Considerations about mass and energy flow in discontinuous evaporating crystallizers

The massecuite circulates in a loop within the evaporating crystallizing vessel. The massecuite flows upwards through the heating tubes. In the room above the calandria the massecuite flow changes its direction to radial inwards and then to vertical downwards. An impeller in the central tube forces the circulation. Below the calandria the main direction of flow is radially outwards until threads of the massecuite stream enter the heating tubes in upwards direction. Within the tubes heat is transferred to the massecuite. At low temperature differences between heating steam and massecuite and higher levels of the massecuite in the crystallizer vapor bubbles are not found in the tubes. Vapor bubbles can be formed at a massecuite level in the crystallizer where the temperature of the massecuite is higher than the local boiling temperature of water, which depends on the local pressure (including the static pressure of the massecuite at this point) and the boiling point elevation of the mother liquor. The surface tension of the liquid is a resistance against the bubble formation, which has to be overcome by the local superheating i.e. the part of the enthalpy of the massecuite exceeding the local boiling temperature. The formation and the flow of the bubbles change the density of the massecuite/bubbles mixture and has an influence on the massecuite flow. The formation of a vapour bubble is connected with a local drop of the massecuite temperature which changes the local supersaturation. Today the heat transfer into the magma is quite well known but the process of bubble formation is quite unknown. Some basic considerations about the formation of bubbles and its influence on local supersaturation based on calculation of heat and mass balances and models of bubble formation are be given and discussed. Experiments for basic investigations are proposed.

ASYMPTOTICS FOR CRITICAL FIELDS IN AN APPROXIMATE GINZBURG–LANDAU MODEL IN THE LARGE SIZE LIMIT

Pursuing a study of the superheating field for the Ginburg–Landau equations performed in Ref. 8, we consider an approximate model for a film on a bounded interval when the thickness 2e is large in comparison with the inverse of the characteristic κ of the material. We show for this problem the existence of a local superheating field, and recover, as e tends to +∞, the superheating field for a similar approximate model on a semi-infinite interval which has been studied in Ref. 8.