Sublimation rate

Beryllium Nitride. BeryUium nitride [1304-54-7], Be N2, is prepared by the reaction of metaUic beryUium and ammonia gas at 1100°C. It is a white crystalline material melting at 2200°C with decomposition. The sublimation rate becomes appreciable in a vacuum at 2000°C. Be2N2 is rapidly oxidized by air at 600°C and like the carbide is hydrolyzed by moisture. The oxide forms on beryllium metal in air at elevated temperatures, but in the absence of oxygen, beryllium reacts with nitrogen to form the nitride. When hot pressing mixtures of beryUium nitride and sUicon nitride, Si N, at 1700°C, beryllium sUicon nitride [12265-44-0], BeSiN2, is obtained. BeSiN2 may have appHcation as a ceramic material. 

The above reaction shows that the oxychloride decomposes at the sublimation temperature into the volatile tetrachloride and the nonvolatile oxide. Reduction starts as soon as the chloride vapour contacts the molten magnesium, and this exothermic reaction raises the temperature of the reaction mixture. The temperature of the reduction crucible is maintained in the range of 800 to 875 °C. The process is carefully controlled by matching the sublimation rate of zirconium tetrachloride with the reduction rate. The conclusion of the reduction is indicated by a fall in temperature and pressure. 

M. J. Pikal, S. Shah, D. Senior, and J. E. Lang, Physical chemistry of freeze drying measurement of sublimation rates of frozen aqueous solutions by a microbalance technique, J. Pharm. Sci., 72, 635-650 (1983). 

Equation (5) is equivalent to stating that sublimation and subsequent transport of 1 g of water vapor into the chamber demands a heat input of 650 cal (2720 J) from the shelves. The vial heat transfer coefficient, Kv, depends upon the chamber pressure, Pc and the vapor pressure of ice, P0, depends in exponential fashion upon the product temperature, Tp. With a knowledge of the mass transfer coefficients, Rp and Rs, and the vial heat transfer coefficient, Kv, specification of the process control parameters, Pc and 7 , allows Eq. (5) to be solved for the product temperature, Tp. The product temperature, and therefore P0, are obviously determined by a number of factors, including the nature of the product and the extent of prior drying (i.e., the cake thickness) through Rp, the nature of the container through Kv, and the process control variables Pc and Ts. With the product temperature calculated, the sublimation rate is determined by Eq. (4). 

Figure 15 A schematic of the model for evaluating sublimation rate and evaporation rate from kinetic theory.

The product temperatures were -21.2°C for KC1 and -31.0°C for povidone. The arrows mark the values of the vapor pressure of ice at the operating temperatures. The normalized dried product resistances increase smoothly with pressure as the vapor pressure of ice is approached and exceeded. Thus, the sublimation rate decreases smoothly throughout this pressure range and does not drop to zero at a total system pressure which exceeds the vapor pressure of ice. This observation is completely consistent with the theoretical concepts developed... 

Figure 35 Intervial and array position variability in vial heat transfer vial placement on the shelf and mean percent deviation in sublimation rates. (From Ref. 5.)... 

Volatilization sublimation rate constant of 1.1 x 10+ s+ was measured as loss from glass surface at 24°C at an air flow rate of 3 L/min (Cope Kalkwarf 1987)... 

Urticants, even solids, have relatively high vapor pressure and evaporation or sublimation rates are nearly the same as water. 

Kobayashi, M. Vial variance of the sublimation rate in shelf freeze-drying. Paper 312. International Institute of Refrigeration (Montreal 1991)... 

Fig. 2.16.2. Ice sublimation rate (kg/m2 h) for five different types of tray.

With this information the maximum flow of energy can be estimated, which can be transported during freezing and main drying at a desired temperature difference between inlet and outlet temperature of the brine at the shelves, e. g. 2000 kj/h at a temperature difference of 3 °C. With this amount of energy approx. 0.7 kg ice could be sublimated per hour. (This estimate gives only the maximum possible sublimation-rate, whether it can be achieved or not depends from heat -and mass transfer conditions in the process (see Section 1.2.1 and Eq. (12)). 

Fig. 3.15. Sublimation rate as function of the water content for different product layers.

Authors note The measured independence of the sublimation rate from the layer thickness shows, that the sublimation rate under the conditions of the experiment depends only from the heat transfer to the product and not from the water vapor transportation through the dried product.)... 

Distillation, sublimation This can be used to remove the metals from Ta (from crucibles, etc. dissolved by the molten R and re-precipitated). The volatile R (Sm, Eu, Dy, Ho, Er, Tm, Yb, Sc) are also purified from C, N, O (present as carbides, nitrides, oxides). Gschneidner (1980) underlined that, in order to obtain high purity, a very high vacuum (10 8-10 9mmHg) and a slow sublimation rate must be maintained during the distillation process. 

Sublimation rates of pure solids into turbulent air streams have been successfully correlated by the Gilliland-Sherwood equation(102) ... 

The product yield from an entrainer-sublimation process may be estimated as follows. The mass flowrate G of the inert gas and the mass sublimation rate S are related by ... 

The theoretical maximum yield from an entrainer sublimation process is the difference between the calculated sublimation rates corresponding to the conditions in the vaporisation and condensation stages. 

Dichlorobenzene is a solid which sublimes readily at room temperature. Sublimation rates of... 

Each of the turns in the titanium sublimation pump contains approximately 1.2 g of useable titanium supply. At a heating current of 50 A the surface temperature comes to about 1850 K, the sublimation rate approximately 0.12 g/h, i.e. a turn can be operated continuously for about 10 hours. Since at pressures below 1 10 mbar sublimation is not continuous but rather only at intervals which - at low pressures (below 5 10 mbar) and low gas volumes - are already more than ten times the actual sublimation period, one may assume a pumping period of almost one month at a working pressure of 10 mbar per turn. 

Drying Rates. Drying a frozen material proceeds initially at a constant rate with rapid evolution of water vapor. As Ihe sublimation interface recedes within the product, water-vapor evolution decreases. This is the start of the falling-rate period. When only bound water remains within the cellular structure of the product, the desorption period begins. During the constant-rate period, the sublimation rate can be expressed in terms of the heat of sublimation of ice and the heat-rale equation ... 

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