Modelling the morphological evolution of nanosuspension droplet in constant-rate drying stage

A novel mathematical model of constant-rate stage of nanosuspension droplet drying is proposed. In contrast to previously published literature studies, the developed model considers two morphologically different periods of the constant-rate drying: before the shell formation and after the shell formation; the latter was named “transition period”. The point of initial “locking” between nanoparticles on the droplet surface and beginning of the shell formation is associated with theoretical maximum of solid volume fraction. It is postulated that shrinking and thickening shell of nanoparticles occurs fast, and thus the shell virtually remains submerged in the liquid during the overall transition period. Because of the submerged shrinking shell, in the transition period, the evaporation process still takes place from the droplet surface and the drying rate remains unchanged as it was before the shell formation. Correspondingly, the droplet temperature retains at the level of equilibrium evaporation temperature. The developed theory was successfully validated by the published experiment of silica nanosuspension droplet drying. Finally, the developed model proposes a simple morphology criterion based on comparison between the calculated droplet volume at the end of transition period and the corresponding volume of solid final particle with the given porosity.