A thermodynamic model for the freezing of biological cells has been developed and has been applied to human erythrocytes. Analytical expressions describing the dynamics of water loss during the several stages of the freezing process have been derived from a cell modeled as an open system surrounded by a membrane permeable to water only. The permeability of the membrane to water is the most significant cell parameter in this process and in the present model, and is assumed to be a function of the temperature and osmolality of the extracellular solution. The resulting set of differential equations describing the cell freezing process is solved numerically for various cooling rates. For cooling rates less than 3000 K/min, erythrocytes lose 95 percent of their intracellular water before the eutectic temperature is reached. For cooling rates greater than 3000 K/min, the fraction of intracellular water remaining at the eutectic temperature is a strong function of cooling rate. The effect of supercooling of the extracellular solution on the kinetics of the cell water loss is also analyzed. As a consequence of the supercooling, the volume of water present intracellularly at a given temperature is substantially greater than when no supercooling occurs. This condition favors intracellular ice formation and is consistent with experimental observations in this laboratory.
A prototype reverse Brayton air cycle heat pump water heater has been designed and built for residential applications. The system consists of a compressor/expander, an air-water heat exchanger, an electric motor, a water circulation pump, a thermostat, and fluid management controls. The prototype development program consists of a market analysis, design study, and development testing. The results of a market study of the reverse Brayton cycle water heater revealed that a potential residential market for the new high efficiency water heater is approximately 480,000 units per year. The retail and installation cost of the new high efficiency water heater is estimated to be between $500 and $600 which is approximately $300 more than a conventional electric water heater. The average payback per unit is less than 3-1/2 years and the average recurring energy cost-savings after the payback period is approximately $105 per year at an average seasonal coefficient of performance (COP) of 1.7.
A theoretical model describing the thermodynamics of intracellular ice nucleation is developed for red blood cells as a model biomaterial. Analytical expressions based on current theories of ice nucleation by both homogeneous and heterogeneous nucleation processes are coupled with a thermodynamic model for the loss of intracellular water during freezing. Numerical solutions for both modes of nucleation identify two cooling regions—high cooling rates and low cooling rates—separated by a sharp demarcation zone. The nucleation temperature for high cooling rates is approximately 20° K higher than the nucleation temperature for low cooling rates and is essentially independent of cooling rate in each region. The nucleation temperatures for heterogeneous nucleation are approximately 30° K higher than the nucleation temperatures for homogeneous nucleation in the two regions. For the case of heterogeneous nucleation, it is possible to increase the nucleation temperature by packing of catalysts via the concentration polarization effect. If the cell suspension is allowed to supercool before nucleation occurs in the extracellular medium, the sharp transition from low cooling rates to high cooling rates for heterogeneous nucleation shifts to much lower cooling rates. The dependence of the transition cooling rate on the degree of supercooling has been established for a typical freezing situation.
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