Theoretical Foundation of the Relationship between Three Definitions of Effective Density and Particle Size

Abstract

Effective density (ρe) is universally used in atmospheric science as an alternative measure of the density (ρ) of aerosol particles, and its definitions can be expressed in terms of the particle mass (mp), ρ, mobility diameter (Dm), vacuum aerodynamic diameter (Dva), and dynamic shape factor (χ), as ρeI = 6mp/(π∙Dm3), ρeII = ρ/χ, and ρeIII = Dva/Dm. However, the theoretical foundation of these three definitions of ρe is still poorly understood before their application. Here, we explore the relationship between ρe and aerosol size through theoretical calculation. This study finds, for the first time, that ρeI and ρeIII inherently decrease with increasing size for aspherical particles with a fixed ρ and χ. We further elucidate that these inherent decreasing tendencies are governed by χ, and the ratio of the Cunningham Slip Correction Factor of the volume-equivalent diameter to that of the mobility diameter (Cc(Dve)/Cc(Dm)), but not by ρ. Taking the variable χ into consideration, the relationships of ρeI and ρeIII to particle size become more complicated, which suggests that the values of ρeI and ρeIII have little indication of the size-resolved physicochemical properties of particles. On the contrary, ρeII is independent on size for fixed χ and ρ, which indicates that the change in ρeII with size can better indicate the change in morphology and the transformation of the chemical compositions of particles. Our new insights into the essence of three ρes provide an accurate and crucial theoretical foundation for their application.