. L., Bontoux, N. & Stone, H. A. 2003 Formation of dispersions using “flow focusing" in microchannels. Appl. Phys. Lett. 82, 364–366.CrossRefGoogle Scholar
Ashmore, J., Hosoi, A. E. & Stone, H. A. 2003 The effect of surface tension on rimming flows in a partially filled rotating cylinder. J. Fluid Mech. 479, 65–98.CrossRefGoogle Scholar
Aussillous, P. & Quéré, D. 2000 Quick deposition of a fluid on the wall of a tube. Phys. Fluids 12, 2367–2371.CrossRefGoogle Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Mechanics. Cambridge University Press.Google Scholar
Batchelor, G. K. 1977 Developments in microhydrodynamics. In Theoretical and Applied Mechanics: Proceedings of the 14th International Congress, pp. 33–55. North-Holland.Google Scholar
Berg, H. & Turner, L. 1990 Chemotaxis of bacteria in glass capillary arrays – Escherichia coli, motility, microchannel plate, and light scattering. Biophys. J. 58, 919–930.CrossRefGoogle ScholarPubMed
Biesheuvel, A. & van Heijst, G. J. F. (Ed.) 1998 In Fascination of Fluid Dynamics. Springer.CrossRefGoogle Scholar
Bretherton, F. P. 1961 The motion of long bubbles in tubes. J. Fluid Mech. 10, 166–188.CrossRefGoogle Scholar
Cheung, C., Hwang, Y. H., Choi, H. J. & Wu, X.-L. 1996 Diffusion of particles in free-standing liquid films. Phys. Rev. Lett. 76, 2531–2534.CrossRefGoogle ScholarPubMed
Clément, E., Vanel, L., Rajchenbach, J. & Duran, J. 1996 Pattern formation in a vibrated granular layer. Phys. Rev. E 53, 2972–2975.CrossRefGoogle Scholar
Courbin, L., Denieul, E., Dressaire, E., Roper, M., Ajdari, A. & Stone, H. A. 2007 Imbibition by polygonal spreading on patterned surfaces. Nat. Mater. 6, 661–664.CrossRefGoogle Scholar
Courbin, L. & Stone, H. A. 2006 Impact, puncturing and the self-healing of soap films. Phys. Fluids 18, 091105.CrossRefGoogle Scholar
Crighton, D. G. 1981 Acoustics as a branch of fluid mechanics. J. Fluid Mech. 106, 261–298.CrossRefGoogle Scholar
Deegan, R. D., Bakajin, O., Dupont, T. F., Huber, G., Nagel, S. R. & Witten, T. A. 1997 Capillary flow as the cause of ring stains from dried liquid drops. Nature 389, 827–829.CrossRefGoogle Scholar
DeMenech, M. Menech, M., Garstecki, P., Jousse, F. & Stone, H. A. 2007 Transition from squeezing to dripping in a microfluidic T-shaped junction. J. Fluid Mech. 595, 141–162.Google Scholar
Derjaguin, B. 1943 Thickness of liquid layer adhering to walls of vessels on their emptying and the theory of photo- and motion-picture film coating. C. R. (Dokl.) Acade. Sci. URSS 39, 13–16.Google Scholar
Durand, M. & Stone, H. A. 2006 Relaxation time of the topological T1 process in a two-dimensional foam. Phys. Rev. Lett. 97, 226101-1-4.CrossRefGoogle Scholar
van Dyke, M. 1982 Album of Fluid Motion. Parabolic Press.CrossRefGoogle Scholar
Edwards, D. A., Brenner, H. & Wasan, D. T. 1991 Interfacial Transport Processes and Rheology. Butterworth-Heinemann.Google Scholar
Eggers, J. & Stone, H. A. 2004 Characteristic lengths at a moving contact line for a perfectly wetting fluid: the influence of speed on the dynamic contact angle. J. Fluid Mech. 505, 309–321.CrossRefGoogle Scholar
Faivre, M., Abkarian, M., Bikraj, K. & Stone, H. A. 2006 Geometrical focusing of cells in a microfluidic device: a route to separate blood plasma. Biorheology 43, 147–159.Google Scholar
Fanton, X., Cazabat, A. M. & Quéré, D. 1996 Thickness and shape of films driven by a Marangoni flow. Langmuir 12, 5875–5880.CrossRefGoogle Scholar
Fuerstman, M. J., Lai, A., Thurlow, M. E., Shevkoplyas, S. S., Stone, H. A. & Whitesides, G. M. 2007 The pressure drop along rectangular microchannels containing bubbles. Lab on a Chip 7, 1479–1489.CrossRefGoogle ScholarPubMed
Garstecki, P., Fuerstman, M. J., Stone, H. A. & Whitesides, G. M. 2006 Formation of droplets and bubbles in a microfluidic T-junction – scaling and mechanism of breakup. Lab on a Chip 6, 437–446.CrossRefGoogle Scholar
de Gennes, P. G. 1985 Wetting: statics and dynamics. Rev. Mod. Phys. 57, 857–863.CrossRefGoogle Scholar
deGennes, P. G. Gennes, P. G., Brochard-Wyart, F. & Quéré, D. 2003 Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves. Springer.Google Scholar
Gilet, T. & Bush, J. W. M. 2009 The fluid trampoline: droplets bouncing on a soap film. Chaotic bouncing of a droplet on a soap film. J. Fluid Mech. 625 167–203.CrossRefGoogle Scholar
Happel, J. & Brenner, H. 1983 Low Reynolds Number Hydrodynamics. Martinus Nijhoff.CrossRefGoogle Scholar
Hinch, E. J. 1972 Note on the symmetries of certain material tensors for a particle in Stokes flow. J. Fluid Mech. 54, 423–425.CrossRefGoogle Scholar
Hosoi, A. E. & Bush, J. W. M. 2001 Evaporative instabilities in climbing films. J. Fluid Mech. 442, 217–239.CrossRefGoogle Scholar
Hunt, J. C. R. 1981 Some connections between fluid mechanics and the solving of industrial and environmental fluid-flow problems. J. Fluid Mech. 106, 103–130. 76, 2376–2378.CrossRefGoogle Scholar
Jacobsen, K., Sheets, E. D. & Simson, R. 1995 Revisiting the fluid mosaic model of membranes. Science 268, 1441–1442.CrossRefGoogle Scholar
Kataoka, D. E. & Troian, S. M. 1999 Patterning liquid flow on the microscopic scale. Nature 402, 794–797.CrossRefGoogle Scholar
Koch, D. L. & Ladd, A. J. 1997 Moderate Reynolds number flows through periodic and random arrays of aligned cylinders. J. Fluid Mech. 349, 31–66.CrossRefGoogle Scholar
Koehler, S. A., Hilgenfeldt, S. & Stone, H. A. 1999 Liquid flow through aqueous foams: the node-dominated foam drainage equation. Phys. Rev. Lett. 82, 4232–4235.CrossRefGoogle Scholar
Koehler, S. A., Hilgenfeldt, S. & Stone, H. A. 2004 Foam drainage on the microscale. Part 1. Modelling flow through single Plateau borders. J. Colloid Interface Sci. 276, 420–438.CrossRefGoogle Scholar
Koehler, S. A., Hilgenfeldt, S., Weeks, E. R. & Stone, H. A. 2004 Foam drainage on the microscale. Part 2. Experiments on the scale of single Plateau borders. J. Colloid Interface Sci. 276, 439–449.CrossRefGoogle Scholar
Kuiken, H. K. (Ed.) 1996 The Centenary of a Paper on Slow Viscous Flow by the Physicist H.A. Lorentz. Kluwer Academic.CrossRefGoogle Scholar
Landau, L. & Levich, B. 1942 Dragging of liquid by a plate. Acta Physiochim. USSR 17, 42–54.Google Scholar
Lauga, E., Brenner, M. P. & Stone, H. A. 2007 Microfluidics: the no-slip boundary condition. In Handbook of Experimental Fluid Mechanics (ed. Tropea, C., Yarin, A. & Foss, J. F.), pp. 1219–1240. Springer.Google Scholar
Lauga, E., DiLuzio, W., Whitesides, G. M. & Stone, H. A. 2005 Swimming in circles: Motion of bacteria near solid boundaries. Biophys. J. 90 400–412.CrossRefGoogle ScholarPubMed
Leal, L. G. 1980 Particle motion in a viscous fluid. Annu. Rev. Fluid Mech. 12, 435–476.CrossRefGoogle Scholar
Leal, L. G. 2007 Advanced Transport Phenomena: Laminar Flow and Convective Transport Processes. Cambridge University Press.CrossRefGoogle Scholar
Le Goff, A., Courbin, L., Stone, H. A. & Quéré, D. 2008 Energy absorption in a bamboo foam. Europhys. Lett. 84, 36001-p1-p5.CrossRefGoogle Scholar
Leonard, R. A. & Lemlich, R. 1965 A study of interstial liquid flow in foam. Part I. Theoretical model and application to foam fractionation. AIChE J. 11, 18–24.CrossRefGoogle Scholar
Levich, V. 1962 Physicochemical Hydrodynamics. Prentice Hall.Google Scholar
Lighthill, J. 1975 Mathematical Biofluiddynamics. SIAM.CrossRefGoogle Scholar
Lorentz, H. A. 1896 A general theorem concerning the motion of a viscous fluid and few consequences derived from it. Akad. Wet. Amsterdam 5, 168–175.Google Scholar
Manga, M. & Stone, H. A. 1993 Buoyancy-driven interactions between two deformable viscous drops. J. Fluid Mech. 256, 647–683.CrossRefGoogle Scholar
Mazouchi, A. & Homsy, G. M. 2000 Thermocapillary migration of long bubbles in cylindrical capillary tubes. Phys. Fluids 12, 542–549.CrossRefGoogle Scholar
Mysels, K. J., Shinoda, K. & Frankel, S. 1959 Soap Films. Pergamon Press.Google Scholar
Oron, A., Davis, S. H. & Bankoff, S. G. 1997 Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69, 931–980.CrossRefGoogle Scholar
Pearson, J. R. A. 1981 Wider horizons for fluid mechanics. J. Fluid Mech. 106, 229–244.CrossRefGoogle Scholar
Peregrine, D. H. 1981 The fascination of fluid mechanics. J. Fluid Mech. 106, 59–80.CrossRefGoogle Scholar
Pomeau, Y. & Villermaux, E. 2006 Two hundred years of capillarity research. Phys. Today 39–44.CrossRefGoogle Scholar
Pozrikidis, C. 1992 Boundary Integral and Singularity Methods for Linearized Viscous Flow. Cambridge University Press.CrossRefGoogle Scholar
Probstein, R. F. 1994 Physicochemical Hydrodynamics. John Wiley & Sons.CrossRefGoogle Scholar
Quéré, D. 1999 Fluid coating on a fibre. Annu. Rev. Fluid Mech. 31, 347–384.CrossRefGoogle Scholar
Ramachandran, A. & Khair, A. S. 2009 The dynamics and rheology of a dilute suspension of hydrodynamically Janus spheres in a linear flow. J. Fluid Mech. 633, 233–269.CrossRefGoogle Scholar
Ratulowski, J. & Chang, H. C. 1990 Marangoni effects of trace impurities on the motion of long gas bubbles in capillaries. J. Fluid Mech. 210, 303–328.CrossRefGoogle Scholar
Saffman, P. G. 1976 Brownian motion in thin sheets of viscous fluid. J. Fluid Mech. 73, 593–602.CrossRefGoogle Scholar
Saffman, P. G. & Delbrück, M. 1975 Brownian motion in biological membranes. Proc. Natl Acad. Sci. 72, 3111–3113.CrossRefGoogle ScholarPubMed
Samimy, M., Breuer, K. S., Leal, L. G. & Steen, P. H. (Ed.) 2004 A Gallery of Fluid Motion. Cambridge University Press.CrossRefGoogle Scholar
Sangani, A. & Acrivos, A. 1982 Slow flow past periodic arrays of cylinders with applications to heat transfer. Intl J. Multiph. Flow 8, 193–206.CrossRefGoogle Scholar
Schleier-Smith, J. M. & Stone, H. A. 2001 Convection, heaping, and cracking in vertically vibrated granular slurries. Phys. Rev. Lett. 86, 3016–3019.CrossRefGoogle ScholarPubMed
Scriven, L. E. 1960 Dynamics of a fluid interface: equation of motion for Newtonian surface fluids. Chem. Engng Sci. 12, 98–108.CrossRefGoogle Scholar
Scriven, L. E. & Sternling, C. V. 1960 The Marangoni effects. Nature 187, 186–188.CrossRefGoogle Scholar
Sickert, M., Rondelez, F. & Stone, H. A. 2007 Single-particle Brownian dynamics for characterizing the rheology of fluid Langmuir monolayers. Europhys. Lett. 79, 66005-1–6.CrossRefGoogle Scholar
Singer, S. J. & Nicholson, G. L. 1972 The fluid mosaic model of the structure of cell membranes. Science 175, 720–731.CrossRefGoogle ScholarPubMed
Snoeijer, J. H., Ziegler, J., Andreotti, B., Fermigier, M. & Eggers, J. 2008 Thick films of viscous fluid coating a plate withdrawn from a liquid reservoir. Phys. Rev. Lett. 100, 244502.CrossRefGoogle ScholarPubMed
Squires, T. M. 2008 Electrokinetic flows over inhomogeneously slipping surfaces. Phys. Fluids 20, 092105.CrossRefGoogle Scholar
Stone, H. A. & Ajdari, A. 1998 Hydrodynamics of particles embedded in a flat surfactant layer overlying a subphase of finite depth. J. Fluid Mech. 369, 151–173.CrossRefGoogle Scholar
Tharmalingam, S. & Wilkinson, W. L. 1978 The coating of Newtonian liquids onto a roll rotating at low speeds. Polym. Engng Sci. 18, 1155–1159.CrossRefGoogle Scholar
Tirumkudulu, M. & Acrivos, A. 2001 Coating flows with a rotating horizontal cylinder: lubrication analysis, numerical computations and experimental measurements. Phys. Fluids 13, 14–19.CrossRefGoogle Scholar
Umbanhowar, P. B., Melo, F. & Swinney, H. L. 1996 Localized excitations in a vertically vibrated granular layer. Nature 382, 793–796.CrossRefGoogle Scholar
Wan, J., Ristenpart, W. D. & Stone, H. A. 2008 Dynamics of shear-induced ATP release from red blood cells. Proc. Natl Acad. Sci. 105, 16432–16437.CrossRefGoogle ScholarPubMed
Weaire, D. & Hutzler, S. 1999 The Physics of Foams. Oxford University Press.Google Scholar
Wilson, S. D. R. 1981 The drag-out problem in film coating theory. J. Engng Math. 16, 209–221.CrossRefGoogle Scholar
Wong, H., Radke, C. J. & Morris, S. 1995 a The motion of long bubbles in polygonal capillaries. Part 1. Thin films. J. Fluid Mech. 292, 71–94.CrossRefGoogle Scholar
Wong, H., Radke, C. J. & Morris, S. 1995 b The motion of long bubbles in polygonal capillaries. Part 2. Drag, fluid pressure and fluid flow. J. Fluid Mech. 292, 95–110.CrossRefGoogle Scholar
Young, N. O., Block, J. S. & Goldstein, M. J. 1959 The motion of bubbles in a vertical temperature gradient. J. Fluid Mech. 6, 350–356.CrossRefGoogle Scholar
Youngren, G. K. & Acrivos, A. 1975 Stokes flow past a particle of arbitrary shape: a numerical method of solution. J. Fluid Mech. 69, 377–403.CrossRefGoogle Scholar