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Short-time self-diffusion of nearly hard spheres at an oil–water interface

Published online by Cambridge University Press:  10 January 2009

Y. PENG ,
W. CHEN ,
TH. M. FISCHER ,
D. A. WEITZ  and
P. TONG
Y. PENG
Affiliation:
Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
W. CHEN
Affiliation:
Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
TH. M. FISCHER
Affiliation:
Institute of Experimental Physics V, University of Bayreuth, 95440 Bayreuth, Germany
D. A. WEITZ
Affiliation:
Department of Physics and School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
P. TONG*
Affiliation:
Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
*
†Email address for correspondence: [email protected]
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Abstract

Optical microscopy and multi-particle tracking are used to study hydrodynamic interactions of monodisperse polymethylmethacrylate (PMMA) spheres at a decalin–water interface. The short-time self-diffusion coefficient measured at low surface coverage has the form DSS(n) = αD0(1 − βn), where n is the area fraction occupied by the particles, and D0 is the Stokes–Einstein diffusion coefficient in the bulk suspension of PMMA spheres in decalin. The measured values of α are found to be in good agreement with the numerical calculation for the drag coefficient of interfacial particles. The measured values of β differ from that obtained for bulk suspensions, indicating that hydrodynamic interactions between the particles have interesting new features at the interface.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 618 , 10 January 2009 , pp. 243 - 261
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Antl, L., Goodwin, J. W., HIill, R. D., Ottewil, R. H., Owens, S. M. & Papworth, S. 1986 The preparation of polymethyl methacrylate latices in non-aqueous media. Colloids Surf. 17, 67.CrossRefGoogle Scholar
Auer, S., Poon, W. C. K. & Frenkel, D. 2003 Phase behaviour and crystallization kinetics of poly-12-hydroxystearic-coated polymethylmethacrylate colloids. Phys. Rev. E 67 (1–4), 020401.Google ScholarPubMed
Bausch, A. R., Bowick, M. J., Cacciuto, A., Dinsmore, A. D., Hsu, M. F. & Nelson, D. R., Nikolaides, M. G., Travesset, A. & Weitz, D. A. 2002 Grain boundary scars and spherical crystallography. Science 299, 1716–1718.CrossRefGoogle Scholar
Behrens, S. H. & Grier, D. G. 2001 Pair interaction of charged colloidal spheres near a charged wall. Phys. Rev. E 64 (1–4), 050401.Google Scholar
Bel Fdhila, R. & Duineveld, P. C. 1996 The effect of surfactant on the rise of a spherical bubble at high Reynolds and Péclet numbers. Phys. Fluids 8, 310–321.CrossRefGoogle Scholar
Berne, B. J. & Pecora, R. 1976 Dynamic Light Scattering. Wiley.Google Scholar
Binks, B. P. 1998 Modern Aspects of Emulsion Science. Royal Society of Chemistry.CrossRefGoogle Scholar
Chae, D.-G., Ree, F. H. & Ree, T. 1969 Radial distribution functions and equation of state of the hard-disk fluid. J. Chem. Phys. 50, 1581–1589.CrossRefGoogle Scholar
Chen, W., Tan, S.-S., Ng, T.-K., Ford, W. T. & Tong, P. 2005 Long-ranged attraction between charged polystyrene spheres at aqueous interfaces. Phys. Rev. Lett. 95 (1–4), 218301.CrossRefGoogle ScholarPubMed
Chen, W., Tan, S.-S., Ng, T.-K., Ford, W. T. & Tong, P. 2006 Measured long-ranged attractive interaction between charged polystyrene latex spheres at a water–air interface. Phys. Rev. E 74 (1–14), 021406.Google Scholar
Chen, W. & Tong, P. 2008 Short-time self-diffusion of weakly charged silica spheres at aqueous interfaces. Euro. Phys. Lett. 84, 28003.CrossRefGoogle Scholar
Dahan, M., Levi, S., Luccardini, P., Rostaing, C., Riveau, B. & Triller, A. 2003 Diffusion dynamics of Glycine receptors revealed by single-quantum dot tracking. Science 302, 442–443.CrossRefGoogle ScholarPubMed
Danov, K., Aust, R., Durst, F. & Lange, U. 1995 Influence of the surface viscosity on the hydrodynamic resistance and surface diffusivity of a large Brownian particle. J. Colloid Interface Sci. 175, 36–45.CrossRefGoogle Scholar
Dimova, R., Danov, K., Pouligny, B. & Ivanov, I. B. 2000 Drag of a solid particle trapped in a thin film or at an interface: influence of surface viscosity and elasticity. J. Colloid Interface Sci. 226, 35–43.CrossRefGoogle Scholar
Dinsmore, A. D., Hsu, M. F., Nikolaides, M. G., Marquez, M., Bausch, A. R. & Weitz, D. A. 2002 Colloidosomes: selectively permeable capsules composed of colloidal particles. Science 298, 1006–1009.CrossRefGoogle ScholarPubMed
Fernández-Toledano, J. C., Moncho-Jordá, A., Martinez-López, F. & Hidalgo-Álvarez, R. 2004 Spontaneous formation of mesostructures in colloidal monolayers trapped at the air–water interface: a simple explanation. Langmuir 20, 6977–6980.CrossRefGoogle ScholarPubMed
Fischer, T. M. 2004 Comment on ‘shear viscosity of Langmuir monolayers in the low-density limit’. Phys. Rev. Lett. 92, 139603.CrossRefGoogle ScholarPubMed
Fischer, T. M., Dhar, P. & Heinig, P. 2006 The viscous drag of spheres and filaments moving in membranes or monolayers. J. Fluid Mech. 558, 451–475.CrossRefGoogle Scholar
Helmer, M. 2005 Surfaces and interfaces. Nature 437, 637–637.CrossRefGoogle Scholar
Hurd, A. J. & Shaefer, D. W. 1985 Diffusion-limited aggregation in two dimensions. Phys. Rev. Lett. 54, 1043–1046.CrossRefGoogle ScholarPubMed
Kollmann, M., Hund, R., Rinn, B., Nägele, G., Zahn, K., König, H., Maret, G., Klein, R., & Dhont, J. K. G. 2002 Structure and tracer-diffusion in quasi-two-dimensional and strongly asymmetric magnetic colloidal mixtures. Europhys. Lett. 58, 919–925.CrossRefGoogle Scholar
Leunissen, M. E., Van Blaaderen, A., Hollingsworth, A. D., Sullivan, M. T. & Chaikin, P. M. 2007 Electrostatics at the oil–water interface, stability, and order in emulsions and colloids. PNAS 104, 2585–2590.CrossRefGoogle ScholarPubMed
Levich, V. G. 1962 Physicochemical Hydrodynamics. Prentice Hall.Google Scholar
Lipowsky, P., Bowick, M. J., Meinke, J. H., Nelson, D. R. & Bausch, A. R. 2005 Direct visualization of dislocation dynamics in grain-boundary scars. Nat. Mater. 4, 407–411.CrossRefGoogle ScholarPubMed
Nikolaides, M. G., Bausch, A. R., Hsu, M. F., Dinsmore, A. D., Brenner, M. P., Gay, C. & Weitz, D. A. 2002 Electric-field-induced capillary attraction between like-charged particles at liquid interfaces. Nature 420, 299–301.CrossRefGoogle ScholarPubMed
Onada, G. Y. 1985 Direct observation of two-dimensional, dynamic clustering and ordering with colloids. Phys. Rev. Lett. 55, 226–229.CrossRefGoogle Scholar
Pieranski, P. 1980 Two-dimensional interfacial colloidal crystals. Phys. Rev. Lett. 45, 569–572.CrossRefGoogle Scholar
Prasad, V., Koehler, S. A. & Weeks, E. R. 2006 Two-particle microrheology of quasi-two-dimensional viscous systems. Phys. Rev. Lett. 97 (1–4), 176001.CrossRefGoogle Scholar
Pusey, P. N. 1991 In Liquids, Freezing and Glass Transition (ed. Hansen, J.-P., Levesque, D. & Zinn-Justin, J.), chapter 10. North-Holland.Google Scholar
Qiu, X., Wu, X. L., Xue, J. Z., Pine, D. J., Weitz, D. A. & Chaikin, P. M. 1990 Hydrodynamic interactions in concentrated suspensions. Phys. Rev. Lett. 65, 516–519.CrossRefGoogle ScholarPubMed
Radoev, B., Nedjalkov, M. & Djakovich, V. 1992 Brownian motion at liquid–gas interfaces. Part 1. Diffusion coefficients of macroparticles at pure interfaces. Langmuir 8, 2962–2965.CrossRefGoogle Scholar
Rinn, B., Zahn, K., Maass, P. & Maret, G. 1999 Influence of hydrodynamic interactions on the dynamics of long-range interacting colloidal particles. Europhys. Lett. 46, 537–541.CrossRefGoogle Scholar
Royall, C. P., Leunissen, M. E. & Van Blaaderen, A. 2003 A new colloidal model system to study long-range interactions quantitatively in real space. J. Phys.: Condens. Matter 15, S3581–S3596.Google Scholar
Russel, W. B., Saville, D. A. & Schowalter, W. R. 1989 Colloidal Dispersion. Cambridge University Press.CrossRefGoogle Scholar
Sackmann, E. 1996 Supported membranes: scientific and practical applications. Science 271, 43–48.CrossRefGoogle ScholarPubMed
Saffman, P. G. 1976 Brownian motion in thin sheets of viscous fluid. J. Fluid Mech. 73, 593–603.CrossRefGoogle Scholar
Saffman, P. G. & Delbrück, M. 1975 Brownian motion in biological membranes. PNAS 72, 3111–3113.CrossRefGoogle ScholarPubMed
Schofield, A. 2007 Personal website. http://www.ph.ed.ac.uk/~abs/.Google Scholar
Schofield, A. 2008 Private communication.Google Scholar
Segre, P. N., Behrend, O. P. & Pusey, P. N. 1995 Short-time Brownian motion in colloidal suspensions: experiment and simulation. Phys. Rev. E 52, 5070–5083.Google ScholarPubMed
Sickert, M. & Rondelez, F. 2003 Shear viscosity of Langmuir monolayers in the low-density limit. Phys. Rev. Lett. 90 (1–4), 126104.CrossRefGoogle ScholarPubMed
Sickert, M. & Rondelez, F. 2004 Reply. Phys. Rev. Lett. 92 (1), 139604.CrossRefGoogle Scholar
Sickert, M., Rondelez, F. & Stone, H. A. 2007 Single-particle Brownian dynamics for characterizing the rheology of fluid Langmuir monolayers. Euro. Phys. Lett 79 (1–6), 66005.CrossRefGoogle Scholar
Stone, H. & 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
Tolnai, G., Agod, A., Kabai-Faix, M., Kovacs, A. L., Ramsden, J. J. & Horvolgyi, Z. 2003 Evidence for secondary minimum flocculation of Stöber silica nanoparticles at the air–water interface: film balance investigations and computer simulations. J. Phys. Chem. B 107, 11109–11116.CrossRefGoogle Scholar
Tong, P., Ye, X., Ackerson, B. J. & Fetters, L. J. 1997 Sedimentation of colloidal particles through a polymer solution. Phys. Rev. Lett. 79, 2363–2367.CrossRefGoogle Scholar
Van Blaaderen, A., Peetermans, J., Maret, G., & Dhont, J. K. G. 1992 Long-time self-diffusion of spherical colloidal particles measured with fluorescence recovery after photo-bleaching. J. Chem. Phys. 96, 4591–4603.CrossRefGoogle Scholar
Van Megan, W., Underwood, S. M., Ottewill, R. H., Williams, N.St., J. & Pusey, P. N. 1987 Particle diffusion in concentrated dispersions. Faraday Discuss. Chem. Soc. 83, 47–57.Google Scholar
Wu, M.-M. & Gharib, M. 2002 Experimental studies on the shape and path of small air bubbles rising in clean water. Phys. Fluids 14, L49–L52.CrossRefGoogle Scholar
Ye, X., Tong, P. & Fetters, L. J. 1998 Transport of probe particles in semidilute polymer solutions. Macromolecules 31, 5785–5793.CrossRefGoogle Scholar
Yethiraj, A. & Van Blaaderen, A. 2003 A colloidal model system with an interaction tunable from hard sphere to soft and dipolar. Nature 421, 513–517.CrossRefGoogle ScholarPubMed
Zahn, K., Mendez-Alcaraz, J. M. & Maret, G. 1997 Hydrodynamic interactions may enhance the self-diffusion of colloidal particles. Phys. Rev. Lett. 79, 175–178.CrossRefGoogle Scholar