Mass-Transfer

Characteristic timescale for aqueous-phase diffusion within a droplet — Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 12, Eq. 12.75. The aqueous-phase diffusion timescale τ_da = R_p²/(π²D_aq) is the characteristic time for a dissolved species to diffuse throughout the interior of a droplet of radius R_p with aqueous-phase diffusivity D_aq. It is the e-folding decay time of the fundamental (slowest) mode of the spherical diffusion equation, whose lowest eigenvalue contributes the π² factor. Migrated from Aerosol.jl AqueousDiffusionTimescale.

Characteristic timescale for a gas to equilibrate with aqueous aerosol particles — Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 12, Eq. 12.147. The aqueous equilibration timescale τ_a is the solid-particle equilibration timescale τ_s scaled by the dimensionless buffering factor m_w/K_A, where m_w is the aerosol water mass concentration and K_A is an equilibrium constant. The factor accounts for the additional buffering effect of Henry's-law dissolution of the gas into the aerosol aqueous phase: a larger aqueous reservoir m_w relative to K_A lengthens the time to reach equilibrium. Migrated from Aerosol.jl AqueousEquilibrationTimescale.

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`.

Transition-regime condensation/evaporation model coupling mass and heat transfer via Dahneke (1983) correction factors β and β_q. Inlines DahnekeMassTransportCorrection (Eqs. 6.2, 3.6, 5.5) and DahnekeHeatTransportCorrection (Eq. 5.7) subsystems and adds the Maxwell flux equations (Eqs. 2.1–2.2) and Dahneke-corrected rates (Eqs. 5.4, 5.6). Migrated from Aerosol.jl src/dahneke_brownian_diffusion.jl:157.

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`.

Characteristic timescale for gas-phase diffusion of a species to an aerosol particle — Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 12, Eq. 12.49. The gas-phase diffusion timescale τ_dg = R_p²/(4·D_g) is the characteristic time for a gas-phase concentration perturbation to diffuse to the surface of a particle of radius R_p, given the gas-phase molecular diffusivity D_g of the species. It is one of the family of mass-transfer timescales in Ch. 12 — gas-phase diffusion, interfacial transport, aqueous-phase diffusion, aqueous-phase reaction — that are compared against one another to identify the rate-limiting step in gas-to-particle conversion: a short τ_dg means gas-phase diffusion is fast and not the bottleneck. The timescale grows quadratically with the particle radius and inversely with the diffusivity. Migrated from Aerosol.jl GasDiffusionTimescale.

Characteristic timescale to achieve equilibrium at the gas-particle interface for a gas exchanging with an aqueous aerosol droplet — Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 12, Eqs. 12.61-12.62. Two limiting regimes are computed. For very soluble gases the approach to interfacial equilibrium is controlled by interfacial (accommodation-limited) mass transport, τ_p_soluble ≈ R_p·H*·√(2π·M_A·R·T)/(3α) (Eq. 12.61). For low-solubility gases it is instead controlled by aqueous-phase diffusion within the droplet interior, τ_p_insoluble ≈ R_p²/(π²·D_aq) (Eq. 12.62). Migrated from Aerosol.jl InterfacialTimescale.

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).

Gas-phase mass transfer coefficient K_c to a falling raindrop, from Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 20 (Wet Deposition), Eq. 20.12. K_c is computed from a Sherwood-number correlation K_c = (D_g/D_p)·[2 + 0.6·Re^(1/2)·Sc^(1/3)], where the drop Reynolds number Re = ρ_air·U_t·D_p/μ_air measures the convective flow past the falling drop and the gas Schmidt number Sc = μ_air/(ρ_air·D_g) is the ratio of the momentum to the mass boundary-layer thickness. The leading 2 is the still-air diffusive limit (Sh→2 for an isolated sphere); the 0.6·Re^(1/2)·Sc^(1/3) term is the ventilation enhancement from the drop's fall. K_c sets the gas-uptake rate at the raindrop surface and feeds the below-cloud gas scavenging coefficient computed by the sibling GasScavengingCoeff / BelowCloudGasScavenging components. Migrated from AtmosphericDeposition.jl@e4468c79 src/seinfeld_pandis_2006_ch20.jl:60 (`MassTransferCoeff` @component). Algebraic (observed-only) system: K_c is the single algebraic output (the upstream component's lone `@variable`); D_g, D_p, U_t are input parameters and ρ_air_sp, μ_air_sp are the migrated upstream module `@constants`.

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`.