Aerosol Capture in Granular Beds in the Sedimentation and Diffusion Dominated Regimes

Abstract

Single grain capture efficiencies η for low speed gas flow through clean granular beds are reported. The aerosol particles were liquid dioctyl phthalate droplets ranging in diameter D _p from 0.15 to 4.7 μm. The grains were spheres of diameter D _G equal to 2.13, 3.69, or 15.6 mm and crushed oil shale rock with volume equivalent spherical diameter of 2.2 or 17 mm. The superficial gas velocity was downward and varied from 2.5 to 80 mm/s. Sedimentation and Brownian diffusion are the dominant capture mechanisms for these conditions. Consequently, the Gravity number Grv = ρ_pD² _pC_pg/18μU and the Peclet number Pe = D_GU/ D _p=3πμD_pD_GU/KTC_p are important dimensionless groups for correlating data. An approximate solution to the convective diffusion equation for point particles shows that η/Grv is a function of the combination 2^1/3A^1/3Pe^−2/3Grv⁻¹ only, when Grv « 1 and Pe » 1. A(α_G, Re) is a known function of the fraction solids α_G in the bed and the grain Reynolds number Re = ρD_GU/μ. Our data are successfully correlated by this approach. In the sedimentation dominated regime, theory (η=Grv) is in quantitative agreement with the data. In the diffusion dominated regime, theory (η = 3.97 A^1/3 Pe^−2/3) gives quantitaive agreement with the data, provided the numerical coefficient 3.97 is changed to 2.4. When capture efficiencies for both sedimentation and diffusion are very small (of order 0.001), measured efficiencies are several times larger than the predictions for point particles. If this increase is attributed to interception, then the present theory, extended to include interception, significantly underestimates its influence at small values of the interception number R=D_p/D_G. The discrepancy may be due to deficiencies of present flow models or to some other weak capture mechanism coming into play. Results obtained for beds of spheres can be applied to beds of crushed shale rock, provided a suitable “effective” grain diameter is chosen.