A receding interface model for the drying of slurry droplets

Abstract

A receding interface model of the drying of single drops of slurries of sodium sulfate decahydrate has been developed to describe the drying characteristics of this material and to estimate the drying rates of particulate slurries. The simultaneous heat and mass transfer rate equations have been solved numerically, and the results obtained have been compared with those obtained experimentally by drying single drops suspended on the tip of a glass filament.Single drops of slurries, 1.0 to 1.5 x m dia., were suspended on the tip of a flexible glass cantilever inserted in a vertical wind tunnel. A 50pm dia. nickel wire passed through the center of the glass beam and the outer surface was coated with a thin film of copper, thereby forming a thermocouple that measured the temperature of the core of the drop; the deflection of the beam gave the loss in weight during drying. In this way the instantaneous drying rate and drop temeprature were determined and compared with those predicted by the receding interface model. In all cases the agreement between the predictions of the model and experimental results was good. SCOPEOne of the prerequisites for the optimum design of processes involving evaporation of a spray is an understanding of the controlling mechanisms in the heat and mass transfer processes during drying. Although a great deal of fundamental research had been carried out on the evaporation of pure liquid drops (WhytlawGray and Patterson, 1932;Langstroth et at. 1950;Ranz and Marshall, 1952;Pasternak and Gauvin, 1960), experimental data on the drying of drops containing solids is limited. This can be attributed in part to the complexities in analyzing the heat and mass transfer processes after a solid crust has formed. Heat is transferred by convection from the drying medium to the outer surface of the crust and then by conduction through the solid portion of the crust to the interior. Evaporation occurs and moisture diffuses through the pores in the crust into the surroundings. As the particle dries, the crust increases in thickness, resulting in an increase in the resistance to heat and mass transfer. This invariably decreases the core temperature, initially causing a reduction in the partial pressure driving force. However when the temperature of the core of the drop is considerably below that of the drying medium, the core temperature afterwards increases and the drying rate consequently increases. The transfer process is therefore highly complex and difficult to model mathematically.The present study was initiated to further the understanding of the mechanisms involved in the drying of drops containing solids, and more specifically to formulate a mathematical model to predict the drying rate under conditions that might be encountered in spraydrying equipment. CONCLUSIONS AND SIGNIFICANCEThe filament thermocouple developed for this investigation provided valuable insight into the drying process not normally obtainable from a simple mass balance.

A new model for the drying of droplets containing suspended solids after shell formation

“…In contrast to several previous implementations which assumed constant dry crust properties, [e.g. 10,13], porosity variations in the dry shell are tracked in the present model.…”

“…The continuous phase is assumed to continue wetting the surface particles during the thickening regime, which means that evaporation proceeds at the external surface of the droplet. Consequently, the external radius of the particle continues to decrease according to (10). Assuming the volume fraction of solids in the thickening shell remains at the critical value, ε crit , the inner boundary of this shell at r = S (t) = R − T must move inwards according to…”

“…The dry shell model is, in its simplest form, a classical shrinking core type analysis whereby a central core of wetted material contracts as moisture evaporates from a receding interface, [2,10]. The dry shell is defined to be the region beyond this wetted core.…”

“…Here the fluid flow has been expressed in terms of the mass flux of solvent from the particle,ṁ , which is simply related to the rate of shrinkage by (10). The permeability is estimated using the Carmen-Kozeny relation, [11],…”

“…The most common way to handle particle formation is by a receding-interface, or shrinking core type approach [10,13,28,37]. Such models assume ideal shrinkage initially until a pre-specified critical moisture content is attained.…”