Interface-mediated interactions between particles: A geometrical approach
- 29 December 2005
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 72 (6), 061407
- https://doi.org/10.1103/physreve.72.061407
Abstract
Particles bound to an interface interact because they deform its shape. The stresses that result are fully encoded in the geometry and described by a divergence-free surface stress tensor. This stress tensor can be used to express the force on a particle as a line integral along any conveniently chosen closed contour that surrounds the particle. The resulting expression is exact (i.e., free of any “smallness” assumptions) and independent of the chosen surface parametrization. Additional surface degrees of freedom, such as vector fields describing lipid tilt, are readily included in this formalism. As an illustration, we derive the exact force for several important surface Hamiltonians in various symmetric two-particle configurations in terms of the midplane geometry; its sign is evident in certain interesting limits. Specializing to the linear regime, where the shape can be analytically determined, these general expressions yield force-distance relations, several of which have originally been derived by using an energy-based approach.Keywords
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This publication has 45 references indexed in Scilit:
- Indirect interactions of membrane-adsorbed cylindersThe European Physical Journal E, 2003
- Anisotropic capillary interactions and jamming of colloidal particles trapped at a liquid-fluid interfacePhysical Review E, 2002
- Effective interactions in soft condensed matter physicsPhysics Reports, 2001
- Colloidal interactionsJournal of Physics: Condensed Matter, 2000
- Long-range attraction between colloidal spheres at the air-water interface: The consequence of an irregular meniscusPhysical Review E, 2000
- Capillary interactions between particles bound to interfaces, liquid films and biomembranesAdvances in Colloid and Interface Science, 2000
- Membrane Mediated Attraction and Ordered Aggregation of Colloidal Particles Bound to Giant Phospholipid VesiclesPhysical Review Letters, 1999
- Stresses in lipid membranes and interactions between inclusionsJournal of the Chemical Society, Faraday Transactions, 1995
- Long-Range Forces in Heterogeneous Fluid MembranesEurophysics Letters, 1993
- General RelativityPublished by University of Chicago Press ,1984