Foundations of modeling in cryobiology—II: Heat and mass transport in bulk and at cell membrane and ice-liquid interfaces

• Published in: Cryobiology 2019-12, Vol.91, p.3-17
• Main Authors: Anderson, Daniel M., Benson, James D, Kearsley, Anthony J.
• Format: Article
• Language: English
• Subjects: Animals; Cell Membrane - physiology; Cryobiology; Cryobiology - methods; Cryopreservation - methods; Hot Temperature; Ice; Interfacial conditions; Membrane boundary conditions; Thermodynamics; Transport processes
• ISSN: 0011-2240; 1090-2392; 1090-2392
• DOI: 10.1016/j.cryobiol.2019.09.014

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.