Advances in Colloid and Interface ScienceŽ.85 2000 145᎐192Capillary interactions between particlesbound to interfaces, liquid films andbiomembranesPeter A. Kralchevskya,b, Kuniaki Nagayamaa,UaLaboratory of Ultrastructure Research, National Institute for Physiological Sciences,Myodaiji-cho, Okazaki 444-8585, JapanbLaboratory of Thermodynamics and Physicochemical Hydrodynamics, Faculty of Chemistry,Uni¨ersity of Sofia, Sofia 1126, BulgariaAbstractŽThis article is devoted to an overview, comparison and discussion of recent results both.theoretical and experimental about lateral capillary forces. They appear when the contactof particles or other bodies with a fluid phase boundary causes perturbations in theinterfacial shape. The capillary interaction is due to the overlap of such perturbations whichcan appear around floating particles, vertical cylinders, particles confined in a liquid film,inclusions in the membranes of lipid vesicles or living cells, etc. In the case of floatingparticles the perturbations are due to the particle weight; in this case the force decreaseswith the sixth power of the particle size and becomes immaterial for particles smaller thanapproximately 10 m. In all other cases the interfacial deformations are due to the particlewetting properties; the resulting ‘immersion’ capillary forces can be operative even betweenvery small particles, like protein globules. In many cases such forces can be responsible forthe experimentally observed two-dimensional particle aggregation and ordering. An analogybetween capillary and electrostatic forces enables one to introduce ‘capillary charges’ of theattached particles, which characterize the magnitude of the interfacial deformation andcould be both positive and negative. Moreover, the capillary interaction between particleand wall resembles the image force in electrostatics. When a particle is moving bound to aninterface under the action of a capillary force, one can determine the surface dragUCorresponding author. Tel: q81-564-55-7811; fax:q 81-564-52-7913.Ž.E-mail address: [email protected] K. Nagayama .0001-8686r00r$ - see front matter 䊚 2000 Elsevier Science B.V. All rights reserved.Ž.PII: S 0 0 0 1 - 8 6 8 6 9 9 00016-0()P.A. Kralche¨sky, K. Nagayama r Ad¨ances in Colloid and Interface Science 85 2000 145᎐192146coefficient and the surface viscosity supposedly the magnitude of the capillary force isŽ.known. Alternative but equivalent energy and force approaches can be used for thetheoretical description of the lateral capillary interactions. Both approaches require theLaplace equation of capillarity to be solved and the meniscus profile around the particles tobe determined. The energy approach accounts for contributions due to the increase of themeniscus area, gravitational energy andror energy of wetting. The second approach is basedon calculating the net force exerted on the particle, which can originate from the hydrostaticpressure, interfacial tension and bending moment. In the case of small perturbations, thesuperposition approximation can be used to derive an asymptotic formula for the capillaryforces, which has been found to agree well with the experiment. Capillary interactionsbetween particles bound to spherical interfaces are also considered taking into account thespecial geometry and restricted area of such phase boundaries. A similar approach can beŽ.applied to quantify the forces between inclusions transmembrane proteins in lipid mem-branes. The deformations in a lipid membrane, due to the inclusions, can be describedtheoretically in the framework of a mechanical model of the lipid bilayer, which accounts forŽ.its ‘hybrid’ rheology neither elastic body nor fluid . In all considered cases the lateralcapillary interaction originates from the overlap of interfacial deformations and is subject toa unified theoretical treatment, despite the fact that the characteristic particle size can varyfrom 1 cm down to 1 nm. 䊚 2000 Elsevier Science B.V. All rights reserved.Keywords: Capillary forces; Lipid membranes containing inclusions; Liquid films containing particles;Surface viscosity measurements; Two-dimensional aggregationContents1. Introduction ..............................................1472. Overview of results about lateral capillary forces.......................1502.1. Interaction between two particles.............................1502.2. Measurements of lateral capillary forces........................1532.3. Particle᎐wall interactions, capillary image forces and their application.....1573. Energy approach to the lateral capillary interactions.....................1623.1. The linearized Laplace equation for fluid interfaces and thin films.......1623.2. Flotation force: energy approach in superposition approximation........1633.3. Immersion force: energy approach in superposition approximation.......1653.4. General expression for the grand thermodynamic potential............1663.5. Interactions at fixed slope and fixed elevation.....................1674. Force approach to the lateral capillary interactions.....................1684.1. Integral expressions for the capillary force.......................1684.2. Asymptotic expression for the capillary force.....................1714.3. Shape of the contact line on the particle surface...................1735. Capillary forces between particles at a spherical interface, film and membrane....1745.1. Origin of the ‘capillary charge’ in the case of spherical interface.........1745.2. Forces between particles entrapped in a spherical film...............177()P.A. Kralche¨sky, K. Nagayama r Ad¨ances in Colloid and Interface Science 85 2000 145᎐1921476. Lateral capillary forces between inclusions in lipid membranes ..............1826.1. Perturbation of the lipid molecules due to inclusions in the membrane.....1826.2. Sandwich model of a lipid bilayer.............................1826.3. Capillary interaction between inclusions........................1857. Summary and conclusion......................................188Acknowledgements............................................190References..................................................1901. IntroductionIt is known from the experiment and practice that particles floating on a fluidinterface attract each other and form clusters. Such effects are observed andwxutilized in some extraction and separation flotation processes 1,2 . As noticed bywxNicolson 3 these lateral capillary
View Full Document
Unlocking...