Sublimation-dehydration in the continuum, transition and free-molecule flow regimes

Abstract

A theoretical analysis is presented for heat and mass transfer during sublimation-dehydration. The energy equations in the dried and frozen regions are solved. Equations are presented for hydrodynamic and diffusionsl flow in the dried region for free-molecule, transition, and continuum flow regimes. The energy and vapor flow equations are coupled to give closed; form solutions for the interface temperature as a function of the flow regime, interface position, transport property data, and externally controlled boundary conditions. The equations are valid for simultaneous hydrodynamic and diffusional flow in the continuum and transition flow regimes, and are valid for molecular diffusion in the free-molecule regime. Closed form equations are presented for the interface position as a function of time for cases where the interface temperature is either constant or a linear function of the interface position. The results indicate that if heat is transferred through both the dried and frozen layers, the interface temperature will change as the interface position changes. Numerical calculations for freeze-drying beef show that this relationship is approximately linear for chamber pressures between 0.5 and 4.0 torr. It is also found that the pressure which gives the fastest drying rate for beef is between 0.5 and 1.0 torr. For all beet samples 1.5 inches thick or less, drying is taster when it takes place from both faces than when it takes place from only one face and heat is conducted through the back face. Numerical calculations are presented which show the feasibility of atmospheric freeze-drying of thin samples.