Moisture transport and diffusive instability during bread baking

H. Huang, Ping Lin, W. Zhou

    Research output: Contribution to journalArticlepeer-review

    20 Citations (Scopus)


    In this paper we study multiphase models for simultaneous heat and mass transfer processes during bread baking. Our main objective is to provide an explanation and a remedy to the observed erroneous and/or divergent results associated with an instantaneous phase change model used in the literature. We propose a reaction-diffusion model based on the Hertz–Knudsen equation, where phase change is not instantaneous but determined by an evaporation/condensation rate. A splitting scheme is designed for the reaction-diffusion model so that a link between these two models can be established and the nonintuitive numerical instability associated with the instantaneous phase change model can be identified and eliminated. The evaporation/condensation rate is estimated by comparing results of the reaction-diffusion model with experimental observations reported in the literature. For evaporation/condensation rate beyond the estimated value, oscillatory solution with multiple regions of dry and two-phase zones is observed. We show that these are caused by an instability intrinsic to the model (which we call diffusive instability) using linear stability analysis and numerical tests.
    Original languageEnglish
    Pages (from-to)222-238
    Number of pages17
    JournalSIAM Journal on Applied Mathematics
    Issue number1
    Publication statusPublished - 2007


    • Diffusive instability
    • Finite difference methods
    • Heat
    • Linear stability analysis
    • Multiphase modelling
    • Phase change
    • Reaction-diffusion equations
    • Mass transfer


    Dive into the research topics of 'Moisture transport and diffusive instability during bread baking'. Together they form a unique fingerprint.

    Cite this