IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v605y2022ics0378437122006185.html
   My bibliography  Save this article

Exponential and Weibull models for spherical and spherical-shell diffusion-controlled release systems with semi-absorbing boundaries

Author

Listed:
  • Carr, Elliot J.

Abstract

We consider the classical problem of particle diffusion in d-dimensional radially-symmetric systems with absorbing boundaries. A key quantity to characterise such diffusive transport is the evolution of the proportion of particles remaining in the system over time, which we denote by P(t). Rather than work with analytical expressions for P(t) obtained from solution of the corresponding continuum model, which when available take the form of an infinite series of exponential terms, single-term low-parameter models are commonly proposed to approximate P(t) to ease the process of fitting, characterising and interpreting experimental release data. Previous models of this form have mainly been developed for circular and spherical systems with an absorbing boundary. In this work, we consider circular, spherical, annular and spherical-shell systems with absorbing, reflecting and/or semi-absorbing boundaries. By proposing a moment matching approach, we develop several simple one and two parameter exponential and Weibull models for P(t), each involving parameters that depend explicitly on the system dimension, diffusivity, geometry and boundary conditions. The developed models, despite their simplicity, agree very well with values of P(t) obtained from stochastic model simulations and continuum model solutions.

Suggested Citation

  • Carr, Elliot J., 2022. "Exponential and Weibull models for spherical and spherical-shell diffusion-controlled release systems with semi-absorbing boundaries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 605(C).
  • Handle: RePEc:eee:phsmap:v:605:y:2022:i:c:s0378437122006185
    DOI: 10.1016/j.physa.2022.127985
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437122006185
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

    File URL: https://libkey.io/10.1016/j.physa.2022.127985?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ignacio, M. & Slater, G.W., 2021. "Using fitting functions to estimate the diffusion coefficient of drug molecules in diffusion-controlled release systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    2. Ignacio, Maxime & Chubynsky, Mykyta V. & Slater, Gary W., 2017. "Interpreting the Weibull fitting parameters for diffusion-controlled release data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 486-496.
    3. Gomes-Filho, Márcio Sampaio & Barbosa, Marco Aurélio Alves & Oliveira, Fernando Albuquerque, 2020. "A statistical mechanical model for drug release: Relations between release parameters and porosity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    4. D. Grebenkov & M. Filoche & B. Sapoval, 2003. "Spectral properties of the Brownian self-transport operator," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 36(2), pages 221-231, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Filippini, Luke P. & Simpson, Matthew J. & Carr, Elliot J., 2023. "Simplified models of diffusion in radially-symmetric geometries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 626(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Filippini, Luke P. & Simpson, Matthew J. & Carr, Elliot J., 2023. "Simplified models of diffusion in radially-symmetric geometries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 626(C).
    2. Ignacio, M. & Slater, G.W., 2021. "Using fitting functions to estimate the diffusion coefficient of drug molecules in diffusion-controlled release systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    3. Sapoval, B. & Andrade, J.S. & Baldassarri, A. & Desolneux, A. & Devreux, F. & Filoche, M. & Grebenkov, D. & Russ, S., 2005. "New simple properties of a few irregular systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 357(1), pages 1-17.
    4. Gomes-Filho, Márcio Sampaio & Barbosa, Marco Aurélio Alves & Oliveira, Fernando Albuquerque, 2020. "A statistical mechanical model for drug release: Relations between release parameters and porosity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    5. Ignacio, M. & Slater, G.W., 2022. "A Lattice Kinetic Monte Carlo method to study drug release from swelling porous delivery systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    6. Singh, Kulveer & Satapathi, Soumitra & Jha, Prateek K., 2019. "“Ant-Wall” model to study drug release from excipient matrix," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 519(C), pages 98-108.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:605:y:2022:i:c:s0378437122006185. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.