Reaction-diffusion-advection equation in binary tree networks and optimal size ratio

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    2 Citations (Scopus)

    Abstract

    A simple reaction-diffusion-advection equation is proposed in a dichotomous tree network to discuss an optimal network. An optimal size ratio r is evaluated by the principle of maximization of total reaction rate. In the case of reaction-limited conditions, the optimal ratio can be larger than (1/2)1/3 for a fixed value of branching number n, which is consistent with observations in mammalian lungs. We find furthermore that there is an optimal branching number nc when the Péclet number is large. Under the doubly optimal conditions with respect to the size ratio and branching number, the optimal value of r is close to (1/2)1/3.

    Original languageEnglish
    Article number040801
    JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
    Volume90
    Issue number4
    DOIs
    Publication statusPublished - Oct 10 2014

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    Advection-diffusion-reaction Equation
    Tree Networks
    Binary Tree
    advection
    lungs
    Branching
    reaction kinetics
    Reaction Rate
    Lung

    All Science Journal Classification (ASJC) codes

    • Statistical and Nonlinear Physics
    • Statistics and Probability
    • Condensed Matter Physics

    Cite this

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    abstract = "A simple reaction-diffusion-advection equation is proposed in a dichotomous tree network to discuss an optimal network. An optimal size ratio r is evaluated by the principle of maximization of total reaction rate. In the case of reaction-limited conditions, the optimal ratio can be larger than (1/2)1/3 for a fixed value of branching number n, which is consistent with observations in mammalian lungs. We find furthermore that there is an optimal branching number nc when the P{\'e}clet number is large. Under the doubly optimal conditions with respect to the size ratio and branching number, the optimal value of r is close to (1/2)1/3.",
    author = "Hidetsugu Sakaguchi",
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    AB - A simple reaction-diffusion-advection equation is proposed in a dichotomous tree network to discuss an optimal network. An optimal size ratio r is evaluated by the principle of maximization of total reaction rate. In the case of reaction-limited conditions, the optimal ratio can be larger than (1/2)1/3 for a fixed value of branching number n, which is consistent with observations in mammalian lungs. We find furthermore that there is an optimal branching number nc when the Péclet number is large. Under the doubly optimal conditions with respect to the size ratio and branching number, the optimal value of r is close to (1/2)1/3.

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