Brownian-Diffusion

Brownian (Stokes-Einstein) diffusion coefficient for aerosol single-particle dynamics. Migrated from Aerosol.jl@c8c640bb src/single_particle_dynamics.jl:172 (`BrownianDiffusion` @component). Computes the Brownian diffusivity D of a particle via the Stokes-Einstein relation with Cunningham slip correction (Seinfeld & Pandis 2006, Chapter 9, Eq. 9.73).

Gravitational settling velocity and Brownian diffusivity of an aerosol particle, from Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 19 (Dry Deposition). Two algebraic outputs are computed from the particle and air properties. The settling (terminal) velocity v_s = rho_p*D_p^2*g*C_c/(18*mu) (Eq. 19.18) is the steady gravitational drift speed of a particle in the Stokes (low-Reynolds-number) regime, where aerodynamic drag balances gravity; the Cunningham slip correction factor C_c (>= 1) accounts for the non-continuum reduction in drag when the particle diameter approaches the mean free path of air. The Brownian diffusivity D_diff = k_B*T*C_c/(3*pi*mu*D_p) (Eq. 19.20) is the Stokes-Einstein diffusion coefficient describing the particle's thermal random walk. The two quantities have opposite size dependence -- v_s grows as D_p^2 while D_diff falls as 1/D_p -- which is the physical origin of the dry-deposition-velocity minimum for accumulation-mode (~0.1-1 um) aerosol: such particles settle too slowly to deposit gravitationally yet are too large to diffuse efficiently to the surface. Both quantities feed the Zhang et al. (2001) quasi-laminar resistance and the overall particle dry deposition velocity computed by the sibling sp_ch19 components. Migrated from AtmosphericDeposition.jl@e4468c79 src/seinfeld_pandis_ch19.jl:182 (`ParticleSettling` @component). Observed-only algebraic model: rho_p, D_p, mu, T, C_c are input parameters, g/k_B/pi_val are physical-constant parameters, and v_s and D_diff are the two algebraic outputs, each fixed by one equation with no time derivative.