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Bulk-mediated Surface Diffusion on a Cylinder in the Fast Exchange Limit

  • A. V. Chechkin (a1), I. M. Zaid (a2), M. A. Lomholt (a3), I. M. Sokolov (a4) and R. Metzler (a5)...
Abstract

In various biological systems and small scale technological applications particles transiently bind to a cylindrical surface. Upon unbinding the particles diffuse in the vicinal bulk before rebinding to the surface. Such bulk-mediated excursions give rise to an effective surface translation, for which we here derive and discuss the dynamic equations, including additional surface diffusion. We discuss the time evolution of the number of surface-bound particles, the effective surface mean squared displacement, and the surface propagator. In particular, we observe sub- and superdiffusive regimes. A plateau of the surface mean-squared displacement reflects a stalling of the surface diffusion at longer times. Finally, the corresponding first passage problem for the cylindrical geometry is analysed.

In various biological systems and small scale technological applications particles transiently bind to a cylindrical surface. Upon unbinding the particles diffuse in the vicinal bulk before rebinding to the surface. Such bulk-mediated excursions give rise to an effective surface translation, for which we here derive and discuss the dynamic equations, including additional surface diffusion. We discuss the time evolution of the number of surface-bound particles, the effective surface mean squared displacement, and the surface propagator. In particular, we observe sub- and superdiffusive regimes. A plateau of the surface mean-squared displacement reflects a stalling of the surface diffusion at longer times. Finally, the corresponding first passage problem for the cylindrical geometry is analysed.

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Corresponding author
Corresponding author. E-mail: rmetzler@uni-potsdam.de
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Mathematical Modelling of Natural Phenomena
  • ISSN: 0973-5348
  • EISSN: 1760-6101
  • URL: /core/journals/mathematical-modelling-of-natural-phenomena
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