PARTICLE MORPHOLOGY- AND KNUDSEN TRANSITION-EFFECTS ON THERMOPHORETICALLY DOMINATED TOTAL MASS DEPOSITION RATES FROM “COAGULATION-AGED” AEROSOL POPULATION

Abstract

Smokes or mists of industrial and environmental interest are typically comprised of particles both large and small compared to the prevailing gas mean-free-path. This fact complicates accurate predictions of, say, total mass deposition rates to confining cold walls or immersed cooled objects by the mechanism of particle thermophoresis (with Sc⪢1) (across laminar—or turbulent-, forced—or natural—convection boundary layers) since particle thermophoretic diffusivities can be sensitive to the prevailing Knudsen number based on individual particle diameter. When taken into account over the entire particle size spectrum, this often reduces the contribution that the largest particles make to the total deposition rate, especially if they are excellent thermal conductors (e.g. unaggregated metals). In the present paper we extend previous results from this group [Rosner,1989, ‘Total mass deposition rates from polydispersed aerosols’. A.I.Ch.E. J. 34(1), 164–167; Rosner and Tassopoulos,1989, ‘Deposition rates from polydispersed particle populations of arbitrary spread’. A.I.Ch.E. J 35(9), 1497–1508; Rosner and Khalil, 1997, ‘Morphology effects on polydispersed aerosol deposition rates’. Trans. Amer. Nucl. Soc. 77 TANSAO 77-1-560, 425–427], to show how total mass deposition rates from a dilute flowing stream of coagulation-aged polydispersed spherical particles in the Knudsen transition regime can be conveniently predicted by systematically correcting results more easily calculated for the (hypothetical) reference case of ‘monodispersed’ spheres in the free-molecule limit at the same particle mass-loading, ΔT/T w , Reynolds-(or Grashof-) number and thermal conductivity ratio: k p /k g . For this purpose we carry out “once-and-for-all” quadratures over the Talbot et al. (1980) “transition-regime” thermophoretic coefficient function, convoluted with appropriate quasi-self-preserving particle size distribution (PSD-) functions, using recent information on the effective spreads ( σ g,eff ) of these near-log-normal PSDs associated with Brownian coagulation in the transition regime (Otto et al., 1994). This leads us to rational, “universal” deposition rate ratio correlations of our formally exact quadrature results, expressible in terms only of a prevailing Knudsen number based on mean particle size in the population, and the intrinsic thermal conductivity ratio: κ≡k p /k g . The availability of these new computational results and dimensionless correlations, remarkably applicable to both laminar and turbulent boundary layer particle transport and natural or forced-convection, will dramatically simplify and accelerate such multi-size particle thermophoretically dominated aerosol deposition rate calculations in a wide variety of engineering applications. While a comprehensive theory for aggregate thermophoresis is not yet available (see, e.g. Rosner et al., 1991), provisional results are also included here for the morphologically opposite limiting case of aggregated particles (fractal morphology; not “fully dense” spheres). Our results indicate that the thermophoretic deposition rates of aggregates of conductive materials will remain high at all Knudsen numbers due to the poor effective thermal conductivity of such aggregates.