Applied and Computational Mathematics Division, National Institute of Standards and Technology, Gaithersburg, MD, 20899-8910, USA; Department of Mathematical Sciences, George Mason University, Fairfax, VA, 22030, USA.
Applied and Computational Mathematics Division, National Institute of Standards and Technology, Gaithersburg, MD, 20899-8910, USA; Department of Biology, University of Saskatchewan, Saskatoon, SK, S7N 5E2, Canada.
Cryobiology. 2019 Dec;91:3-17. doi: 10.1016/j.cryobiol.2019.09.014. Epub 2019 Oct 4.
Modeling coupled heat and mass transport in biological systems is critical to the understanding of cryobiology. In Part I of this series we derived the transport equation and presented a general thermodynamic derivation of the critical components needed to use the transport equation in cryobiology. Here we refine to more cryobiologically relevant instances of a double free-boundary problem with multiple species. In particular, we present the derivation of appropriate mass and heat transport constitutive equations for a system consisting of a cell or tissue with a free external boundary, surrounded by liquid media with an encroaching free solidification front. This model consists of two parts-namely, transport in the "bulk phases" away from boundaries, and interfacial transport. Here we derive the bulk and interfacial mass, energy, and momentum balance equations and present a simplification of transport within membranes to jump conditions across them. We establish the governing equations for this cell/liquid/solid system whose solution in the case of a ternary mixture is explored in Part III of this series.
对生物系统中的传热传质进行建模对于理解低温生物学至关重要。在本系列的第一部分中，我们推导出了输运方程，并对低温生物学中使用输运方程所需的关键组成部分进行了热力学推导。在这里，我们将其细化为具有多个物种的双自由边界问题的更具低温生物学相关性的实例。具体来说，我们给出了由具有自由外部边界的细胞或组织组成的系统的适当质量和热传输本构方程的推导，该系统被侵入的自由凝固前沿的液体介质包围。该模型由两部分组成——即远离边界的“体相”中的传输和界面传输。在这里，我们推导出体相和界面的质量、能量和动量平衡方程，并给出了穿过它们的跳跃条件的膜内传输的简化。我们建立了这个细胞/液体/固体系统的控制方程，在本系列的第三部分中，我们探讨了三元混合物情况下的解。
