Chemical Reactions with Single Microparticles
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and ammonia gas. As the reaction proceeded the reaction rate was greatly reduced by the formation of crystalline ammonium phosphate at the droplet surface. Similar weight gain experiments were performed by Straubel and Straubel13 for HCl reactions with ZnCo3 • 3Zn(OH)2 and with Na 2 S 2 0 3 • 5H 2 0, but no attempts were made to interpret the data to obtain reaction velocity constants or other kinetics information. Experimentally, it has become possible to perform précise measurements on single aérosol droplets by means of electrodynamic and electrostatic balances, which are outgrowths of the classical Millikan oil drop experiment. Davis14 surveyed the principles and applications of thèse balances, and Arnold15 reviewed the work related to the spectroscopy of single levitated micrometer-sized particles, which is based on such balances. The electrodynamic balance with light-scattering capabilities can be used to measure precisely the size, refractive index, mass, and numerous other properties of microdroplets in the 0.1 to 100 /j.m size range. By coupling a single-particle balance to a spectrometer it is also possible to study microparticle chemistry and chemical reaction rates. We will use the term "microparticle" to mean either solid particles or liquid droplets. This article will also examine the principles involved in processing microparticles and review récent developments in the study of microparticle reactions. Heat and Mass Transfer with Chemical Reaction in Aérosol Droplets In gênerai, the rate of a microparticle reaction is determined by the rates of
heat and mass transfer to the particle and also by the chemical reaction rate, but a small particle such as a métal alkoxide droplet may often be treated as a simple limiting case, as we will illustrate. That limiting case is a perfectly well-mixed isothermal reactor. Consider the chemical reaction between a soluble reactive gas B and a constant volume droplet of solvent A with radius a. The concentration of soluté in the droplet, CB, is governed by the unsteady state diffusion équation,
£ = ^B?)-^.c„,,a, where, for an irréversible homogeneous reaction, the depletion of reactant B is written in the form ¥(CA,CB) = /cm+nCA-"CB".
(2)
Hère km+n is the reaction rate constant, and CA is the concentration of reactant A in the droplet. Equation 1 must be solved subject to appropriate boundary and initial conditions, which may be written CB(r,0) = limr 2 —5(r,t) = 0, r->0
(3)
dr
and dC
DAB—C(a,t) = K c t p - - P(a, t)]
= § [ C : - C ( a , t ) ] , (4) where KG is the gas phase mass transfer coefficient, and H is Henry's law constant. We assume that Henry's law applies at the gas-liquid interface, that is, C(a,t) = C^ = Hp(a,t). Hère DAB is the diffusion coefficient for the soluté in the solvent, and p„ is the partial pressure of the reactive vapor in the bulk gas phase. For a sparingly soluble gas H is small, and Equation 4 approximates to C(a,t) = C * = Hp„. Zhang and Davis16 and Taflin and Davis17 studied mass transfer from microdroplets, and they recommended
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