Modeling of particle formation by spray pyrolysis using droplet internal circulation ☆ Morteza Eslamian, Nasser Ashgriz ⁎ Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, Ontario, Canada M5S 3G8 Available online 17 May 2006 Abstract A mathematical model is developed to predict the morphology of powders prepared by spray pyrolysis process. For high velocity solution droplets, the contours of constant solute concentration and temperature coincide with the streamlines. Based on this fact, the liquid phase transport equations are simplified and solved, numerically. Variation of droplet surface temperature and solute mass fraction versus time are presented. In addition, the temperature and the solute mass fraction distributions within the droplet are provided. Using the solute mass fraction distribution, the model predicts whether the final particle is fully-filled or hollow with two cavities. © 2006 Elsevier Ltd. All rights reserved. Keywords: Droplet evaporation; Spray drying; Spray pyrolysis; Internal circulation 1. Introduction Droplet evaporation is a key process in spray drying and pyrolysis. The properties of powders produced by spray drying and pyrolysis strongly depend on the droplet evaporation which is determined by the process precursors and the operating conditions. Understanding the thermal history of the evaporating droplets in the process, and the effects of the operating parameters are important to the production of desired particles. Droplet evaporation is also of significant importance in the combustion of fuel droplets. As such, droplet evaporation process has been the subject of many studies (e.g. [1–8]). If the relative velocity of the droplet and the surrounding gas is low, the droplet evaporates in a spherically symmetric manner. For instance, in ultrasonic atomization, in which a mist of low velocity droplets is generated, it is reasonable to assume that the evaporation is spherically symmetric; therefore, it is very likely that the final particles have symmetric crusts. On the other hand, if the relative velocity of the moving droplet and the surrounding air is high, the internal motion of the fluid may change the droplet evaporation rate. Although, the droplet internal motion has been considered in fuel evaporation models (e.g. [2,3]), it is usually ignored in spray drying and pyrolysis models (e.g. [6,7]). As such, the purpose of the present article is to develop a spray pyrolysis model, which considers the effect of droplet internal circulation on the evaporation process. To model the internal circulation, Hill's vortex approximation is employed. Then assuming that the liquid phase Pe number is high, the concentration and energy equations for the droplet interior are developed. The equations are incorporated into a computer code. Finally, the numerical results are presented and discussed. International Communications in Heat and Mass Transfer 33 (2006) 863 – 871 www.elsevier.com/locate/ichmt ☆ Communicated by W.J. Minkowycz. ⁎ Corresponding author. E-mail address: ashgriz@mie.toronto.edu (N. Ashgriz). 0735-1933/$ - see front matter © 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2006.04.002