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Diffusion coefficients and MSD measurements on curved membranes and porous media

  • Topical Review - Flowing Matter
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Abstract

We study some geometric aspects that influence the transport properties of particles that diffuse on curved surfaces. We compare different approaches to surface diffusion based on the Laplace–Beltrami operator adapted to predict concentration along entire membranes, confined subdomains along surfaces, or within porous media. Our goal is to summarize, firstly, how diffusion in these systems results in different types of diffusion coefficients and mean square displacement measurements, and secondly, how these two factors are affected by the concavity of the surface, the shape of the possible barriers or obstacles that form the available domains, the sinuosity, tortuosity, and constrictions of the trajectories and even how the observation plane affects the measurements of the diffusion. In addition to presenting a critical and organized comparison between different notions of MSD, in this review, we test the correspondence between theoretical predictions and numerical simulations by performing finite element simulations and illustrate some situations where diffusion theory can be applied. We briefly reviewed computational schemes for understanding surface diffusion and finally, discussed how this work contributes to understanding the role of surface diffusion transport properties in porous media and their relationship to other transport processes.

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Acknowledgements

We thank the División de Ciencias Básicas e Ingeniería of UAM-Iztapalpa for financial support under the Programa Especial de Apoyo a Proyectos de Docencia e Investigación, 2023 and PRODEP program.

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  1. A. Ledesma-Durán and L. H. Juárez-Valencia contributed equally to this work.

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    Aldo Ledesma-Durán & L. Héctor Juárez-Valencia

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A.L.D conceived of the presented idea. A.L.D and H.J.V performed the numerical computations. A.L.D verified the analytical methods. All authors discussed the results and contributed to the final manuscript.

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Ledesma-Durán, A., Juárez-Valencia, L.H. Diffusion coefficients and MSD measurements on curved membranes and porous media. Eur. Phys. J. E 46, 70 (2023). https://doi.org/10.1140/epje/s10189-023-00329-z

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