Pergamon Inf. J. Heat Mass Transfer. Vol. 38, No. 12. 2259-2267, 1995 pp. CopyrIght 0 1995 Elsevier Science Ltd Printed in Great Britam All rights reserved 0017-9310195 $9.50+0.00 0017-9310(94)00337-8 Evaporation of liquid droplets containing small solid particles T. ELPERIN and B. KRASOVITOV Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering, Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel zyxwvutsrqponmlkjihgfedcbaZ (Received 17 February 1994 and injinalform I October 1994) Abstract-Evaporation of a liquid droplet containing small solid particles (slurry droplets) is analyzed in a quasi-steady approximation. The developed model takes into account effects of compressibility and filtration of a gas-vapor mixture within the porous shell. It is shown that in the case of small temperature differences Ln the neighborhood of a slurry droplet at the second stage of drying (evaporation through a porous shell), the regime of slow evaporation and saturation (negligibly small drying rate) occurs. In the case of high temperature differences in the neighborhood of a slurry droplet at the second stage of drying, the pressure of the gas-vapor mixture within the porous shell significantly increases leading to the fragmentation of a porous shell. The comparison of the proposed model with the diffusion model, which neglects the Stefan’s flux shows that the diffusion model incorrectly describes evaporation of a slurry droplet at the final stage of drying. 1. INTRODUCTION Evaporation of droplets containing small solid par- ticles (slurry droplets) is encountered in various engin- eering fields, e.g. pharmaceutical industry, bioen- gineering, food industry [l-3]. Coal-water slurries are used as a liquid fuel for boilers [4, 51. Moreover aero- sol generation of materials has seen many new devel- opments in recent years. One of the new applications of this technology is spray pyrolysis. Spray pyrolysis is an aerosol process commonly used to form a wide variety of materials in powder form, including metals, metal oxides, nonoxide ceramics, superconducting materials, fullerenes, and nanophase materials [6]. In spite of the importance of slurry droplet evaporation for engineering applications there are few publications analyzing this problem. The purpose of this research is to develop a comprehensive model for slurry droplet evaporation and drying. In the literature the problem of evaporation of droplets containing small solid par- ticles is treated with the aid of the two models : (1) droplet wit:h crust [7-lo] ; (2) droplet with bubble [ll, 121. Both models consider the evaporation and drying of slurry droplets to occur in two stages (see Fig. 1). During the first stage, immediately after the injection of a slurry droplet into the ambient hot air, the droplet is assumed to be composed mainly of liquid and its evaporation rate is assumed to be controlled by the gas phase resistance. During evaporation the amount of liquid mass, ln,, decreases while the solid mass remains constant and droplet diameter continuously shrinks. At some critical solid-liquid mass ratio (m&m,), the discrete insoluble solid particles form an agglomerate (or cannot contract anymore), while the voids between particles are still filled with liquid. At this moment, which is assumed to occur at the pre- specified critical solid-liquid mass ratio, the second stage of drying begins. In ref. [7] this critical mass ratio for coal-water and coal-lime slurry droplets was calculated to be 5.35. This value was obtained from a minimum void fraction attained in packing of spheri- cal particles. Since the densities of solid particles and liquid may differ considerably, it is more convenient to employ the notion of the critical solid-liquid volume ratio 6 = VJV,. The first stage of drying is assumed to occur when 6 < 6, (where 6, is value of critical solid-liquid volume ratio). When 6 = 6, the second stage of drying begins. During the second stage of drying the process is determined by the ambient conditions (ambient tem- perature, pressure etc.). If the ambient temperature is in the range 2@2OO”C, the drying rate is not large. In this case, evaporating liquid flows through the porous spherical shell between r, and r,, where ri and r0 are inner and outer radii of the solid shell. Mass flux of the volatile species depends primarily on the per- meability of the formed porous crust for the passage of vapor and heat and on the parameters of the ambi- ent gas. In ref. [7] this flux was calculated from the following equation, which considers a Stefan-type diffusion : _ MAP, ln PT - PYI R*T,,, PT -pYO’ (1) In equation (l), CI is the void fraction of the dry crust, and the exponent b is assumed to be equal to 1, T,,, is the average temperature defined as TaYe = 0.5 2259