Capillary interactions between particles bound to interfaces, liquid filmsand biomembranes

This article is devoted to an overview, comparison and discussion of recent results (both theoretical and experimental) about lateral capillary forces . They appear when the contact of particles or other bodies with a fluid ph ase boundary causes perturbations in the interfacial shape. The capillary i nteraction is due to the overlap of such perturbations which can appear aro und floating particles, vertical cylinders, particles confined in a liquid film, inclusions in the membranes of lipid vesicles or living cells, etc. I n the case of floating particles the perturbations are due to the particle weight; in this case the force decreases with the sixth power of the partic le size and becomes immaterial for particles smaller than approximately 10 mu m. In all other cases the interfacial deformations are due to the partic le wetting properties; the resulting 'immersion' capillary forces can be op erative even between Very small particles, like protein globules. In many c ases such forces can be responsible for the experimentally observed two-dim ensional particle aggregation and ordering. An analogy between capillary an d electrostatic forces enables one to introduce 'capillary charges' of the attached particles, which characterize the magnitude of the interfacial def ormation and could be both positive and negative. Moreover, the capillary i nteraction between particle and wall resembles the image force in electrost atics. When a particle is moving bound to an interface under the action of a capillary force, one can determine the surface drag coefficient and the s urface viscosity supposedly the magnitude of the capillary force is known. Alternative (but equivalent) energy and force approaches can be used for th e theoretical description of the lateral capillary interactions, Both appro aches require the Laplace equation of capillarity to be solved and the meni scus profile around the particles to be determined. The energy approach acc ounts for contributions due to the increase of the meniscus area, gravitati onal energy and/or energy of wetting. The second approach is based on calcu lating the net force exerted on the particle, which can originate from the hydrostatic pressure, interfacial tension and bending moment. In the case o f small perturbations, the superposition approximation can be used to deriv e an asymptotic formula for the capillary forces, which has been found to a gree well with the experiment. Capillary interactions between particles bou nd to spherical interfaces are also considered taking into account the spec ial geometry and restricted area of such phase boundaries. A similar approa ch can be applied to quantify the forces between inclusions (transmembrane proteins) in lipid membranes. The deformations in a lipid membrane, due to the inclusions, can be described theoretically in the framework of a mechan ical model of the lipid bilayer, which accounts for its 'hybrid' rheology ( neither elastic body nor fluid). In all considered cases the lateral capill ary interaction originates from the overlap of interfacial deformations and is subject to a unified theoretical treatment, despite the fact that the c haracteristic particle size can vary from 1 cm down to 1 nm. (C) 2000 Elsev ier Science B.V. All rights reserved.