Facile Model for Predicting Sweat Mass and Concentration in Layer Melt Crystallization

Sweating is an important purification process involved in the layer melt crystallization technique. Modeling of the sweating process remains difficult due to the complicated association of mass balance, heat balance, and fluid flow through a dynamic crystal layer. A model of sweating was proposed in this work, attempting to give a facile prediction of the dynamic sweat mass and concentration based on the initial crystal layer structure other than empirical correlations. Heat balance equations were taken as the governing equations to calculate the crystal layer temperature and residual melt concentration. A curved capillary bundle model that obeys fractal distribution was adapted to describe the dynamic porous crystal layer. By combining mass balance, the nonlinear variation of melted mass with sweating time was estimated. Subsequently, para-xylene was used as the model material to validate the sweating model. A quasiequilibrium between solid and liquid was found at a slow sweating rate range in this work, which verified the model assumption and greatly simplify the calculation. It revealed that the melting amount of the crystal layer and the imbibition melt increased nonlinearly with the increase of temperature. The curved capillary bundle model was found to be able to give an accurate estimation of sweat mass according to the experimental data. The model has accurate predictions on the S-shaped curve of sweat mass and sweat concentration compared to the experimental sweating results.