Ind. Eng. C h e m . Res. 1988,27, 105-110
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Design of Laminar Flow Condensers for Production of Monodisperse Aerosols Sotiris E. Pratsinis* Department of Chemical and Nuclear Engineering, University o f Cincinnati, Cincinnati, Ohio 45221 -01 71
Toivo T . Kodas IBM Almaden Research Center, S a n Jose, California 95120
Ajay Sood Alumina and Chemicals Division, A L C O A Laboratories, A L C O A Technical Center, Alcoa Center, Pennsylvania 15069
Production of aluminum sec-butoxide aerosol (a precursor to alumina powder) by vapor condensation on seed nuclei in laminar flows is studied theoretically. The effects of process parameters (condenser inlet and wall temperature, carrier gas flow rate) and condenser configuration (tubular and annular) on product aerosol characteristics (average size and polydispersity) and the condenser length required for complete vapor condensation are examined. Operation with large Lewis numbers (Le > 2) results in nearly monodisperse aerosol regardless of the carrier gas or condenser configuration provided that the condenser length is sufficient t o condense out most of the inlet vapor and that homogeneous nucleation is suppressed by the seed nuclei. Aerosol processes are attractive for production of ceramic powders with controlled size distributions and compositions. These processes are used for production of several commodity products such as carbon blacks, pigments, reinforcing agents, and lightguide preforms (Ulrich, 1984). Aerosol processes are also promising for large-scale production of ceramic powders used for manufacture of electronic components (alumina substrates for computer chips), automobile engine parts, and “adiabatic” diesel engines (Bowen, 1980; Isakoff, 1984). At present, these powders are made by grinding and wet chemistry (sol gel) processes (Sanders, 1984). A common aerosol method for production of ceramic powders begins with an organometallic or metallic chloride vapor. The vapor is cooled to form droplets by condensation which are then converted into the solid product by in situ chemical reaction with a gas. The key step in this sequence is formation of the liquid organometallic or metallic chloride aerosol by condensation since this step determines the size distribution of the product powder. Nearly monodisperse refractory oxide powders such as A1203and TiOz have been produced by using this method (Ingrebrethsen and Matijevic, 1980; Ingebrethsen et al., 1983). Several laboratory-scale studies of aerosol generation by condensation in laminar flows have been carried out (see review by Pesthy et al. (1983)). Particle formation by condensation has also been examined theoretically. Davis and Liao (1975) modeled aerosol formation by condensation on seed nuclei. Pesthy et al. (1983) improved and extended this theory to account for aerosol formation by homogeneous nucleation. Brock et al. (1986) examined aerosol condensation in a laminar coaxial jet, approximating the aerosol size distribution by a unimodal lognormal function. Previous experimental and theoretical studies were concerned with understanding the behavior of laboratory-scale systems; relatively little work has been done regarding scale-up. The goal of this paper is to identify the process parameters controlling aerosol production by condensation and to determine quantitatively their effect on product aerosol characteristics. Aluminum sec-butoxide (alkoxide) is studied here since it is a precursor to Also3, a compound commonly used in “high-tech” ceramic ap0888-5885/88/2627-0105$01.50/0
plications (Isakoff, 1984). Vapor condensation on seed nuclei is considered since this method has been shown to produce powders with characteristics such as high purity and narrow size distribution (Ingebrethsen and Matijevic, 1980) which are desirable for production of advanced ceramics (Bowen, 1980).
Model Alkoxide aerosol formation by condensation on uniform size seed nuclei is considered. Figure 1shows a schematic of the process. Alkoxide vapor is introduced into a carrier gas by a conventional or falling film boiler (vaporizer). The carrier gas-alkoxide vapor-seed nuclei mixture with temperature Td,alkoxide concentration C,l, seed nuclei concentration N‘, and seed radius a( enters the condenser tube of radius R’in fully developed laminar flow a t flow rate Q. Alkoxide vapor condensation takes place on the seed nuclei as the gas mixture is cooled. In this paper, alkoxide aerosol formation by condensation is studied in tubular and annular condensers under the following assumptions. 1. The flow is laminar and fully developed. 2. Free convective effects are not important. This is true as long as the process parameters (the Reynolds number and the product of Prandtl and Grashof numbers) are in the forced laminar flow regime (Re < 2000, GrPr < lo6)for a constant condenser wall temperature (Kays and Perkins, 1973). 3. The temperature and alkoxide vapor concentration at the condenser inlet are radially uniform, and the carrier gas is saturated with alkoxide vapor. 4. The temperature along the condenser walls is uniform and the alkoxide vapor is a t saturation conditions there. 5. Aerosol formation occurs by condensation onto monodisperse spherical seed nuclei that are perfectly wetted by the vapor. 6. Homogeneous nucleation is suppressed by the seed nuclei. This assumption cannot be checked a priori since the type of nucleation theory (for example, Becker-Doering or Lothe-Pound (Springer, 1978)) followed by aluminum sec-butoxide is unknown. The lack of a predictive theory for homogeneous nucleation precludes calculation of aerosol formation rates for most compounds unless experimental data for their nucleation rates are available. If the 0 1988 American Chemical Society
106 Ind. Eng. Chem. Res., Vol. 27, No. 1, 1988
for noncontinuum effects during aerosol growth (Chapter 9 of Friedlander (1977)) 1 + Kn F= (5) 1 + 1.71Kn + 1.333Kn2 The alkoxide vapor concentration in equilibrium with an alkoxide droplet of radius a’is obtained from the Kelvin relation (Chapter 8 of Friedlander (1977))
Figure 1. Schematic of the laminar flow aerosol condenser.
nucleation rate is known, then this assumption can be checked by including new particle formation in the model (see, for example, Pratsinis et al. (1986)). 7. The physical properties of the carrier gas are not altered by the alkoxide vapor and aerosol. This is a valid assumption as long as the volume fraction of the condensing species (here, alkoxide) is much smaller than that of the carrier gas. 8. Heat conduction and alkoxide vapor diffusion in the axial direction are negligible compared to convection (Pe,, Pe, >> 1). 9. The latent heat of condensation does not affect the temperature distribution in the condenser (/3
