Knudsen-Number

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 Brownian coagulation rate constant K for two aerosol particle species using the Dahneke (1983) non-continuum correction formula (Eqs. 8.8, 8.13, 8.15). Computes particle masses, Stokes friction coefficients, Einstein diffusion coefficients, mean thermal velocities, mutual transport quantities, collision radius, diffusion Knudsen number Kn_D, continuum-limit coagulation constant K_o, and the Dahneke non-continuum correction β₂ as intermediate observed variables before assembling K. Migrated from Aerosol.jl src/dahneke_brownian_diffusion.jl:235.

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.

Correction factor β_q for heat conduction to a sphere, valid across all Knudsen numbers from the continuum to the free-molecular regime. Exactly parallel to the Dahneke mass transport correction. Computes the heat transfer Knudsen number Kn_K = 2κ/(c̄'n'_gas m_gas c_v r) and the correction factor β_q = (Kn_K+1)/(2Kn_K(Kn_K+1)/α+1). Migrated from Aerosol.jl src/dahneke_brownian_diffusion.jl:93.

Correction factor β for diffusional mass transport to a sphere, valid across all Knudsen numbers from the continuum to the free-molecular regime (Dahneke 1983, Eq. 5.5). Computes the mean thermal velocity c̄, diffusional mean-free-path ℓ_D, diffusion Knudsen number Kn_D, and the correction factor β = (Kn_D+1)/(2Kn_D(Kn_D+1)/δ_m+1) as purely algebraic observed variables. Migrated from Aerosol.jl src/dahneke_brownian_diffusion.jl:33.

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`.