Measurement and numerical analysis of freezing in solutions enclosed in a small container

Ramachandra V. Devireddy, Perry H. Leo, John S. Lowengrub, John C. Bischof

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35 Scopus citations


The latent heat of fusion, L of the cryobiological media (a solute laden aqueous solution) is a crucial parameter in the cryopreservation process and has often been approximated to that of pure water (∼335 mJ/mg). This study experimentally determines the magnitude and dynamics of latent heat during freezing of 14 different pre-nucleated solute laden aqueous systems using a differential scanning calorimeter (DSC-Pyris 1). The latent heat of the solutions studied is found to be significantly less than that of pure water and is dependent on both the 'amount' and 'type' of solutes (or solids) in solution. DSC experiments are also performed at 1, 5 and 20 °C/min in five representative cryobiological media to determine the kinetics of ice crystallization. The total magnitude of the latent heat release, L is found to be independent of the cooling rate. However, the experimental data show that at a fixed temperature, the fraction of heat released at higher cooling rates (5 and 20 °C/min) is lower than that at 1 °C/min for all the solutions studied. We present a model to predict the experimentally measured behavior based on the full set of heat and mass transport equations during the freezing process in a DSC sample pan. Analysis of the parameters relevant to the transport processes reveals that heat transport occurs much more rapidly than mass transport. The model also reveals the important physical parameters controlling the mass transport at the freezing interface i.e., diffusion limited and further elucidates the measured temperature and time dependence of the latent heat release.

Original languageEnglish (US)
Pages (from-to)1915-1931
Number of pages17
JournalInternational Journal of Heat and Mass Transfer
Issue number9
StatePublished - Mar 4 2002

Bibliographical note

Funding Information:
This work was supported by grants from the National Science Foundation (NSF – BES # 9703326 and NSF – DMS # 9706831) and a grant from the Materials Research Science and Engineering Center (MRSEC) at the University of Minnesota. We also wish to acknowledge support from the Minnesota Supercomputer Institute. Special thanks to Agouron Pharm, San Diego, CA (in particular, Dr. Ernest Villafranca and Robert Aust) for providing the AFPs.


  • Biological media
  • Cryoprotective solutions and bound water
  • Differential scanning calorimetry
  • Phase change


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