Mass_transfer

Dahneke transition-regime correction factor f_D for gas-particle mass transfer. f_D is the ratio J/J_c of the actual particle-surface flux to the continuum-regime flux (Seinfeld & Pandis 2006, Chapter 12, Eq. 12.42): f_D = (1 + Kn) / (1 + 2 Kn(1 + Kn) / α). In the continuum limit (Kn ≪ 1) f_D → 1, recovering J_c with no correction; in the free-molecular limit (Kn ≫ 1) f_D ≈ α / (2 Kn) → 0, reflecting strong reduction in flux for very small particles or very long mean free paths. Migrated from Aerosol.jl src/mass_transfer.jl `Dahneke`.

Fuchs-Sutugin transition-regime correction factor for aerosol mass transfer. f_FS = J/J_c is the ratio of the actual flux to the continuum-regime flux J_c; it interpolates between f_FS → 1 in the continuum limit (Kn ≪ 1) and f_FS → 0 in the free-molecular limit (Kn ≫ 1). The formula f_FS = 0.75α(1+Kn)/(Kn²+Kn+0.283Kn·α+0.75α) (Seinfeld & Pandis 2006, Chapter 12, Eq. 12.43) is the most widely used semi-empirical interpolation across the full Knudsen number range, and extends the original Fuchs (1934) result with an explicit accommodation-coefficient correction due to Sutugin. Migrated from Aerosol.jl src/mass_transfer.jl `FuchsSutugin`.

Knudsen number Kn = λ/R_p — the ratio of the gas mean free path λ to the particle radius R_p. Kn determines the transport regime: Kn ≪ 1 (continuum, Fick's law applies), Kn ≫ 1 (free-molecular, kinetic theory applies), Kn ~ 1 (transition regime, interpolation formulas such as Fuchs-Sutugin required). At standard atmospheric conditions λ ≈ 65 nm; Kn ≈ 0.65 for a 100 nm particle and Kn ≈ 0.0065 for a 10 µm droplet. Migrated from Aerosol.jl src/mass_transfer.jl `KnudsenNumber`.

Complete transition-regime mass transfer model combining mean molecular speed, air density, mean free path, Knudsen number, Fuchs-Sutugin correction, and continuum-regime flux to produce the transition-regime corrected molar flow rate J for particle growth/evaporation across all Knudsen number regimes (Seinfeld & Pandis 2006, Chapter 12, Sections 12.1.1–12.1.4, Eqs. 12.12, 12.24, 12.31, 12.43). Migrated from Aerosol.jl src/mass_transfer.jl `MassTransfer` (esm-44h).

Combined gas-phase and interfacial mass transfer coefficient k_mt for gas-particle exchange. k_mt is the inverse of the total resistance to mass transfer, which is the sum of two resistances in series: (1) gas-phase diffusion resistance tau_g = R_p²/(3 D_g), and (2) interfacial resistance tau_i = (R_p/3α) √(2πM_A/(RT)) arising from the finite accommodation probability and molecular speed. The reciprocal relation k_mt = 1/(tau_g + tau_i) (Seinfeld & Pandis 2006, Chapter 12, Eq. 12.116) determines the overall rate at which a gaseous species is transferred to or from the particle surface. Migrated from Aerosol.jl src/mass_transfer.jl `MassTransferCoefficient`.

Continuum-regime molar flux of a gas species to a spherical particle. In the continuum limit (Kn ≪ 1) the steady-state diffusive flux is governed by Fick's law on a spherical geometry: J_c = 4πR_p D_g (c_∞ − c_s) (Seinfeld & Pandis 2006, Chapter 12, Eq. 12.12). A positive J_c indicates net uptake (c_∞ > c_s); a negative value indicates net evaporation or desorption (c_s > c_∞). Migrated from Aerosol.jl src/mass_transfer.jl `MaxwellianFlux`.

Mean free path of gas molecules in air for aerosol mass transfer. Uses the kinetic-theory relation λ = 2μ/(ρ_air c̄_air) where μ is the dynamic viscosity, ρ_air = PM_air/(RT) is the ideal-gas air density, and c̄_air = √(8RT/(πM_air)) is the mean molecular speed of air (S&P 2006, Chapter 12, Section 12.1.3). The resulting λ is the mean free path used to compute the Knudsen number Kn = λ/R_p (see knudsen.esm) and hence the appropriate mass-transfer regime (continuum, transition, or free-molecular). At standard conditions (T=298.15 K, P=101325 Pa) λ ≈ 65 nm. Migrated from Aerosol.jl src/mass_transfer.jl `MeanFreePathMassTransfer`.

Mean molecular speed of gas molecules using kinetic theory (Seinfeld & Pandis 2006, Chapter 12, Eq. 12.24). Computes c̄ = √(8kT/(πm_A)) where m_A = M_A/N_Av is the molecular mass and k_B, N_Av are folded as numeric literals. Migrated from Aerosol.jl src/mass_transfer.jl `MeanMolecularSpeed` (esm-1i9).

Rate of change of particle radius due to condensation or evaporation of a trace gas. Models diffusion-limited radial growth in the continuum regime via Eq. 12.14 of Seinfeld & Pandis (2006): dR_p/dt = (D_g M_A / (ρ_p R_p)) (c_∞ − c_s). The quadratic-in-R_p growth law R_p(t)² = R_p0² + 2Kt (K = D_g M_A (c_∞ − c_s)/ρ_p) is the classical result for condensation onto an absorbing sphere in the continuum limit. Migrated from Aerosol.jl src/mass_transfer.jl `ParticleGrowthRate`.

Effective uptake coefficient γ for gas-particle mass transfer. γ is the net probability that a gas molecule striking the particle surface is irreversibly taken up; it accounts for three resistances in series: (1) gas-phase diffusion to the surface (term_diff), (2) surface accommodation (term_acc), and (3) aqueous-phase reaction-diffusion within the droplet (term_rxn). The reciprocal relation 1/γ = term_diff + term_acc + term_rxn (Seinfeld & Pandis 2006, Chapter 12, Eq. 12.121) expresses resistances additively, analogous to resistors in series. Migrated from Aerosol.jl src/mass_transfer.jl `UptakeCoefficient`.