Geometry of surface-mediated interactionsM. M. Müller1, M. Deserno1 and J. Guven2
1 Max-Planck-Institut für Polymerforschung Ackermannweg 10, 55128 Mainz, Germany
2 Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México Apdo. Postal 70-543, 04510 México D.F., Mexico
received 24 August 2004; accepted in final form 26 November 2004
published online 12 January 2005
Soft interfaces can mediate interactions between particles bound to them. The force transmitted through the surface geometry on a particle may be expressed as a closed line integral of the surface stress tensor around that particle. This contour may be deformed to exploit the symmetries present; for two identical particles, one obtains an exact expression for the force between them in terms of the local surface geometry of their mid-plane; in the case of a fluid membrane the sign of the interaction is often evident. The approach, by construction, is adapted directly to the surface and is independent of its parameterization. Furthermore, it is applicable for arbitrarily large deformations; in particular, it remains valid beyond the linear small-gradient regime.
87.16.Dg - Membranes, bilayers, and vesicles.
68.03.Cd - Surface tension and related phenomena.
02.40.Hw - Classical differential geometry.
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