Sulfate

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.

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.