Aerosol

Absorptive partitioning model for equilibrium gas–particle partitioning of semivolatile organic compounds. A compound distributes between the gas phase and an absorbing organic aerosol phase according to a mass-based partition coefficient K_om and the total absorbing organic aerosol mass C_oa. From Seinfeld and Pandis (2006), Chapter 9, Section 9.4, Equation 9.23.

Equivalent particle diameters for aerosol single-particle dynamics. Migrated from Aerosol.jl@c8c640bb src/single_particle_dynamics.jl:390 (`AerodynamicDiameter` @component). Computes the classical aerodynamic diameter D_ca (the diameter of a unit-density sphere with the same settling velocity) and its continuum-limit approximation (Seinfeld & Pandis 2006, Chapter 9, Eqs. 9.110 and 9.112).

ModelingToolkit implementation of a multi-modal lognormal atmospheric aerosol size distribution, from Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 8 ("Properties of the Atmospheric Aerosol"). The model represents the aerosol number, surface-area and volume distributions as a sum of three lognormal modes (Eq. 8.54), and reports the total number/surface/volume concentrations, the mode-1 Hatch-Choate diameters, and the vertical aerosol mass profile (Eq. 8.55). Migrated from Aerosol.jl AerosolDistribution. Purely algebraic: ten observed outputs, no differential states, an empty equations array. The upstream length-n_modes array parameters are scalarized at the default and documented n_modes = 3; default mode parameters are the Urban distribution of Table 8.3.

Combined aerosol population dynamics: condensation growth (DiameterGrowthRate) and Brownian coagulation (BrownianCoagulationCoefficient + MonodisperseCoagulation), coupled so that the Fuchs-form coagulation coefficient K_12 drives the number-concentration ODE and the shared temperature T and particle density ρ_p parameterize both growth and coagulation. Implements Seinfeld & Pandis (2006) Ch. 13 Eqs. 13.11-13.13 (condensation), 13.47 and Table 13.1 (coagulation coefficient), and 13.65-13.67 (number-concentration dynamics). Migrated from Aerosol.jl src/dynamics.jl:279 (esm-540).

Extinction, scattering, and absorption coefficients for a monodisperse aerosol population, from Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 15, Eqs. 15.6 and 15.27-15.30. For a monodisperse population the bulk optical coefficients (b_ext, b_scat, b_abs) are the product of the single-particle cross-section area (pi/4)*D_p^2 times the number concentration N times the corresponding Mie efficiency (Q_ext, Q_scat, Q_abs). The single-scattering albedo omega = b_scat / b_ext completes the optical description. The Mie efficiencies Q_ext and Q_scat are accepted as input parameters (their default values correspond to the Mie solution at D_p = 0.5 um, lambda = 550 nm, n_refr = 1.5, k_refr = 0 using the Bohren & Huffman algorithm). The size parameter alpha = pi * D_p / lambda is computed as an algebraic observed output for reference. Migrated from Aerosol.jl AerosolExtinction.

Aerosol layer radiative forcing from two-stream scattering-absorbing model — Seinfeld & Pandis (2006) Ch. 24 §24.1, Eqs. 24.1–24.10.

Aerosol scavenging by cloud droplets (Seinfeld & Pandis 2006, Eqs. 17.84-17.92). Computes mass and number scavenging ratios and the scavenging coefficient for a monodisperse cloud-droplet population.

Correction factor Q for the aqueous-phase reaction rate when intra-droplet diffusion limits access to the reactive interior (Seinfeld & Pandis 2006, Chapter 12, Eqs. 12.105 and 12.110). Computes the dimensionless Hatta number q = R_p √(k_rxn/D_aq) and the corresponding correction factor Q = 3(q·coth q − 1)/q², which scales the effective reaction rate from the well-mixed limit (Q = 1) down toward zero as the droplet becomes increasingly diffusion-limited. Migrated from Aerosol.jl src/aqueous_transport.jl:14.

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.

Coupled gas-aqueous chemical equilibrium for cloud droplets and aerosol water. Migrated from Aerosol.jl@c8c640bb src/aqueous_equilibria.jl:642. Composes WaterEquilibrium, CO2Equilibria, SO2Equilibria, NH3Equilibria, HNO3Equilibria, H2O2Equilibria, and O3Equilibria via a quadratic charge-balance approximation for H+. Reference: Seinfeld & Pandis (2016) Ch. 7 §7.3.

BET (Brunauer-Emmett-Teller) adsorption isotherm for multilayer adsorption. Extends the Langmuir model to include formation of additional molecular layers, assuming each adsorbed molecule can serve as an adsorption site for the next layer. From Seinfeld and Pandis (2006), Chapter 14, Section 14.5.3, Equation 14.45.

Binary aqueous molality of an inorganic salt as a function of relative humidity, using the 5th-order polynomial fit from Table 7 of Fountoukis and Nenes (2007). The polynomial m_aw(RH) = (k_0 + k_1*RH + k_2*RH^2 + k_3*RH^3 + k_4*RH^4 + k_5*RH^5) * m_one is used in Equation 16 of ISORROPIA II to compute the ZSR water content contribution from each salt. Multiple BinaryMolality instances (one per salt) are composed into the Aqueous component. Migrated from Aerosol.jl src/isorropia/aqueous.jl BinaryMolality (esm-406).

Brownian coagulation coefficient K_12 for two particles using the Fuchs interpolation formula (Seinfeld & Pandis 2006, Table 13.1). Valid across the continuum, transition, and free-molecular regimes. Computes Knudsen numbers, Cunningham slip corrections, Brownian diffusion coefficients, mean thermal velocities, particle mean free paths, and the Fuchs interpolation parameters g_1, g_2 as intermediate observed variables before assembling K_12. Migrated from Aerosol.jl src/dynamics.jl:75.

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).

Simplified single-component classical nucleation rate (Eq. 11.47) from Seinfeld & Pandis (2006), Chapter 11. Computes only the steady-state nucleation rate J from the Zeldovich pre-exponential factor and the free-energy-barrier exponential. Use this component when the critical-cluster properties (i*, r*, ΔG*) are not needed; see the Nucleation component for the full coupled system.

Cloud albedo from two-stream approximation — Seinfeld & Pandis (2006) Ch. 24 §24.8.1, Eqs. 24.37–24.38.

Sensitivity of cloud albedo to cloud droplet number concentration (Twomey susceptibility) — Seinfeld & Pandis (2006) Ch. 24 §24.8.2, Eqs. 24.40–24.41.

Full cloud chemistry system with pH computed from the electroneutrality condition — Seinfeld & Pandis (2006), Ch. 7. The model composes AqueousEquilibria (quadratic charge-balance H⁺ from dissolved CO2, SO2, NH3, HNO3, H2O2, and O3 equilibria) with SulfateFormation (S(IV) oxidation kinetics via O3, H2O2, and Fe/Mn pathways). Unlike CloudChemistryFixedpH, which prescribes H⁺ from an external pH_input, this model self-consistently solves for the cloud-water pH from the trace-gas composition. Migrated from Aerosol.jl@c8c640bb src/cloud_chemistry.jl:73.

Simplified cloud chemistry system with pH as an externally prescribed input parameter — Seinfeld & Pandis (2006), Ch. 7. Instead of computing pH from the electroneutrality condition (as in the full CloudChemistry model), this variant takes pH_input as an input and derives H_plus = C_ref × 10^(-pH_input). This is useful for sensitivity studies that vary pH, for cases where unmeasured ions affect pH, or for quick calculations that bypass the full equilibrium solve. The model composes seven aqueous-equilibrium subsystems (WaterEquilibrium, CO2Equilibria, SO2Equilibria, NH3Equilibria, HNO3Equilibria, H2O2Equilibria, O3Equilibria) and the SulfateFormation oxidation kinetics module (O3, H2O2, and Fe/Mn-synergism pathways). All equilibria use van't Hoff temperature dependence from Table 7.4. Migrated from Aerosol.jl@c8c640bb src/cloud_chemistry.jl:269.

Dynamic cloud droplet chemistry: time evolution of sulfate concentration as S(IV) is oxidized to S(VI) via O3, H2O2, and Fe/Mn-catalyzed pathways (Seinfeld & Pandis 2006, Chapter 7, Eqs. 7.79-7.102). Gas-liquid equilibria (SO2, H2O2, O3) are assumed instantaneous; the sulfate ODE tracks the kinetic accumulation. Migrated from Aerosol.jl src/cloud_chemistry.jl:422.

Adiabatic cooling and cloud-base thermodynamics — Seinfeld & Pandis (2006), Ch. 17. Computes five purely-algebraic quantities that characterize when and where a lifted air parcel reaches its lifting condensation level (LCL): the dry adiabatic lapse rate Γ_d, the saturation vapor pressure p_sat (Magnus formula), the saturation mixing ratio w_vs, the dew-point temperature T_d (Eq. 17.43), and the LCL height h_LCL (Eq. 17.49). Migrated from Aerosol.jl CloudDynamics.

Kelvin effect on the equilibrium vapor pressure over a curved cloud droplet surface — Seinfeld & Pandis (2006), Ch. 17. Computes the Kelvin length parameter A_K = 4 σ_w M_w / (R T ρ_w) and the Kelvin saturation ratio S_K = exp(A_K / D_p), the factor by which surface curvature enhances equilibrium vapor pressure over a small droplet relative to a flat surface. Used as the curvature term in the Köhler equation (Eq. 17.27). Migrated from Aerosol.jl CloudKelvinEffect.

Cloud optical depth from liquid water content and droplet number concentration — Seinfeld & Pandis (2006) Ch. 24 §24.8.1, Eq. 24.36.

Composed cloud microphysics model (Seinfeld & Pandis 2006, Ch. 17). Flat composition of CloudDynamics (adiabatic thermodynamics, LCL height), IcePhysics (freezing point depression, ice nuclei), RainFormation (collision-coalescence, raindrop spectra), and AerosolScavenging (scavenging ratios and coefficient). Shared physical constants M_w and R unify CloudDynamics and IcePhysics. Ice particle diameter (D_p_ice) and collector drop diameter (D_p_rain) are kept as independent parameters. Migrated from Aerosol.jl src/cloud_physics.jl:735 (esm-c8z).

Thermodynamic properties of water and aqueous solutions for cloud-physics calculations: temperature offset, specific heat of liquid water, latent heats of vaporization and melting, surface tension, and saturation vapor pressure over water and ice. Based on Seinfeld & Pandis (2006), Chapter 17, Equations 17.1–17.6 and Table 17.2. Migrated from Aerosol.jl src/cloud_physics.jl:15.

CO2 dissolution and dissociation equilibria with van't Hoff temperature dependence (Seinfeld & Pandis Ch 7 §7.3.2, Eqs 7.14–7.24). Migrated from Aerosol.jl@c8c640bb src/aqueous_equilibria.jl:140 (`CO2Equilibria` @component). Parameterized as observed-only: T, H_plus, p_CO2 are inputs and the carbonate-system species (CO2_aq, HCO3-, CO3^2-, total dissolved C, effective Henry constant) are algebraic outputs.

Critical cluster properties for classical homogeneous nucleation theory following Seinfeld & Pandis (2006), Chapter 11, Equations 11.27, 11.35, 11.52, and 11.53. Computes the dimensionless surface tension parameter (theta), critical cluster size (i*), critical radius (r*), and free energy barrier (ΔG*) as purely algebraic functions of temperature, saturation ratio, surface tension, and molecular volume. Use this component for parameter sensitivity studies or when the full nucleation rate (ClassicalNucleationRate) is not needed.

Critical single-scattering albedo at which an aerosol layer transitions from cooling to heating — Seinfeld & Pandis (2006) Ch. 24 §24.2, Eq. 24.15.

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`.

Parameters for aerosol penetration through a fine capillary tube via convective diffusion (Dahneke 1983, Section 9). Computes the velocity-profile normalization factor σ and the dimensionless tube length z' = DL/(σv̄R²) from which the penetration fraction ϕ(z') = Σ B_i exp(−ω_i² z') can be evaluated using the tabulated eigenvalues in Tables 3–5 of the reference. Migrated from Aerosol.jl src/dahneke_brownian_diffusion.jl:372.

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.

ModelingToolkit implementation of the Desert atmospheric aerosol size distribution, from Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 8 ("Properties of the Atmospheric Aerosol"), Table 8.3. The Desert distribution is a preset of the multi-modal lognormal AerosolDistribution model: three lognormal modes (N = [726, 114, 0.178] cm^-3, D_g = [0.002, 0.038, 21.60] um, log10 sigma = [0.247, 0.770, 0.438]) — two fine modes plus a coarse mineral-dust mode at 21.6 um. The model represents the aerosol number, surface-area and volume distributions as a sum of the three modes (Eq. 8.54) and reports the total number/surface/volume concentrations, the mode-1 Hatch-Choate diameters, and the vertical aerosol mass profile (Eq. 8.55). Migrated from Aerosol.jl DesertAerosol, a preset wrapper around AerosolDistribution(3). Purely algebraic: ten observed outputs, no differential states, an empty equations array. The upstream length-n_modes array parameters are scalarized at n_modes = 3 with the Desert Table 8.3 mode parameters as defaults.

Diameter growth rate due to vapor condensation in the continuum regime (Seinfeld & Pandis 2006, Ch. 13, Eq. 13.11-13.13). Algebraic growth parameter A = 4·D_diff·M_i·Δp / (R_gas·T·ρ_p), algebraic growth rate I_D = A/D_p, ODE D(D_p) = I_D. Source: Aerosol.jl@c8c640bb:src/dynamics.jl:22.

5-bin discrete coagulation model for a monodisperse initial distribution with constant coagulation coefficient (Seinfeld & Pandis 2006, Ch. 13, Eqs. 13.59, 13.67, 13.71). Tracks the evolution of five k-mer bins (N1..N5) under Brownian coagulation. Source: Aerosol.jl@c8c640bb:src/dynamics.jl:221 (n_bins=5 instantiation, esm-isv).

Temperature-dependent deliquescence relative humidity (DRH) of a crystalline inorganic salt — Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 10, Equation 10.72. DRH is the relative humidity at which a crystalline salt spontaneously absorbs water and forms a saturated aqueous solution; it shifts away from its 298 K reference value with temperature according to the salt's enthalpy of solution and its solubility-vs-temperature polynomial. Migrated from Aerosol.jl DRHTemperature at the upstream default parameterization salt = :NH4NO3.

Diffusional growth rate of a cloud droplet by condensation of water vapor. Accounts for vapor-phase diffusion (D_v), the kinetic correction to the diffusivity (D_v'), thermal conductivity of air (k_a and k_a'), and the curvature + solute (Köhler) contributions to the equilibrium saturation ratio S_eq over the droplet surface. Output is the droplet-diameter growth rate dD_p/dt (m/s) from Seinfeld & Pandis (2006) Eq. 17.70. Source: Aerosol.jl@c8c640bb src/cloud_physics.jl:322 (mtk2esm-scaffolded, mdl-43a).

Coupled gas-phase and aqueous-phase mass balance for cloud droplet chemistry. Tracks the time evolution of bulk gas-phase partial pressure and aqueous-phase concentration, including gas-to-aqueous mass transfer and aqueous-phase chemical reaction (Seinfeld & Pandis 2006, Ch. 12, Eqs. 12.122-12.123). Migrated from Aerosol.jl src/aqueous_transport.jl:112.

Elemental carbon (EC) tracer method for estimating secondary organic carbon (OC) from measurements of total OC and EC. Primary OC is estimated as combustion-related OC (proportional to EC via the OC-to-EC ratio) plus noncombustion OC; secondary OC is the non-negative remainder. From Seinfeld and Pandis (2006), Chapter 14, Section 14.3.2, Equations 14.3–14.4.

Effective Henry's law constant for species that dissociate in water, accounting for the enhancement due to aqueous dissociation products. The effective constant H* exceeds the intrinsic H because dissolved dissociation products add to the total aqueous loading. Covers diprotic species (CO₂, SO₂) and monoprotic species (HNO₃, K₂=0). From Seinfeld & Pandis Chapter 7, Equations 7.24 (CO₂), 7.41 (SO₂), 7.61 (HNO₃).

Electrical mobility and migration velocity for aerosol single-particle dynamics. Migrated from Aerosol.jl@c8c640bb src/single_particle_dynamics.jl:273 (`ElectricalMobility` @component). Computes the particle charge q, the electrical mobility B_e relating particle velocity to electric-field strength, and the electrical migration velocity v_e of a charged particle in an electric field (Seinfeld & Pandis 2006, Chapter 9, Eqs. 9.49, 9.50 and 9.51).

A holder for elemental carbon (EC) concentrations in the atmosphere. By default it does not include any dynamics — EC is treated as a conserved tracer whose concentration is set as an initial condition and carried forward unchanged. The model carries particle physical properties (density, diameter, temperature, pressure) so that coupled models (e.g. Mie scattering, mass transfer) can access them through the shared system. Particle density default from Fierce et al. (2023).

Equilibrium constant parameterized by Equation 5 of Fountoukis and Nenes (2007): log K(T) = log K(T0) + H_coeff*(T0/T - 1) + C_coeff*(1 + ln(T0/T) - T0/T), where T0 = 298.15 K. Migrated from Aerosol.jl@c8c640bb src/isorropia/equilibria.jl:5 (`EqConst` @component). Parameters logK0, H_coeff, and C_coeff are reaction-specific values from Table 2 of Fountoukis and Nenes (2007). T is an input (driven by parent EquilibriumConstants in the coupled system); logK_eq is an algebraically observed output.

Aggregated equilibrium constants for ISORROPIA II. Composes 27 EqConst sub-components (r1...r27) from Table 2 of Fountoukis and Nenes (2007). Each ri.logK_eq(T) = logK0_i + H_i*(T0/T-1) + C_i*(1+ln(T0/T)-T0/T). A single T is broadcast to all subsystems via coupling equations. Migrated from Aerosol.jl@c8c640bb src/isorropia/equilibria.jl:22 (esm-y4v).

FHH (Frenkel-Halsey-Hill) adsorption isotherm for multilayer adsorption on flat surfaces governed by van der Waals forces. Relates adsorbed volume to the gas-phase saturation ratio via two empirical parameters. From Seinfeld and Pandis (2006), Chapter 14, Section 14.5.3, Equation 14.46.

ModelingToolkit implementation of the Free troposphere atmospheric aerosol size distribution, from Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 8 ("Properties of the Atmospheric Aerosol"), Table 8.3. The Free troposphere distribution is a preset of the multi-modal lognormal AerosolDistribution model: three lognormal modes (N = [129, 59.7, 63.5] cm^-3, D_g = [0.007, 0.250, 0.520] um, log10 sigma = [0.645, 0.253, 0.425]) — a nucleation/ultrafine mode at 7 nm plus two sub-micron accumulation modes. The model represents the aerosol number, surface-area and volume distributions as a sum of the three modes (Eq. 8.54) and reports the total number/surface/volume concentrations, the mode-1 Hatch-Choate diameters, and the vertical aerosol mass profile (Eq. 8.55). Migrated from Aerosol.jl FreeTroposphereAerosol, a preset wrapper around AerosolDistribution(3). Purely algebraic: ten observed outputs, no differential states, an empty equations array. The upstream length-n_modes array parameters are scalarized at n_modes = 3 with the Free troposphere Table 8.3 mode parameters as defaults.

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.

H2O2 gas-aqueous dissolution and (weak) dissociation equilibria with van't Hoff temperature dependence. Migrated from Aerosol.jl@c8c640bb src/aqueous_equilibria.jl:519 (`H2O2Equilibria` @component). Implements Seinfeld & Pandis Ch 7 §7.3.6: K_H(H2O2, 298 K) = 1.0×10⁵ M/atm, ΔH_sol = −14.5 kcal/mol; K_h1(H2O2, 298 K) = 2.2×10⁻¹² M (temperature-independent, very weak). Parameterized as observed-only: T, H_plus, and p_H2O2 are inputs; H_H2O2, K_h1, H2O2_aq, HO2_minus, H2O2_total, H_H2O2_eff are algebraic outputs.

Basic Henry's law equilibrium at fixed temperature (Seinfeld & Pandis 2006, Chapter 7, Eq. 7.3). Computes the aqueous-phase concentration C_aq = H_A × p_A, where H_A is the Henry's law constant at the reference temperature and p_A is the gas-phase partial pressure of species A. Migrated from Aerosol.jl src/henrys_law.jl `HenrysLaw` (esm-3ro).

Temperature-dependent Henry's law equilibrium for gas–liquid partitioning of soluble atmospheric species. Computes the temperature-corrected Henry's law constant H_T via the van't Hoff equation (Eq. 7.5), the aqueous concentration C_aq via Eq. 7.3, and the liquid-water distribution diagnostics w_L (Eq. 7.1), f_A (Eq. 7.7), and X_aq (Eq. 7.9). From Seinfeld & Pandis (2006), Chapter 7, Section 7.2.

HNO3 gas-aqueous dissolution and dissociation equilibria. Migrated from Aerosol.jl@c8c640bb src/aqueous_equilibria.jl:438 (`HNO3Equilibria` @component). Implements Seinfeld & Pandis Ch 7 §7.3.5 (Eq 7.53–7.54, 7.58, 7.61): K_H(HNO3, 298 K) = 2.1×10⁵ M/atm (temperature-independent, dH≈0), K_n1(HNO3, 298 K) = 15.4 M (temperature-independent). HNO3 is a strong acid (pKa ≈ −1.2) that essentially completely dissociates at all atmospheric pH values. Parameterized as observed-only: T, H_plus, and p_HNO3 are inputs; H_HNO3, K_n1, HNO3_aq, NO3_minus, HNO3_total, H_HNO3_eff are algebraic outputs.

Ice nucleation and ice-water equilibrium thermodynamics (Seinfeld & Pandis 2006, Eqs. 17.100-17.103). Computes freezing point depression for solutions, equilibrium freezing temperature from water activity, Kelvin curvature factor for ice particles, and empirical ice-nuclei concentration.

First indirect aerosol effect (Twomey effect): change in shortwave forcing from aerosol-induced increase in cloud droplet number concentration — Seinfeld & Pandis (2006) Ch. 24 §24.8.2, Eqs. 24.42–24.43.

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.

Kelvin effect on the equilibrium vapor pressure over a curved droplet surface — Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 10. Computes the Kelvin saturation ratio S = p_A/p°_A (Eq. 10.86), the factor by which surface curvature enhances the equilibrium vapor pressure of a small droplet relative to a flat surface: S = exp(2 σ M / (R T ρ_l R_p)). The enhancement is significant for nanometre-scale droplets and decays toward unity as the droplet radius grows. Migrated from Aerosol.jl KelvinEffect.

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`.

Köhler theory for cloud condensation nucleus (CCN) activation — Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., §17.3–17.4. Computes the equilibrium saturation ratio S_eq over a solution droplet of diameter D_p (Köhler equation, Eq. 17.50), the critical activation diameter D_pc, and the critical supersaturation sc. S_eq combines the Kelvin curvature enhancement (coefficient A = 4 M_w σ / (R T ρ_w)) and the Raoult solute suppression (coefficient B = 6 n_s M_w / (π ρ_w)); at D_p = D_pc the Köhler curve reaches its maximum and the droplet activates spontaneously. Migrated from Aerosol.jl src/cloud_physics.jl:232.

Langmuir adsorption isotherm for the formation of a monolayer of adsorbed molecules on particle surfaces. Assumes all adsorption sites are equivalent, no horizontal interactions, and uniform heat of adsorption. From Seinfeld and Pandis (2006), Chapter 14, Section 14.5.3, Equation 14.44.

ModelingToolkit implementation of the Marine atmospheric aerosol size distribution, from Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 8 ("Properties of the Atmospheric Aerosol"), Table 8.3. The Marine distribution is a preset of the multi-modal lognormal AerosolDistribution model: three lognormal modes (N = [133, 66.6, 3.1] cm^-3, D_g = [0.008, 0.266, 0.580] um, log10 sigma = [0.657, 0.210, 0.396]) — a dilute marine boundary-layer background with a nucleation mode, an accumulation mode, and a coarse mode at 0.58 um. The model represents the aerosol number, surface-area and volume distributions as a sum of the three modes (Eq. 8.54) and reports the total number/surface/volume concentrations, the mode-1 Hatch-Choate diameters, and the vertical aerosol mass profile (Eq. 8.55). Migrated from Aerosol.jl MarineAerosol, a preset wrapper around AerosolDistribution(3). Purely algebraic: ten observed outputs, no differential states, an empty equations array. The upstream length-n_modes array parameters are scalarized at n_modes = 3 with the Marine Table 8.3 mode parameters as defaults.

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`.

Mass transport limitation criteria for aqueous-phase chemistry (Seinfeld & Pandis 2006, Chapter 12, Eqs. 12.85, 12.86, 12.93). Computes the threshold values of k₁H* and k₁ below which gas-phase diffusion, aqueous-phase diffusion, and interfacial mass transfer do not limit the aqueous-phase reaction rate by more than 10%. Migrated from Aerosol.jl src/aqueous_transport.jl:53.

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 air molecules. Migrated from Aerosol.jl@c8c640bb src/single_particle_dynamics.jl:22 (`MeanFreePath` @component). Calculates the mean free path from dynamic viscosity, pressure, molecular weight, and temperature (Seinfeld & Pandis 2006, Chapter 9, Eq. 9.6).

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).

Mie theory scattering and extinction efficiencies, cross sections, and mass efficiencies for a spherical particle, from Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 15, Eqs. 15.3–15.6, 15.41–15.43. The size parameter α = π D_p / λ is algebraic; Q_ext and Q_scat (computed upstream by the Bohren–Huffman algorithm via @register_symbolic Mie functions, ESS gap gt-p3ep) are lifted to input parameters with Mie-computed defaults at D_p = 0.5 µm, λ = 550 nm, n_refr = 1.5, k_refr = 0. Q_abs, ω, the three cross sections (C_scat, C_abs, C_ext), and the three mass efficiencies (E_scat, E_abs, E_ext) are algebraic outputs. Migrated from Aerosol.jl MieScattering.

Total aerosol number concentration evolution for a monodisperse aerosol undergoing Brownian coagulation with constant coagulation coefficient (Seinfeld & Pandis 2006, Ch. 13, Eqs. 13.65-13.67). ODE: dN/dt = -K·N²/2; algebraic characteristic coagulation time τ_c = 2/(K·N₀). Source: Aerosol.jl@c8c640bb:src/dynamics.jl:178.

Ammonia gas-aqueous dissolution and dissociation equilibria with van't Hoff temperature dependence. Migrated from Aerosol.jl@c8c640bb src/aqueous_equilibria.jl:345 (`NH3Equilibria` @component). Implements Seinfeld & Pandis Ch 7 §7.3.4 (Eq 7.46–7.51) and Table 7.4. Parameterized as observed-only: T, H_plus, and p_NH3 are inputs; H_NH3, K_a1, K_w, OH_minus, NH3_aq, NH4_plus, NH3_total, H_NH3_eff are algebraic outputs.

ModelingToolkit implementation of ammonium nitrate (NH4NO3) gas-aerosol equilibrium from Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 10, Section 10.4.3. NH4NO3 is a semi-volatile aerosol species whose gas-particle partitioning depends strongly on temperature and relative humidity. The component evaluates three temperature- and humidity-dependent quantities: the natural log of the solid-phase dissociation constant ln(Kp) for NH3(g) + HNO3(g) <-> NH4NO3(s) (Eq. 10.91), the deliquescence relative humidity DRH of NH4NO3 (Eq. 10.88), and a phase indicator that is 1 when the ambient RH exceeds the DRH (aqueous aerosol) and 0 otherwise (solid aerosol). Migrated from Aerosol.jl NH4NO3Equilibrium. Purely algebraic: no differential states, three observed outputs and an empty equations array.

Gas-particle partitioning model for a secondary organic aerosol (SOA) compound that does not interact with preexisting aerosol. The compound condenses as a pure substance once the reacted ROG exceeds a threshold set by the saturation concentration; below the threshold all product remains in the gas phase. From Seinfeld and Pandis (2006), Chapter 14, Section 14.5.2, Equations 14.6–14.18.

Full coupled homogeneous nucleation system following classical nucleation theory from Seinfeld & Pandis (2006), Chapter 11. Derives saturation ratio and monomer concentration from partial pressures, then computes critical cluster properties (size, radius, free-energy barrier) and the nucleation rate J. Use this component when the full coupled system is needed; see ClassicalNucleationRate for a lighter variant that takes S and N_1 as direct parameters.

Ozone (O3) aqueous dissolution equilibrium via temperature-dependent Henry's law. Migrated from Aerosol.jl@c8c640bb src/aqueous_equilibria.jl:589 (`O3Equilibria` @component). Implements Seinfeld & Pandis Ch 7 Table 7.3: K_H(O3, 298 K) = 1.1×10⁻² M/atm, ΔH_sol = −5.04 kcal/mol. O3 does not ionize in water; dissolution is purely described by Henry's law with van't Hoff temperature dependence.

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`.

Particle mechanical mobility for aerosol single-particle dynamics. Migrated from Aerosol.jl@c8c640bb src/single_particle_dynamics.jl:230 (`ParticleMobility` @component). Computes the particle mobility B, which relates an external force on a particle to the steady drift velocity it produces; via the Einstein relation D = B k T it also fixes the Brownian diffusivity (Seinfeld & Pandis 2006, Chapter 9, Eq. 9.78).

ModelingToolkit implementation of the Polar atmospheric aerosol size distribution, from Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 8 ("Properties of the Atmospheric Aerosol"), Table 8.3. The Polar distribution is a preset of the multi-modal lognormal AerosolDistribution model: three lognormal modes (N = [21.7, 0.186, 3.0e-4] cm^-3, D_g = [0.138, 0.75, 8.6] um, log10 sigma = [0.245, 0.300, 0.291]) — a dilute accumulation mode plus two coarse modes characteristic of the very clean polar atmosphere. The model represents the aerosol number, surface-area and volume distributions as a sum of the three modes (Eq. 8.54) and reports the total number/surface/volume concentrations, the mode-1 Hatch-Choate diameters, and the vertical aerosol mass profile (Eq. 8.55). Migrated from Aerosol.jl PolarAerosol, a preset wrapper around AerosolDistribution(3). Purely algebraic: ten observed outputs, no differential states, an empty equations array. The upstream length-n_modes array parameters are scalarized at n_modes = 3 with the Polar Table 8.3 mode parameters as defaults.

Rain formation by collision and coalescence (Seinfeld & Pandis 2006, Eqs. 17.104-17.108). Computes collection efficiency, continuous accretion rate, and raindrop size distributions (Best CDF and Marshall-Palmer number density).

Rayleigh scattering coefficient and maximum visual range for a clean Rayleigh atmosphere. The scattering coefficient b_sg scales as λ^-4 (Seinfeld & Pandis 2006, Chapter 15, Problem 15.1A), and the maximum visual range x_v_max = 3.912/b_sg (Eq. 15.36). Both outputs depend only on temperature, pressure, and wavelength — no aerosol loading. Migrated from Aerosol.jl src/mie_scattering.jl `RayleighAtmosphere`.

Optical scattering, absorption, and extinction properties of small particles in the Rayleigh regime (size parameter α = πD_p/λ << 1), from Seinfeld & Pandis (2006) Atmospheric Chemistry and Physics, 2nd ed., Chapter 15, Eqs. 15.4, 15.5, 15.19, 15.21, and 15.41-15.43. Computes the size parameter α, the Clausius-Mossotti factor (m²-1)/(m²+2), and from them the Rayleigh scattering efficiency Q_scat, absorption efficiency Q_abs, extinction efficiency Q_ext, single-scattering albedo ω, and mass efficiencies E_ext/E_scat/E_abs. The two upstream @register_symbolic helper functions (rayleigh_m2_factor_real, rayleigh_m2_factor_imag) are resolved as closed-form algebraic AST, closing the gt-p3ep blocking gap. Migrated from Aerosol.jl src/mie_scattering.jl.

ModelingToolkit implementation of the characteristic timescale for aqueous-phase chemical reaction within a cloud droplet or wetted aerosol particle, from Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 12, Eqs. 12.76-12.78. The component reports two diagnostics for a first-order aqueous reaction: the aqueous-phase reaction timescale τ_ra = 1/k_rxn (Eq. 12.76), the e-folding time of a dissolved species consumed by a first-order reaction of rate constant k_rxn; and the gas-phase reference reaction timescale τ_rg = τ_ra/(H*·R·T) (Eq. 12.78), the same timescale referenced to the gas phase through the dimensionless effective Henry's law solubility H*·R·T. Migrated from Aerosol.jl ReactionTimescale. Purely algebraic: no differential states, two observed outputs and an empty equations array.

ModelingToolkit implementation of the Remote-continental atmospheric aerosol size distribution, from Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 8 ("Properties of the Atmospheric Aerosol"), Table 8.3. The Remote-continental distribution is a preset of the multi-modal lognormal AerosolDistribution model: three lognormal modes (N = [3200, 2900, 0.3] cm^-3, D_g = [0.020, 0.116, 1.800] um, log10 sigma = [0.161, 0.217, 0.380]) — a number-rich continental background of two fine modes plus a sparse coarse mode at 1.8 um. The model represents the aerosol number, surface-area and volume distributions as a sum of the three modes (Eq. 8.54) and reports the total number/surface/volume concentrations, the mode-1 Hatch-Choate diameters, and the vertical aerosol mass profile (Eq. 8.55). Migrated from Aerosol.jl RemoteContinentalAerosol, a preset wrapper around AerosolDistribution(3). Purely algebraic: ten observed outputs, no differential states, an empty equations array. The upstream length-n_modes array parameters are scalarized at n_modes = 3 with the Remote-continental Table 8.3 mode parameters as defaults.

ModelingToolkit implementation of the Rural atmospheric aerosol size distribution, from Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 8 ("Properties of the Atmospheric Aerosol"), Table 8.3. The Rural distribution is a preset of the multi-modal lognormal AerosolDistribution model: three lognormal modes (N = [6650, 147, 1990] cm^-3, D_g = [0.015, 0.054, 0.084] um, log10 sigma = [0.225, 0.557, 0.266]) — three sub-micron continental-background modes, with no coarse mode. The model represents the aerosol number, surface-area and volume distributions as a sum of the three modes (Eq. 8.54) and reports the total number/surface/volume concentrations, the mode-1 Hatch-Choate diameters, and the vertical aerosol mass profile (Eq. 8.55). Migrated from Aerosol.jl RuralAerosol, a preset wrapper around AerosolDistribution(3). Purely algebraic: ten observed outputs, no differential states, an empty equations array. The upstream length-n_modes array parameters are scalarized at n_modes = 3 with the Rural Table 8.3 mode parameters as defaults.

Terminal settling velocity and relaxation time for aerosol single-particle dynamics. Migrated from Aerosol.jl@c8c640bb src/single_particle_dynamics.jl:113 (`SettlingVelocity` @component). Computes the terminal settling velocity v_t and the relaxation time τ (time constant for velocity adjustment) for a spherical particle falling under gravity in a viscous fluid (Seinfeld & Pandis 2006, Chapter 9, Eqs. 9.38 and 9.42).

Comprehensive composed model combining all single-particle aerosol dynamics equations. Migrated from Aerosol.jl@c8c640bb src/single_particle_dynamics.jl:440 (`SingleParticleDynamics` @component). Composes MeanFreePath, SlipCorrection, and SettlingVelocity as coupled subsystems, then adds the Brownian diffusion and related properties inline. Covers Seinfeld & Pandis (2006), Chapter 9, Eqs. 9.6, 9.1, 9.34, 9.38, 9.42, 9.73, 9.78, 9.87, 9.88, 9.112.

Cunningham slip correction factor for noncontinuum aerosol effects. Migrated from Aerosol.jl@c8c640bb src/single_particle_dynamics.jl:64 (`SlipCorrection` @component). Calculates the slip correction factor C_c and Knudsen number Kn for particle-gas interactions.

SO2 gas-aqueous dissolution and dissociation equilibria with van't Hoff temperature dependence. Migrated from Aerosol.jl@c8c640bb src/aqueous_equilibria.jl:240 (`SO2Equilibria` @component). Implements Seinfeld & Pandis Ch 7 §7.3.3 (Eq 7.33-7.35, 7.39, 7.41, 7.43-7.45) and Table 7.4. Parameterized as observed-only: T, H_plus, and p_SO2 are inputs; H_SO2, K_s1, K_s2, SO2_aq, HSO3_minus, SO3_2minus, S_IV_total, H_SO2_eff, alpha_0, alpha_1, alpha_2 are algebraic outputs.

A solid-phase aerosol species placeholder in the ISORROPIA II inorganic thermodynamic equilibrium model. Holds the molarity of a single solid salt in air. In isolation the concentration is conserved (D(M)/dt = 0); source and sink terms are added through the coupling mechanism when Solid instances are composed into the full Isorropia system. Reference: Fountoukis and Nenes (2007), ISORROPIA II.

Characteristic timescale for a gas to equilibrate with solid aerosol particles — Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 12. Computes the solid-particle gas-equilibration timescale in two equivalent forms: τ_s = ρ_p R_p²/(3 D_A m_p f) expressed via the aerosol mass concentration m_p (Eq. 12.135), and τ_s_alt = 1/(4π N R_p D_A f) expressed via the particle number concentration N and radius R_p (Eq. 12.139). The two forms coincide when the mass and number parameterizations are mutually consistent. Migrated from Aerosol.jl SolidEquilibrationTimescale.

Aggregate container for the 19 solid-phase salt species in the ISORROPIA II inorganic thermodynamic equilibrium model. Composes 19 named Solid instances — one per solid salt that can form in the K⁺-Ca²⁺-Mg²⁺-NH₄⁺-Na⁺-SO₄²⁻-NO₃⁻-Cl⁻-H₂O system — into a single subsystem bundle. Each Solid carries a single state variable M(t) [mol/m³] representing the molarity of that salt in air; in isolation M is conserved (D(M)/dt = 0). Source/sink terms are injected through the coupling mechanism when Solids is composed into the parent Isorropia system. Reference: Fountoukis and Nenes (2007), ISORROPIA II.

Conserved total concentration of a single inorganic aerosol species (e.g. NH, Na, Ca, K, Mg, Cl, NO3, SO4) in the ISORROPIA v1 thermodynamic equilibrium model. The total concentration `total` is held constant over time (D(total)/dt = 0), representing the user-supplied input constraint: the total moles per unit air volume of that ionic group across all phases (gas + aqueous + solid). This component is instantiated once per tracked ion group inside the top-level Isorropia system. Migrated from Aerosol.jl src/isorropia/isorropia.jl `Species`.

Two-moment stochastic collection equation (SCE) for cloud-droplet coalescence (Tzivion, Feingold & Levin 1989), scalarized to I=5 mass-doubling categories. Two models, one per collection kernel: StochasticCollectionConstant (K=K0) and StochasticCollectionGolovin (K=C(x+y)). Each tracks number concentration N_k and mass concentration M_k in every category and closes the higher moments with the non-dimensional parameter xi_p. Migrated from the array-variable @component in Aerosol.jl src/stochastic_collection.jl @ c8c640bb636b22f2425460e9ed5cba50793bfee1 (esm-ar1e); the upstream @arrayop/@makearray array operations were scalarized to flat scalar states and equations.

Two-moment stochastic collection equation (SCE) for cloud-droplet coalescence (Tzivion, Feingold & Levin 1989), scalarized to I=5 mass-doubling categories. Two models, one per collection kernel: StochasticCollectionConstant (K=K0) and StochasticCollectionGolovin (K=C(x+y)). Each tracks number concentration N_k and mass concentration M_k in every category and closes the higher moments with the non-dimensional parameter xi_p. Migrated from the array-variable @component in Aerosol.jl src/stochastic_collection.jl @ c8c640bb636b22f2425460e9ed5cba50793bfee1 (esm-ar1e); the upstream @arrayop/@makearray array operations were scalarized to flat scalar states and equations.

Stokes number and stop distance for aerosol single-particle dynamics. Migrated from Aerosol.jl@c8c640bb src/single_particle_dynamics.jl:329 (`StokesNumber` @component). Computes the particle relaxation time τ, the stop distance s_p (the distance a particle travels before coming to rest), and the dimensionless Stokes number St characterizing particle inertia relative to a flow (Seinfeld & Pandis 2006, Chapter 9, Eqs. 9.38, 9.98 and 9.101).

Combined aqueous-phase S(IV)->S(VI) oxidation kinetics — Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 7, Section 7.5, with the Section 7.4 rate conversions. The model composes five S(IV)-oxidation pathway subsystems — O3 (Eqs. 7.79-7.80), H2O2 (Eq. 7.84), Fe(III)-catalyzed (Eq. 7.92), Mn(II)-catalyzed (Eq. 7.101), and Fe/Mn synergism (Eq. 7.102) — wired to shared cloud-droplet inputs by coupling equations. The total oxidation rate R_total sums the O3, H2O2 and Fe/Mn-synergism rates (the femn_ox subsystem already carries Fe-only and Mn-only terms, so the standalone fe_ox/mn_ox rates are excluded to avoid double-counting). It also reports sulfate production S_VI_production = R_total and three Section 7.4 diagnostics: the rate in ppb/hr (Eq. 7.75) and %/hr (Eq. 7.76) and the SO2 lifetime tau_SO2 (Eq. 7.78). Migrated from Aerosol.jl SulfateFormation as a subsystem-composed model (ESS spec §4.7).

ModelingToolkit implementation of the aqueous-phase S(IV)→S(VI) oxidation rate catalyzed by dissolved Fe(III), from Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 7, Eq. 7.92. The component reports a single diagnostic, the Fe(III)-catalyzed oxidation rate R_Fe = k·[Fe(III)]·[S(IV)]/[H+], for the low-pH (pH 0-3.6) regime: the rate rises in proportion to the dissolved-iron catalyst and the total S(IV) substrate, and falls inversely with the hydrogen-ion concentration. Migrated from Aerosol.jl SulfateFormationFe. Purely algebraic: no differential states, one observed output and an empty equations array.

ModelingToolkit implementation of the S(IV) → S(VI) aqueous-phase oxidation rate catalysed by O2 with Fe(III)/Mn(II) synergism, from Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 7, Section 7.5.5, Eq. 7.102. The component reports the three additive contributions to the catalysed oxidation rate of dissolved S(IV) — a Mn(II)-only term (k_Mn·[Mn(II)]·[S(IV)]), an Fe(III)-only term (k_Fe·[Fe(III)]·[S(IV)]), and a synergistic term (k_FeMn·[Mn(II)]·[Fe(III)]·[S(IV)]) that is greatly enhanced when both transition metals are present — together with their sum R_FeMn. Migrated from Aerosol.jl SulfateFormationFeMn. Purely algebraic: no differential states; the four rate outputs are algebraic states defined by four equations.

Aqueous-phase S(IV)→S(VI) oxidation rate by hydrogen peroxide — Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 7, Section 7.5.2, Eq. 7.84. Hydrogen peroxide is the dominant oxidant converting dissolved sulfur(IV) (SO2·H2O, HSO3-, SO3^2-) to sulfate in cloud and fog droplets at low pH, where the competing O3 oxidation pathway is slow. The rate law R_H2O2 = k·[H+]·[H2O2]·[HSO3-]/(1+K_eq·[H+]) is first-order in aqueous H2O2 and in bisulfite, rises with acidity, and saturates toward k·[H2O2]·[HSO3-]/K_eq at very high [H+]. Because the equilibrium bisulfite concentration itself scales as 1/[H+], the overall H2O2 oxidation rate (when [HSO3-] is tied to gas-phase SO2) is famously almost pH-independent across cloud-water pH 2-6 — but within this standalone component [HSO3-] is an independent input, so the rate computed here does scale with [H+]. Migrated from Aerosol.jl SulfateFormationH2O2.

Mn(II)-catalyzed aqueous-phase S(IV) oxidation rate (sulfate formation) — Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 7, Section 7.5.4, Eq. 7.101. In cloud and fog droplets, dissolved S(IV) (SO2·H2O, HSO3⁻, SO3²⁻) is oxidized to S(VI) (sulfate) by dissolved O2, a reaction strongly accelerated by transition-metal catalysts. This component implements the manganese(II)-catalyzed pathway in the low-S(IV) (< 1 µM) regime, where the rate law R_Mn = k0·[Mn(II)]·[S(IV)] is first-order in both the Mn(II) catalyst and the total dissolved S(IV). (In the high-S(IV) regime, > 100 µM, the rate instead becomes zero-order in S(IV) and second-order in Mn — a separate regime not implemented here.) The Mn(II) pathway, together with the O3, H2O2, and Fe(III) pathways and the Fe/Mn synergistic term, controls how fast SO2 is converted to sulfate aerosol within clouds — a dominant route for atmospheric sulfate production. Migrated from Aerosol.jl SulfateFormationMn.

Aqueous-phase S(IV)→S(VI) oxidation rate by dissolved ozone — Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 7, Section 7.5.1, Eqs. 7.79-7.80. Dissolved S(IV) (sulfur in the +4 oxidation state) partitions in cloud and fog droplets among three species — un-ionized SO₂·H₂O, bisulfite HSO₃⁻, and sulfite SO₃²⁻ — set by the S(IV) acid-dissociation equilibria. Each is oxidized to S(VI) (sulfate) by dissolved ozone through a parallel second-order channel, and the total oxidation rate is their sum: R_O3 = (k0·[SO₂·H₂O] + k1·[HSO₃⁻] + k2·[SO₃²⁻])·[O₃(aq)], first-order in each S(IV) species and first-order in dissolved O₃. The three rate constants climb steeply with the degree of ionization — k0 = 24, k1 = 370, k2 = 1.5×10⁶ m³ mol⁻¹ s⁻¹ — so the channel is strongly pH-dependent: at high droplet pH the sulfite term dominates and oxidation is fast, at low pH it is slow. The S(IV)+O₃ pathway is one of the principal in-cloud sulfate-production routes. Migrated from Aerosol.jl SulfateFormationO3.

TwO-Moment Aerosol Sectional (TOMAS) Brownian-coagulation model with five mass-doubling size bins. Each bin k carries two moments - particle number concentration N_k and mass concentration M_k - and the bins are coupled by Brownian coagulation: intra- and inter-bin collisions remove particles and transfer mass toward larger bins at rates set by a precomputed 5x5 coagulation-coefficient matrix. f_k and psi_k are the within-bin linear number-distribution reconstruction coefficients of the two-moment scheme, evaluated algebraically from N_k. Migrated from the module-level script Aerosol.jl src/TOMAS.jl @ c8c640bb636b22f2425460e9ed5cba50793bfee1; the upstream array-variable ODESystem was scalarized to 20 scalar unknowns and mtk2esm-scaffolded. All coagulation coefficients, bin masses and the bin-spacing factor xi are baked in as numeric literals, so the model has no free parameters.

Two-product model for secondary organic aerosol (SOA) formation (Odum et al., 1996). Represents the complex mixture of oxidation products from a reactive organic gas (ROG) as two lumped surrogate products that partition between gas and aerosol phases according to an ideal-solution absorptive-partitioning equilibrium. Yields and saturation concentrations correspond to alpha-pinene oxidation from Seinfeld and Pandis (2006) Table 14.12.

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`.

ModelingToolkit implementation of the Urban atmospheric aerosol size distribution, from Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 8 ("Properties of the Atmospheric Aerosol"), Table 8.3. The Urban distribution is a preset of the multi-modal lognormal AerosolDistribution model: three lognormal modes (N = [99300, 1110, 36400] cm^-3, D_g = [0.013, 0.014, 0.050] um, log10 sigma = [0.245, 0.666, 0.337]) — a nucleation mode and an Aitken mode at sub-20 nm plus an accumulation mode at 50 nm, characteristic of polluted urban air. The model represents the aerosol number, surface-area and volume distributions as a sum of the three modes (Eq. 8.54) and reports the total number/surface/volume concentrations, the mode-1 Hatch-Choate diameters, and the vertical aerosol mass profile (Eq. 8.55). Migrated from Aerosol.jl UrbanAerosol, a preset wrapper around AerosolDistribution(3). Purely algebraic: ten observed outputs, no differential states, an empty equations array. The upstream length-n_modes array parameters are scalarized at n_modes = 3 with the Urban Table 8.3 mode parameters as defaults.

Visibility calculation from extinction coefficient. Computes visual range using the Koschmeider equation (Eq. 15.36) and related visibility metrics. Visual range is the distance at which a black object against a white background reaches the threshold contrast of 0.02.

Water autoionization equilibrium with van't Hoff temperature dependence. Migrated from Aerosol.jl@c8c640bb src/aqueous_equilibria.jl:76 (`WaterEquilibrium` @component). Serialized via EarthSciAST.mtk2esm. Implements Seinfeld & Pandis Ch 7 Eq 7.10–7.13 and Table 7.4. Parameterized as observed-only: T and [H+] are inputs, K_w/[OH-]/pH are algebraic outputs.

Temperature-dependent physical properties of water for nucleation calculations following Seinfeld & Pandis (2006), Chapter 11, Tables 11.1 and 11.4. Provides surface tension, molecular volume, molecular mass, and saturation vapor pressure as functions of temperature.

ZSR (Zdanovskii-Stokes-Robinson) mixing rule for aerosol liquid water content — Seinfeld & Pandis (2006), Atmospheric Chemistry and Physics, 2nd ed., Chapter 10. Computes the total aerosol liquid water content W of a multicomponent inorganic-salt solution as the sum over species of the water each salt holds in its own binary solution at the ambient water activity (Eq. 10.98), with the water activity set equal to the relative humidity for an equilibrium aerosol (Eq. 10.63). Migrated from Aerosol.jl ZSRWaterContent at the upstream default parameterization n_species = 3.