A Theoretical Model for Deposition of Aerosols in Rising Spherical Bubbles due to Diffusion, Convection, and Inertia

Abstract

ABSTRACT. A novel approximate theoretical analysis is proposed whereby the deposition of aerosols in expanding and shrinking spherical bubbles rising in stagnant liquid due to the combined effects of molecular diffusion, convection, and inertia is modeled. The bubble internal circulation is assumed to be similar to Hill's vortex flow.Using the new method, parametric calculations representing conditions where bubbles remain spherical and nonoscillating, and diffusion, convection, and inertia are the dominant aerosol removal mechanisms, are performed, and the contribution of the inertial transport mechanism is discussed. It is also suggested that the common practice of using Fuchs's methodology, where aerosol fluxes resulting from different mechanisms are separately calculated using simple models and added together to find the total aerosol flux, is inadequate.

Transmission of Alkali Aerosols through Sampling Systems

“…For removal by inertia during internal circulation, the heavier particles try to follow a tangential direction starting from where they are located and are dislocated towards the gas-to-solvent interface. Inertia removal increases with the particle mass [37] and with decreasing bubble diameter. This effect enhances the mass transfer [41].…”

“…Hence, the solvent may be regarded as an infinite sink. Mass transfer can take place as diffusion (Brownian motion), convection, transport by inertia [37], or a combination of both. Diffusion of particles is considered to be similar to the diffusion of gases [38], however, any convective contribution will outperform the purely diffusive part [39].…”

Monte-carlo simulation of aerosol transport in rising spherical bubbles with internal circulation

“…4(a) -(c) also indicate that, in comparison with the present MonteCarlo model, the GY-1997 generally over estimates the contribution of inertial particle transport mechanism and this over-prediction becomes more signiÿcant as particle size and/or bubble size are increased. An issue that may contribute to the apparent over-prediction of inertial mechanism's contribution by the GY-1997 model is that the model assumes that particles essentially follow the bubble internal circulation streamlines, an assumption that does not apply to a zone surrounding the center of the bubble internal recirculation vortex with a characteristic dimension equal to 34:4 Pe −1=2 R B (Ghiaasiaan and Yao, 1997), where…”

“…(A.1) is not considered in the model of Ghiaasiaan and Yao (1995), referred to as GY-1995 below, but is included in Ghiaasiaan and Yao (1997) (GY-1997). Both models account for the convective particle removal resulting from bubble growth and shrinkage.…”

“…This discrepancy is due to the coupling among various mechanisms that can complicate their cumulative contribution. For example, when Brownian and inertial mechanisms are both signiÿcant (Ghiaasiaan & Yao, 1997), inertial particle motion can result in a particle concentration gradient inside the bubble that is in fact favorable to particle di usion towards the interior and away form the bubble surface. Experimental veriÿcation of these models is di cult, however, and would require measurements involving individual bubbles.…”