Based on a modified form of the freezing point depression equation we have derived a set of rigorous, broadly applicable equations for effective heat capacity during the freezing and thawing of foods and biological materials. The equations have been integrated with respect to temperature, thereby providing a set of useful equations for enthalpy during freezing and thawing. The validity and utility of the equations are demonstrated using data from the literature. Methods for adjusting the equations to account for changes in water content and fat content are presented. The enthalpy equations are useful for calculating heattransfer loads during freezing and thawing, and the heat capacity equations can be advantageously used in differential equations for calculating freezing and thawing heat-tra,nsfer rates. THE CALCULATIONof cooling and heating loads and rates are central problems in designing food freezing and thawing systems. To facilitate such calculations we have developed a generalized equation for effective heat capacity during freezing and thawing. It provides much of the same information as the enthalpy -moisture content -temperature diagrams developed by Riedel (1956; 1957a, b), but it is more compact and convenient, and is directly usable in a broader range of problem situations.Foods start to freeze at lower temperatures than pure water. Their freezable water content changes to ice over a range of temperatures rather than at a single temperature. Since the ice forms over a range of temperatures, the associated latent heat effect per degree can be added to the normal heat capacity, yielding an effective heat capacity Ce which is a function of temperature. Values of Ce vs temperature have been calorimetrically determined for meat and fish by Jason and Long (195 5), Fleming (1969) and by Rolfe (1968) using the calorimetric data of Riedel (1956; 1957a, b). Heldman (1974a, b) has used the freezing point depression equation to calculate ice content and enthalpy changes for small temperature changes during freezing, and from these values he calculated values for C,. We utilize the same equation in a somewhat different fashion in this paper. Freezing point depression Foods, during freezing, obey the freezing point depression equation. The differential and integral forms of this equation are : 3 Ina,-1 aa, _ I~AHT --__--aT a, aT RT2 Ina,= 18&T -To) RToT(2) where a, is the water activity, To the freezing point of pure water, T the freezing point of the solution (T and To are absolute temperatures), R the gas law constant (1.987 BTU/lb mole OR or 1.987 Cal/g mole OK), AHT the heat of fusion per unit weight at T and AH the average heat of fusion over the range between To and T. Since AH = H, -HI, where H, and HI are the specific enthalpy of water and ice respectively; dAH/dT the temperature coefficient of latent heat = dH,/dT -dHI/dT = C, -CI = ACp, where ACp is the difference between Cw the heat capacity of water and CI the heat capacity of ice. By integrating the temperature coefficient of latent heat between To a...

No abstract

No abstract

No abstract

Crystal sizes were measured photographically versus elapsed time for non-uniform ice crystal populations mixed at equilibrium temperatures with sugar solutions. The mass of ice did not change, but crystals smaller than a "neutral diameter," D(n), tended to melt because of their excess surface energy. This subcooled the solution with respect to larger crystals, which consequently grew. This process, "ripening," which slowly increases mean crystal sizes and D(n) is used to produce ice crystals large enough to be cleanly separated from freeze concentrated solutions. "Sequential analysis" was used to determine D(n) and follow changes in the diameters, D(i), of fractions of the ice crystal populations. Rates of change in D(i) for both growth and melting were roughly proportional to (I/D(n) - 1/D(i). Overall mass-transfer coefficients were not markedly different for growth and melting, and decreased from roughly 2 mm/s to roughly 0.5 mm/s as sugar concentration increased 10% to 42%. In 10% sucrose solutions, mass-transfer coefficients decreased from roughly 2 mm/s to roughly 1 mm/s when gelatin was added at levels which increased from 0% to 0.5%. Ripening in freeze concentrated liquid foods apparently can be accelerated by manipulating initial crystal size distributions and temporarily removing high molecular weight components.

No abstract

The effects of winds, waves, and currents, and the physical properties of oil and water on the drift rates of oil spills were studied in tests carried out in a combined water basin wind tunnel On calm water, oil drifted at a fairly constant percentage of the wind speed regardless of the nature and spreading tendencies of the oil, the spill size, and water temperature, depth, and salinity. Percent drift varied with wind tunnel height. Extrapolation to infinite height indicated that on calm open water wind drift should be 3.7%. Shallow water waves, which produced no significant drift themselves, reduced wind drift. Analysis indicated that deep water waves produced by the wind should produce significant drift, complicating wind drift prediction, but the magnitude of the wind wave interaction effects is not yet known. Test wind drifts and current drifts were found not to be directly additive.

No abstract