Hostname: page-component-5447f9dfdb-9hml6 Total loading time: 0 Render date: 2025-07-30T06:42:51.901Z Has data issue: false hasContentIssue false
  • English
  • Français

Lateral capillary interaction between particles protruding from a spherical liquid layer

Published online by Cambridge University Press:  26 April 2006

P. A. Kralchevsky ,
V. N. Paunov  and
Kuniaki Nagayama
P. A. Kralchevsky
Affiliation:
Laboratory of Thermodynamics and Physico-chemical Hydrodynamics, University of Sofia, Faculty of Chemistry, Sofia 1126, Bulgaria
V. N. Paunov
Affiliation:
Laboratory of Thermodynamics and Physico-chemical Hydrodynamics, University of Sofia, Faculty of Chemistry, Sofia 1126, Bulgaria
Kuniaki Nagayama
Affiliation:
Protein Array Project, ERATO, JRDC; 5-9-1 Tokodai, Tsukuba 300-26, Japan
Get access Rights & Permissions [Opens in a new window]

Abstract

The lateral capillary interaction between two particles immersed in a spherical thin liquid film is investigated. The interfacial shape, the lateral capillary force and the interparticle energy are calculated by using the numerical solution of the linearized Laplace equation of capillarity. Orthogonal bipolar coordinates on a sphere (inducing biconical coordinates in space) are introduced as a helpful instrument for solving this problem and other problems of similar geometry. We consider two types of boundary conditions at the particle surfaces: fixed contact angle and fixed contact line. We established that for particles of fixed contact angle the capillary interaction energy depends monotonically on the interparticle distance whereas for particles of fixed contact line the interaction energy exhibits a maximum. The numerical results show that in both cases the capillary interaction is much larger than the thermal energy kT and can induce aggregation and ordering of submicrometre particles. These theoretical findings can be important for understanding the properties of Pickering emulsions (stabilized by particles) and liposomes or biomembranes containing incorporated membrane proteins.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 299 , 25 September 1995 , pp. 105 - 132
Copyright
© 1995 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.)

Article purchase

Temporarily unavailable

References

Brand, L. 1947 Vector and Tensor Analysis. Wiley.
Bussel, S. J., Koch, D. L. & Hammer, D. A. 1992 The resistivity and mobility functions for a model system of two equal-sized proteins in a lipid bilayer. J Fluid Mech. 243, 679–697.Google Scholar
Camoin, C., Roussel, J. F., Faure, R. & Blanc, R. 1987 Mesure des forces d'attraction entre sphéres partiellment immergées: Influence des interfaces. Europhys. Lett. 3, 449–457.Google Scholar
Chan, D. Y. C., Henry, J. D. & White, L. R. 1981 The interaction of colloidal particles collected at fluid interfaces. J. Colloid Interface Sci. 79, 410–418.Google Scholar
Constantinides, A. 1987 Applied Numerical Methods with Personal Computers. McGraw-Hill.
Denkov, N. D., Velev, O. D., Kralchevsky, P. A., Ivanov, I. B., Yoshimura, H. & Nagayama, K. 1992 Mechanism of formation of two-dimensional crystals from latex particles on substrata. Langmuir 8, 3183–3190.Google Scholar
Denkov, N. D., Velev, O. D., Kralchevsky, P. A., Ivanov, I. B., Yoshimura, H. & Nagayama, K. 1993 Dynamics of two-dimensional crystallization. Nature 361, 26.Google Scholar
Derjaguin, B. V., Churaev, N. V. & Muller, V. M. 1987 Surface Forces. Plenum.
Dukhin, S. S., Ruliov, N. N. & Dimitrov, D. S. 1986 Coagulation and Dynamics of Thin Films. Naukova Dumka, Kiev (in Russian).
Hockney, R. W. & Eastwood, J. W. Computer Simulation Using Particles. McGraw-Hill.
Israelachvili, J. N. 1977 Refinement of the fluid-mosaic model of membrane structures. Biochim. Biophys. Acta 469, 221–225.Google Scholar
Israelachvili, J. N. 1992 Intermolecular and Surface Forces, 2nd edn. Academic.
Ivanov, I. B. & Toshev, B. V. 1975 Thermodynamics of thin liquid films: II Film thickness and its relations to the surface tension and the contact angle. Colloid Polymer Sci. 253, 593–602.Google Scholar
Korn, G. A. & Korn, T. M. 1968 Mathematical Handbook. McGraw-Hill.
Kralchevsky, P. A. & Ivanov, I. B. 1990 Micromechanical description of curved interfaces, thin films and membranes. Film surface tension, disjoining pressure and interfacial stress balances. J. Colloid Interface Sci. 137, 234–252.Google Scholar
Kralchevsky, P. A., Paunov, V. N., Ivanov, I. B. & Nagayama, K. 1992 Capillary meniscus interaction between colloidal particles attached to a liquid-fluid interface. J. Colloid Interface Sci. 151, 79–94.Google Scholar
Kralchevsky, P. A., Paunov, V. N., Denkov, N. D., Ivanov, I. B. & Nagayama, K. 1993 Energetical and force approaches to the capillary interactions between particles attached to a liquid-fluid interface. J. Colloid Interface Sci. 155, 420–437.Google Scholar
Kralchevsky, P. A. & Nagayama, K. 1994 Capillary forces between colloidal particles. Langmuir 10, 23–36.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1984 Fluid Mechanics. Pergamon.
Levine, S. & Bowen, B. D. 1991 Capillary interaction of spherical particles adsorbed on the surface of an oil/water droplet stabilized by the particles. Colloids Surfaces 59, 377–386.Google Scholar
McConnell, A. J. 1957 Application of Tensor Analysis. Dover.
Nagayama, K. 1994 Fabrication of protein crystalline films on mercury. Materials Sci Engng C1, 87–94.Google Scholar
Nicolson, M. M. 1949 The interaction between floating particles. Proc. Comb. Phil. Soc. 45, 288–295.Google Scholar
Paunov, V. N., Kralchevsky, P. A., Denkov, N. D., Ivanov, I. B. & Nagayama, K. 1992 Capillary meniscus interaction between a microparticle and a wall. Colloids Surfaces 67, 119–138.Google Scholar
Paunov, V. N., Kralchevsky, P. A., Denkov, N. D. & Nagayama, K. 1993 Lateral capillary forces between floating submillimeter particles. J. Colloid Interface Sci. 157, 100–112.Google Scholar
Petrov, A. G. & Bivas, I. 1984 Elastic and flexoelastic aspects of out-of-plane fluctuations in biological and model membranes. Prog. Surface Sci. 16, 389–511.Google Scholar
Tadros, Th. F. & Vincent, B. 1983 In Encyclopedia of Emulsion Technology (ed. P. Becher), vol. 1, p. 129. M. Dekker.
Veleve, O. D., Denkov, N. D., Kralchevsky, P. A., Paunov, V. N. & Nagayama, K. 1993 Direct measurements of lateral capillary forces. Langmuir 9, 3702–3709.Google Scholar
Weatherburn, C. E. 1939 Differential Geometry of Three Dimensions. Cambridge University Press.
Yoshimura, H., Matsumoto, M., Endo, S. & Nagayama, K. 1990 Two-dimensional crystalization of proteins on mercury. Ultramicroscopy 32, 265–271.Google Scholar