Chacón-Acosta, Guillermo

Dagdug, Leonardo

Pineda, Inti

English

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The Open-Access Journal for the Basic Principles of Diffusion Theory, Experiment and ApplicationProjection of two-dimensional diffusion in a curved midline and narrowvarying width channel on a curved surfaceGuillermo Chacón-Acosta1∗, Inti Pineda2, Leonardo Dagdug21Departamento de Matemáticas Aplicadas y Sistemas,Universidad Autónoma Metropolitana-Cuajimalpa, México, Mexico2Departamento de Fı́sica, Universidad Autónoma Metropolitana-Iztapalapa, México, Mexico∗gchacon@correo.cua.uam.mxThis study focuses on the derivation of a general effective diffusion coefficient to describe the twodimensional (2D) diffusion in a narrow and smoothly asymmetric channel of varying width that lies ona curved surface, in the simple diffusional motion of noninteracting pointlike particles under no externalfield. To this end we extend the generalization of the Kalinay-Percus’ projection method [1, 2] for theasymmetric channels introduced in [3], to project the anisotropic two dimensional diffusion equationon a smooth curved manifold, into an effective one dimensional generalized Fick-Jacobs equation thatis modified due to the curvature of the surface.The lowest order in the perturbation parameter, corresponding to the Fick-Jacobs equation containsan extra term that accounts for the curvature of the surface by the Christoffel symbols. We foundexplicitly the first order correction for the invariant effective concentration, which is defined as thecorrect marginal concentration in one variable, and we obtain the first approximation to the effectivediffusion coefficient analogous to Bradley’s coefficient [4] as a function of metric elements of themanifold.Straightforwardly we study the perturbation series up to the n-th order, and we derive the full effec-tive diffusion coefficient for the two dimensional diffusion in a narrow asymmetric channel, that havemodifications due to the curved metric.Finally, we present some examples of symmetric surfaces and we study some specific channelconfigurations on them.References[1] P. Kalinay, J.K. Percus: Projection of two-dimensional diffusion in a narrow channel onto thelongitudinal dimension. J. Chem. Phys. 122, 204701 (2005)[2] P. Kalinay, J.K. Percus: Corrections to the Fick-Jacobs equation. Phys. Rev. E 74, 041203 (2006)[3] L. Dagdug, I. Pineda: Projection of two-dimensional diffusion in a curved midline and narrowvarying width channel onto the longitudinal dimension. J. Chem. Phys. 137, 024107 (2012)[4] R.M. Bradley: Diffusion in a two-dimensional channel with curved midline and varying width:Reduction to an effective one-dimensional description. Phys. Rev. E 80, 061142 (2009)

Projection of two-dimensional diffusion in a curved midline and narrow varying width channel on a curved surface

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Projection of two-dimensional diffusion in a curved midline and narrow varying width channel on a curved surface

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