3.1.1 Cloud droplets

Figure 2 summarizes the ROS concentrations and the chemical and phase transfer rates for the cloud case at pH = 4.5; the corresponding figures for simulations at pH = 3 and 6 are shown in Fig. S1 (Supplement). The net transfer rates (moles per gram of air per second) into the aqueous phase are shown in the yellow boxes. For FeN<100, the relative contributions (%) of this rate into the iron-free and iron-containing droplets are shown next to the arrows. The phase transfer rates are additionally shown in units of moles per liter per second (using the air density of 1.13 × 10⁻³ g cm⁻³ and LWCs in Table 1), together with the chemical source and loss rates in the aqueous phase (M s⁻¹) and the corresponding aqueous-phase ROS concentrations (M) (white boxes). If the effect of iron is negligible on aqueous-phase concentrations and aqueous-phase rates, there should be no concentration difference between any droplets, neither between the results for FeBulk and FeN<100 nor between the iron-free and iron-containing droplets. In addition, the ratio of the phase transfer rates should also be equal to the ratio of the LWCs of the two drop classes (98 % : 2 %).

Figure 2Multiphase scheme for cloud water showing the phase transfer and chemical source and loss rates in the aqueous phase, m_Fe = 10 ng m⁻³, pH = 4.5. (a) FeBulk approach. (b) FeN<100 approach with a fraction of iron-containing droplets of F_N,Fe = 2 %. Numbers below the species names are aqueous-phase concentrations (M), and chemical and phase transfer rates are shown in moles per liter per second. Net phase transfer rates near the top of the figure are expressed in gas-phase units (moles per gram of air per second); the relative contributions (%) into the iron-free and iron-containing droplets are shown next to the arrows. The bulk concentrations at the bottom of panel (b) represent the bulk concentrations weighted by the contributions of the two droplet classes to total LWC (98 % : 2 %).

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All ROS are predicted to be taken up into cloud water, independently of the iron distribution at pH = 4.5 (Fig. 2), and also their ratio of the phase transfer rates nearly corresponds to the ratio of the LWCs of the two droplet classes (98 % : 2 %). Significant deviations from this theoretical value occur at pH = 3 for HO₂ (Fig. S1b) and at pH = 6 for H₂O₂ that is predicted to evaporate from iron-free droplets (Fig. S1d).

The H₂O₂ concentrations in all droplets under all conditions and pH values (Fig. S1) correspond to the equilibrium concentrations according to Henry's law, in agreement with previous studies that have shown that H₂O₂ is at thermodynamic equilibrium in cloud water (Ervens, 2015). At pH = 3 and 4.5, the efficient H₂O₂ consumption is compensated by a relatively higher uptake rate, resulting in the efficient replenishment of H₂O₂ and equilibrium concentration. The uptake rates (in M s⁻¹) between FeBulk and the iron-free droplets in the FeN<100 approach are similar (e.g., for H₂O₂ : 0.56 and 0.53 M s⁻¹), whereas they are higher for uptake into the iron-containing droplets (2.2 M s⁻¹). Since these droplets only comprise 2 % of the total LWC, this difference is not reflected in the net uptake rate. At pH = 6 (Fig. S1c and d), the majority of cloud droplets are predicted to be a source of H₂O₂; the only exception is the iron-containing droplets in the FeN<100 approach, from which H₂O₂ evaporates due to less efficient chemical H₂O₂ consumption in the aqueous phase.

The OH concentrations differ by nearly 1 order of magnitude between the iron-free and iron-containing cloud droplets (5.8 × 10⁻¹⁴ M vs. 3.3 × 10⁻¹³ M; Fig. 2b); the concentration in the FeBulk model is even slightly lower (4.5 × 10⁻¹⁴ M; Fig. 2a). The reasons for these differences are explored in Sect. 3.2, where the individual chemical processes affecting the concentrations are analyzed.

The bulk aqueous-phase OH concentration in the FeBulk approach is approximately 50 % higher (4.5 × 10⁻¹⁴ M) as compared to 6.4 × 10⁻¹⁴ M for FeN<100 (Fig. 2). A much greater discrepancy of nearly 1 order of magnitude between the two approaches is predicted at pH = 6, whereas the difference in the bulk concentrations at pH = 3 is smaller (Fig. S1). These concentrations corresponded to those in bulk cloud water samples from cloud droplet populations with F_N,Fe = 2 %, provided that chemical processes in the sample upon sampling do not change the ROS levels (Sect. 3.3). For all cases, the chemical source and loss rates of the OH radical compensate for each other, leading to a relatively small uptake rate of the moderately soluble OH radical into the aqueous phase (∼ 10⁻¹⁶ mol g⁻¹ s⁻¹), which is not significantly affected by F_N,Fe.

The concentration difference of HO₂ $/$ O${}_{\mathrm{2}}^{-}$ between iron-free and iron-containing droplets is nearly 2 orders of magnitude (2.4 × 10⁻⁸ M vs. 8.9 × 10⁻¹⁰ M), whereas the concentration for FeBulk is predicted to be between these two values (8.9 × 10⁻⁹ M) (Fig. 2). The difference in the concentrations is even greater (factor > 200) at pH = 6 (Fig. S1d), whereas it is less than a factor of 3 at pH = 3. These trends suggest that the concentrations are dependent on pH (Sect. 3.2). The comparison of the bulk aqueous-phase HO₂ $/$ O${}_{\mathrm{2}}^{-}$ concentrations resulting from the FeN<100 approach (bottom of Figs. 2b, S2b and d) to those in FeBulk shows that at pH = 4.5 and 6, the total HO₂ $/$ O${}_{\mathrm{2}}^{-}$ is underestimated by about 1 order of magnitude. At pH = 3, the chemical loss rate of HO₂ $/$ O${}_{\mathrm{2}}^{-}$ in iron-containing droplets is relatively larger than its chemical source rate (74 × 10⁻⁸ M s⁻¹ vs. 66 × 10⁻⁸ M s⁻¹; Fig. S1b). This imbalance in the chemical rates leads to a very efficient HO₂ uptake into iron-containing droplets. Consequently, the phase transfer into these droplets comprises 13 % of the total uptake rate, whereas at higher pH values the contributions correspond to the ratio of LWCs between the two droplet classes (98 % : 2 %). The higher Henry's law constant of HO₂ and rate constants of O${}_{\mathrm{2}}^{-}$ reactions as compared to those of HO₂ at higher pH lead to increasingly lower HO₂ $/$ O${}_{\mathrm{2}}^{-}$ concentrations with increasing pH.

3.1.2 Aqueous aerosol particles

Since the LWC of the aqueous aerosol particles is smaller by a factor of 2 × 10⁵ than in clouds, the aqueous-phase iron concentration is accordingly higher, and so are all chemical rates of iron reactions. Similar to cloud water, the H₂O₂ concentration is neither significantly affected by the iron distribution nor by iron reactions; i.e., at a given pH value its aqueous-phase concentration is nearly the same in all particles. At pH = 4.5 and 6, evaporation of H₂O₂ is predicted for FeBulk and from the iron-free particles in FeN<100 (Figs. 3b and S2b and d). However, since the uptake rate of H₂O₂ into the iron-containing droplets is much higher, exceeding the evaporation rate by a factor of 25 (−4 % vs. 104 %, pH = 4.5) and ∼ 2 (−143 % vs. 243 % at pH = 6), aqueous particles represent a net sink of H₂O₂.

Figure 3Same as Fig. 2 but for the aerosol case (model parameters in Table 1).

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Similar to the cloud case, the OH concentrations in the aqueous phase of FeBulk are between those in the iron-free and iron-containing particles for FeN<100. The OH concentrations do not show a strong pH dependence, but their bulk values are about a factor of 3 lower for the FeN<100 approach (F_N,Fe = 2 %) than for the FeBulk approach (1.6 × 10⁻¹⁵ M vs. ∼ 4.6 × 10⁻¹⁵ M). Even at the high iron concentrations as present in aerosol water (≤ 0.41 M), the chemical source and loss rates of OH nearly cancel out, leading to a relatively small uptake rate.

The HO₂ $/$ O${}_{\mathrm{2}}^{-}$ concentrations in the FeBulk approach are comparable to those as predicted for cloud water at the same pH value. However, the concentrations in the iron-free and iron-containing particles differ by 4 orders of magnitude at pH = 6 (1.5 × 10⁻⁶ and 1.3 × 10⁻¹⁰ M, Fig. S2d). The resulting bulk aqueous-phase concentrations are at least 1 order of magnitude underestimated by FeBulk (pH = 3); this difference is even a factor of 2000 at pH = 6 (Figs. 3d and S2d). While the chemical loss rate of HO₂ $/$ O${}_{\mathrm{2}}^{-}$ is nearly equal to or even larger than its source rate at pH = 4.5 and 6, at pH = 3 the source rate exceeds the loss rate resulting in evaporation of HO₂ from the 2 % iron-containing particles (Fig. S2b). However, since the uptake rate into the iron-containing particles is larger than this evaporation rate, the net flux of HO₂ is an uptake into the particle phase.

3.1.3 Gas-phase concentrations (OH, HO₂) and mixing ratios (H₂O₂)

The gas-phase concentrations of OH and HO₂ and mixing ratios of H₂O₂ are shown in Fig. S3 as a function of time (t≤7200 s) in the presence of cloud droplets and aerosol particles, respectively, at the three pH values considered here and for the two assumed iron distributions in the aqueous phase. The H₂O₂ mixing ratio in the presence of cloud water is very quickly reduced to about 50 % of its initial concentration (1 ppb) due to partitioning to the aqueous phase. Both the pH value and F_N,Fe have a small effect on the H₂O₂ mixing ratio. The small increase of H₂O₂ over time is in agreement with findings in a recent multiphase box model intercomparison (Barth et al., 2021).

The OH concentrations are on the order of 10⁶ cm⁻³, i.e., typical concentrations as found for continental daytime conditions. These concentrations build up within a few seconds and do not largely change over the time period considered here. The difference of up to a factor of 5 in the OH concentrations in the presence of cloud droplets with a pH value of 3 and 6, respectively, cannot be directly explained by any OH reactions in the aqueous phase but is rather a consequence of the OH–HO₂ cycle in the multiphase system (Fig. 1). At pH = 6, the effective Henry's law constant for HO₂ is highest, and therefore, most HO₂ is partitioned to the aqueous phase, resulting in the lowest fractions of HO₂ in the gas phase. The gas-phase HO₂ concentrations are on the order of 10⁸ cm⁻³, in agreement with predictions from other atmospheric multiphase chemistry models (e.g., Barth et al., 2021). Generally, the pH value and iron distributions cause smaller differences in the presence of aerosol particles as compared to the cloud case, since the liquid water content of particles is smaller by several orders of magnitude, and therefore a smaller fraction of the species is dissolved.

3.1.4 Partitioning coefficient ϵ

The partitioning coefficient ϵ is often used to describe the distribution of species between the aqueous and gas phases in the atmospheric multiphase system, e.g., Ervens (2015). It is defined as

with C_aq and p_g being the aqueous-phase concentration (M) and gas-phase partial pressure (atm) and K_H(eff) the (effective) Henry's law constant (M atm⁻¹). Accordingly, ϵ<1 indicates situations when the aqueous phase is subsaturated.

The ϵ values for the three ROS are summarized in Fig. 4 for the cloud and aerosol simulations at three pH values. The fact that ${\mathit{ϵ}}_{{\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{2}}}$ is ∼ 1 shows that H₂O₂ is in thermodynamic equilibrium and explains why its concentrations do not differ among iron-containing and iron-free droplets (particles) (Figs. 2, 3 and S2).

The ϵ_OH values in the presence of cloud droplets (red symbols, Fig. 4b) are on the order of ∼ 0.01–0.1. The values for iron-containing aerosol particles show a distinct trend with highest ϵ_OH values in iron-containing particles, whereas ϵ_OH in iron-free particles is lower by 2 and 3 orders of magnitude, respectively. The lack of a clear trend in ϵ_OH with pH suggests that the main formation and loss processes of OH are pH-independent. The differences in ϵ_OH scale with the OH concentrations in aerosol particles that differ by 3 orders of magnitude between iron-containing and iron-free particles in the FeN<100 approach and the concentration in the FeBulk case (Fig. 3). The ϵ_OH values in cloud water do not exhibit such strong differences, which is also reflected in the more similar concentrations in all droplets (Fig. 2).

Figure 4Partitioning coefficients ϵ for (a) H₂O₂, (b) OH and (c) HO₂ for pH = 3 , 4.5 and 6 for FeBulk (filled symbols) and FeN<100 in 98 % iron-free (squares) and 2 % iron-containing droplets (triangles). Results are shown for simulations of cloud droplets (green) and aerosol particles (orange) at three pH values (3, 4.5 and 6); lines are added to guide the eye.

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The difference between the concentration in iron-free and iron-containing particles is up to 3 orders of magnitude (pH = 3, Fig. S2b), which is also reflected in the same difference in ϵ (Fig. 4b).

For the HO₂ radical, iron reactions cause a significant deviation from thermodynamic equilibrium at high pH, resulting in decreasing ${\mathit{ϵ}}_{{\mathrm{HO}}_{\mathrm{2}}}$ with increasing pH. At high pH, HO₂ is more efficiently consumed due to the higher rate constants of the O${}_{\mathrm{2}}^{-}$ radical anion as compared to those with the undissociated HO₂ radical. Unlike for OH, for which the smallest ϵ is seen in iron-free particles, the lowest ${\mathit{ϵ}}_{{\mathrm{HO}}_{\mathrm{2}}}$ is found for iron-containing particles – which shows that the concentration differences due to iron distribution for OH and HO₂ have different reasons: whereas iron leads to efficient OH formation, it causes significant HO₂ $/$ O${}_{\mathrm{2}}^{-}$ loss.

3.3.1 Comparison of bulk aqueous-phase concentrations

The values of F_N,Fe = 2 % and 100 % likely represent extreme values for the iron distribution in cloud droplet or particle populations. Depending on abundance and proximity of iron emissions sources, fewer particles (and thus droplets) may also contain iron; this would translate into an even higher iron aqueous-phase concentration. Under such conditions, iron would not be completely dissolved and available for aqueous-phase reactions. Therefore, in the following, we limit our discussion to values of F_N,Fe ≥ 1 %. In order to illustrate the total ROS budget in the aqueous phase, Fig. 6 shows the bulk aqueous-phase concentrations [ROS]_aq,bulk (M) calculated based on the LWC-weighted average ROS concentration in the iron-containing and iron-free droplets or particles:

where [ROS]_ironfree and [ROS]_iron are the ROS concentrations in the iron-free and iron-containing droplets, respectively. (Note that the same calculation was performed for the bulk aqueous-phase concentrations in Figs. 2, 3, S1 and S2). Results are shown for the full range of 1 % ≤ F_N,Fe ≤ 100 %.

The H₂O₂ concentrations do not show any dependence on the iron distribution F_N,Fe (Fig. 6a and d). This trend can be explained because (i) in cloud water the main chemical source and loss processes are independent of iron, whereas (ii) in aerosol water, both the main chemical source and loss reactions are dependent on the Fe(II) concentration. The same set of processes can also explain why the resulting aqueous-phase H₂O₂ concentrations are independent of the total iron mass. In a sensitivity study, we increased m_Fe to 50 ng m⁻³, which results in very similar H₂O₂ concentrations (Fig. S5). Thus, a higher iron mass concentration increases both rates by the same factor, resulting in nearly equal H₂O₂ concentrations for both m_Fe.

The OH concentration in cloud water is underestimated by FeBulk by up to a factor of ∼ 5 (pH = 6, Fig. 6b). The large difference at the highest pH is the consequence of the more efficient OH formation at pH = 6 by the reaction of O${}_{\mathrm{2}}^{-}$ with O₃ (Sect. 3.2). Since in the FeN<100 approach the HO₂ $/$ O${}_{\mathrm{2}}^{-}$ concentration is about 1 order of magnitude higher at this pH value than for FeBulk, the OH concentration is generally underestimated by assuming F_N,Fe = 100 %. It can be concluded that in clean conditions, i.e., when the pH value of cloud water is $\ge \sim$5, even for relatively low iron mass concentrations, iron distribution should be taken into account to obtain the correct OH concentrations in cloud water. The deviations are only slightly higher for m_Fe = 50 ng m⁻³ than for 10 ng m⁻³ (Fig. S5). In aerosol water, the OH concentration is generally overestimated by FeBulk by factors of $\le \sim$ 2 and ∼ 5 for m_Fe = 10 and m_Fe = 50 ng m⁻³ (Figs. 6e and S5e), respectively. The lower OH concentration in the FeN<100 approach is a consequence of the lower Fe(II) concentration (Sect. 4.1), which leads to less OH formation by the Fenton reaction.

Figure 6Bulk aqueous-phase concentrations of H₂O₂, OH and HO₂ for the cloud (a–c) and aerosol (d–f) cases as a function of F_N,Fe using the model parameters listed in Table 1.

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The HO₂ $/$ O${}_{\mathrm{2}}^{-}$ concentrations are underestimated in cloud water by the FeBulk approach, approximately by the same factors (∼ 2–5) as the OH radical, with the highest bias at pH = 6 (Fig. 6c). At pH = 3, the difference between the HO₂ $/$ O${}_{\mathrm{2}}^{-}$ concentrations for the two iron mass concentrations is much larger than for the other pH values. Unlike for the H₂O₂ and OH concentrations, that are very similar for both m_Fe, the HO₂ $/$ O${}_{\mathrm{2}}^{-}$ concentrations more clearly deviate for the two iron masses considered in Fig. S5. This can be explained by the less efficient Fe(III) reduction in the cloud droplets at m_Fe at all pH values (Sect. 4.1).

In aerosol water, the aqueous-phase HO₂ $/$ O${}_{\mathrm{2}}^{-}$ concentrations are nearly identical for wide ranges of F_N,Fe at pH = 3 and 4.5, whereas the difference at F_N,Fe = 1 % and 100 % is about 1 order of magnitude at pH = 6 (Fig. 6f). Thus, the aqueous-phase budget of HO₂ $/$ O${}_{\mathrm{2}}^{-}$ may be significantly underestimated – independently of m_Fe – with increasing pH if the iron distribution across the particle distribution is not properly accounted for.

3.3.2 Enhanced H₂O₂ partitioning into aerosol water: $K_{\mathrm{H},{\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{2}}}$ = 2.7 × 10⁸ M atm⁻¹

Strictly, Henry's law constants are not applicable to highly concentrated aqueous solutions such as aerosol water. Simultaneous measurements of particle-bound and gas-phase H₂O₂ concentrations suggest that it partitions much more efficiently to the particle phase than predicted based on its physical Henry's law constant ($K_{\mathrm{H},{\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{2}}}$ = 1.02 × 10⁵ M atm⁻¹). Despite large uncertainties in such measurements and of related parameters such as the aerosol water content, various studies revealed that the partitioning of H₂O₂ between the gas and the aerosol aqueous phases may be more appropriately described with an effective Henry's law constant of $K_{\mathrm{H},{\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{2}}}$ ≤ 2.7 × 10⁸ M atm⁻¹ (Hasson and Paulson, 2003; Xuan et al., 2020). The observation by Hasson and Paulson (2003) of higher H₂O₂ concentrations in coarse-mode particles than in fine-mode particles might point to a size-dependent chemical particle composition with higher iron content in coarse particles that often contain dust.

To explore the effects of such enhanced partitioning, we performed a sensitivity study, using $K_{\mathrm{H},{\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{2}}}$ ≤ 2.7 × 10⁸ M atm⁻¹. In Fig. S6, the aqueous-phase concentrations and net phase transfer rates of the three ROS are compared to those using the physical Henry's law constant ($K_{\mathrm{H},{\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{2}}}$ = 1.02 × 10⁵ M atm⁻¹). No other parameter was changed as to the best of our knowledge corresponding K_H(eff) values for OH and/or HO₂ are not available. We perform this comparison only for the aerosol case, as numerous measurements have shown that the partitioning of H₂O₂ into cloud water can be satisfactorily described by its K_H (e.g., Ervens, 2015).

As expected, a higher $K_{\mathrm{H},{\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{2}}}$ results in higher H₂O₂ aqueous-phase concentrations by 3 orders of magnitude. Unlike for the low $K_{\mathrm{H},{\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{2}}}$, the higher partitioning leads to smaller H₂O₂ concentrations for FeBulk than for FeN<100 by up to 1 order of magnitude and pH = 6. The OH concentration in the aqueous phase is predicted to decrease with increasing F_N,Fe, unlike in the base case simulation where we showed the opposite trend (Fig. S6b). The higher H₂O₂ concentration generally increases the importance of the Fenton reaction and photolysis for OH production in the aqueous phase. While the HO₂ $/$ O${}_{\mathrm{2}}^{-}$ concentrations for the two $K_{\mathrm{H},{\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{2}}}$ values do not differ at low F_N,Fe, they are significantly smaller by several orders of magnitude for the higher $K_{\mathrm{H},{\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{2}}}$ (Fig. S6c).

4.2.1 Calculation of γ_OH and ${\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}$

The uptake of OH and HO₂ into aerosol particles is often parameterized by the dimensionless reactive uptake coefficient γ that is derived as a function of the first-order radical loss (k^loss) onto aerosol particles. For the derivation of γ based on lab studies, it is assumed that γ solely depends on the molecular speed and the droplet surface. However, it has been discussed that the reactive uptake coefficient in atmospheric applications should also include a term to account for gas-phase diffusion (Jacob, 2000):

with S being the total droplet surface area per air volume and ω the molecular speed,

where M is the molar mass (g mol⁻¹), R is the gas constant and T is the absolute temperature (K) (e.g., Thornton and Abbatt, 2005; Pöschl et al., 2007). Accordingly, the phase transfer rate of radicals into the particle phase can be described as

and the reactive uptake coefficient γ can be derived as

The γ values for OH and HO₂ as a function of F_N,Fe are displayed in Fig. 8. If gas-phase diffusion is neglected in the derivation of γ, the last term in the denominator of Eq. (9) is set to zero (Eq. S.3). To demonstrate the impact of gas-phase diffusion on the reactive uptake parameter, we compare γ values calculated with Eq. (10) to values without consideration of gas-phase diffusion (Sect. S3 in the Supplement).

Figure 8Reactive uptake coefficients γ_OH and ${\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}$ derived from the multiphase model studies at three pH values for (a, b) cloud and (c, d) aerosol conditions.

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4.2.2 Reactive uptake coefficient of the hydroxy radical, γ_OH

The derived values for γ_OH over the full range of F_N,Fe (∼ 2.2 × 10⁻³ ≤γ_OH(cloud) ≤ 6.4 × 10⁻³; γ_OH(aerosol) ∼ 3.8 × 10⁻²) are in good agreement with the average value suggested for pure water surfaces (γ_OH = 0.035) (Hanson et al., 1992). It should be noted that this latter experimental value was derived assuming a Henry's law constant of K_H,OH ≥ 40 M atm⁻¹ and [OH] ≥ 10⁸ cm⁻³. If it were adjusted to atmospherically more relevant conditions ([OH] ∼ 10⁶ cm⁻³) and K_H,OH = 25 M atm⁻¹ as used in our study (Table S4), the resulting γ_OH might be smaller by more than an order of magnitude than the reported one. Molecular dynamics simulations for the mass accommodation of OH on water surfaces showed α_OH = 0.1, which can be considered the upper limit of reactive OH uptake onto water surfaces (Roeselová et al., 2003). The difference between such a value for pure water and the values from our model study demonstrates the high reactivity of the OH radical in the aqueous phase. As its solubility is limited, this high reactivity results in subsaturated conditions (ϵ_OH<1; Fig. 4b). The γ_OH values show little difference at different pH values and F_N,Fe. Thus, the reactive uptake of OH into cloud droplets could be parameterized with a value of γ_OH∼ 2.3 × 10⁻³ for all conditions explored here. Similar to the findings for cloud water, the uptake of the OH radical could be parameterized by a single γ value for the conditions applied here (γ_OH∼ 0.0038). The comparison of the values in Fig. 8a and c to those in Fig. S8a and c reveals that the gas-phase diffusion leads to a significant decrease of γ_OH by a factor of ∼ 3 in clouds and ∼10 % in aerosol particles.

Several previous studies have determined γ_OH on surfaces other than pure water that are more comparable to atmospheric aerosol particles. Hanson et al. (1992) showed that γ_OH increases on acidic solutions from 0.07 (28 % H₂SO₄) to unity on 96 % H₂SO₄. On organic surfaces, γ_OH values are generally higher than on inorganic surfaces which demonstrates the high reactivity of OH with organics in the condensed phase and/or on organic surfaces. In several lab studies, squalane was used as a proxy for long-chain alkanes; the reactive uptake coefficients have been determined in a range of ∼ 0.2 $<{\mathit{\gamma }}_{\mathrm{OH}}<\mathrm{0.5}$ (e.g., Che et al., 2009; Smith et al., 2009; Waring et al., 2011; Houle et al., 2015; Bianchini et al., 2018; Li and Knopf, 2021). A similar value range was also found for a wide variety of other organics (Bertram et al., 2001). In other experimental studies on organic particles, γ_OH>1 was found (γ_OH = 1.64 on wet succinic acid, Chan et al., 2014; 1.3 ± 0.4 on bis(2-ethylhexyl) sebacate, George et al., 2007). γ_OH on organic aerosols may decrease with increasing OH gas-phase concentration because the viscosity of the organic condensed phase prevents efficient uptake and diffusion of OH towards the particle center (Slade and Knopf, 2013; Arangio et al., 2015). Such effects were included in recently developed frameworks to parameterize γ_OH as a function of particle viscosity, size and gas-phase OH concentration (Renbaum and Smith, 2011; Houle et al., 2015).

We did not explore any of these parameters in detail in our current model study. However, the comparison of the tight range of our γ_OH values in Fig. 8, independently of F_N,Fe and cloud or aerosol aqueous conditions, to the wide ranges of literature values leads us to the following conclusions: (i) the similarity of our γ_OH value based on an explicit chemical mechanism to that measured on pure water suggests that ∼ 10${}^{-\mathrm{3}}<{\mathit{\gamma }}_{\mathrm{OH}}$ ∼ 10⁻² may be a good approximation under cloud conditions. (ii) The fact that we cannot reproduce the high γ_OH values as observed on organic aerosols suggests that organic reactions control the reactive uptake of OH, which are not included in our explicit chemistry scheme. (iii) Since organics are likely present in all aerosol particles, the effect of the iron distribution (F_N,Fe) for γ_OH may be overestimated by our chemical mechanism on ambient aerosol particles.

4.2.3 Reactive uptake coefficient of the hydroxy peroxyl radical, ${\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}$

The ${\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}$ values into cloud water are in the range of 0.001–0.004, with higher values at the highest pH (Fig. 8b). In aerosol water, ${\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}$ shows a strong dependence on F_N,Fe, leading to an overestimate of the reactive uptake by FeBulk by up to 2 orders of magnitude at pH = 3 (Fig. 8d). Note that at F_N,Fe = 1 %. no ${\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}$ value is shown as under such conditions, HO₂ is predicted to evaporate. This evaporation is due to the inefficient chemical HO₂ consumption in iron-free particles, whereas efficient uptake occurs into the iron-containing particles. This leads to a great imbalance of the phase transfer rates from and into the two droplet classes as shown in Fig. 2b. We use identical α values for droplet and aqueous particle surfaces. The mass accommodation coefficient α is the upper limit of the maximum value for the uptake coefficient γ. This limit can be seen in Fig. (8d), where ${\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}$ approaches the value of ${\mathit{\alpha }}_{{\mathrm{HO}}_{\mathrm{2}}}$ = 0.05, i.e., the regime in which the uptake is fully controlled by the mass accommodation and not by the chemical loss in the aqueous phase. For the HO₂ radical, gas-phase diffusion may decrease ${\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}$ by a factor of ∼ 2 at pH = 6, whereas the two γ values are nearly identical at pH = 3 (Fig. S8b). In aerosol water, gas-phase diffusion has an insignificant impact on its reactive uptake coefficient onto aerosol water (Fig. S8d).

It has been shown in global model studies that the reactive loss of HO₂ on aerosol surfaces can significantly impact the atmospheric oxidant budget (e.g., Haggerstone et al., 2005; Macintyre and Evans, 2011; Stadtler et al., 2018; Li et al., 2019). A value of ${\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}$ = 0.2 based on the study by Jacob (2000) has been commonly used in global models, which has also been supported by molecular dynamics simulations (Morita et al., 2004). However, recent model studies suggest that this value may be an overestimate and that values on the order of ${\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}$ = 0.05 or 0.08 may be more appropriate (Christian et al., 2017; Tan et al., 2020).

On dry aerosol surfaces, ${\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}$ is usually low: for example, Bedjanian et al. (2005) measured ${\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}$ = 0.075 ± 0.015 on dry soot surfaces, which is comparable to the value of ${\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}$ ≤ 0.031 on dust (Matthews et al., 2014) and ${\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}$ < 0.01 on dry NaCl (Remorov et al., 2002). ${\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}$ increases by more than 1 order of magnitude when RH increases from ∼ 20 % to >90 % (Cooper and Abbatt, 1996; Taketani et al., 2008; Lakey et al., 2015, 2016; Moon et al., 2018). Lakey et al. (2015) showed much higher ${\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}$ values on two humic acids ($\mathrm{0.0007}\le {\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}\le \mathrm{0.06}$ and $\mathrm{0.043}\le {\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}})\le \mathrm{0.09}$, respectively) than on pure long-chain carboxylic acids (${\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}<\mathrm{0.004}$). They ascribed the higher HO₂ uptake to the small concentrations of copper and iron ions in the humic acids, in agreement with previous studies that showed the large impact of TMIs on HO₂ reactive uptake (e.g., Mao et al., 2013, 2017). It was suggested by Lakey et al. (2015) that the HO₂ uptake cannot be solely controlled by the TMI concentration as they did not see any correlation with ${\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}$. This lack of trend is similar to findings by Mozurkewich et al. (1987), who also did not find any clear relationship in ${\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}$ on Cu-doped NH₄HSO₄ and LiNO₃ particles with Cu concentration.

Based on our model results, the lack of such correlation can be qualitatively understood by simultaneous increase of the main chemical HO₂ source and sink rates (Reactions S1 and L4–L6 in Fig. 5f). The absence of a dependence of HO₂ uptake on wet particle diameter in the study by Mozurkewich et al. (1987) is also in agreement with our sensitivity studies in which we varied the particle diameter by a factor of ± 2 (Fig. S9). This implies that the interfacial mass transfer is not a limiting step in the HO₂ uptake. The HO₂ uptake on Cu-doped ammonium sulfate particles was observed to be higher under neutral (${\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}$ = 0.2) as opposed to acidic conditions (${\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}$ = 0.05) (Thornton and Abbatt, 2005). Similar results were observed by Mao et al. (2013) who generally found somewhat higher values than in our study (${\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}>\mathrm{0.4}$) and highest values for the lowest $\mathrm{Cu}/\mathrm{Fe}$ ratios (i.e., highest iron concentration at a constant copper concentration) and highest pH. However, overall their differences in ${\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}$ due to the $\mathrm{Fe}/\mathrm{Cu}$ ratio and/or pH are smaller than those that we predict for different F_N,Fe (∼ 10⁻⁴ $\le {\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}$ $\le \sim$ 10⁻², at pH = 3). This suggests that ${\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}$ parameterizations that take into account the dependence on Cu concentration, total aerosol mass and particle size (e.g., Guo et al., 2019 and Song et al., 2020) should be further refined to also include the iron distribution.

We note that our results are not quantitatively comparable to those on Cu-doped particles, as our chemical scheme includes only reactions of iron as the only TMI. The corresponding reactions with ${\mathrm{Cu}}^{+/\mathrm{2}+}$ generally have higher rate constants than those of iron reactions (Ervens et al., 2003; Deguillaume et al., 2004); however, as copper concentrations in ambient aerosols are usually lower than iron concentrations, the effect of both TMIs might be similar. We did not perform the equivalent simulations for copper in the present study as to our knowledge, there are no data available that give single-particle information on the distribution of iron and copper within droplet or particle populations. However, if iron and copper originated from different emission sources, the number concentration of TMI-containing particles might be relatively high. However, in such situations the synergistic effects of Fe and Cu affecting HO_x cycling and uptake as suggested by Mao et al. (2013) might be reduced.

Measurements of ${\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}$ on ambient aerosol populations showed ranges of 0.13 $\le {\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}$ ≤ 0.34 (Mt. Tai) and 0.09 $\le {\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}\le$ 0.4 (Mt. Mang) (Taketani et al., 2012). No systematic trend with total iron concentration that exceeded 1 µg m⁻³ at Mt. Mang and 10 µg m⁻³ at Mt. Tai was observed. The acidity of the aerosols was not reported in that study; however, the derived ${\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}$ values did not show any significant trend with the molar NH${}_{\mathrm{4}}^{+}$ $/$ (SO${}_{\mathrm{4}}^{\mathrm{2}-}+$ NO${}_{\mathrm{3}}^{-}$) ratios that ranged from ∼ 1 to ∼ 2 and ∼ 2 to ∼ 3, pointing to moderately acidic to fully neutralized aerosol. The fact that the ambient data do not show any trend with acidity might either point to a high number fraction of TMI-containing particles and/or to a relatively high pH, i.e., to conditions under which our model results do not show a large effect of F_N,Fe (Fig. 8d). Two studies of ambient aerosol at urban locations revealed similar average values as compared to the mountain sites, with ${\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}$ = 0.23 ± 0.22 in Yokohama, Japan (Zhou et al., 2021), and 0.24 (0.08 $\le {\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}$ ≤ 0.36) in Kyoto, Japan (Zhou et al., 2020). No significant trend in the γ values was observed as a function of aerosol or air mass characteristics (coastal or mainland).

Given the large ranges of ${\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}$ values on lab-generated and ambient aerosol, it is difficult to reconcile differences between lab data and observations with our model results. However, our results might provide an explanation for the discrepancies of lab-derived or theoretical ${\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}$ values in the range of 0.2–1 to those determined on ambient aerosol (<0.4). We cannot say for sure that these differences indeed stem from different assumptions of iron distribution or other factors affecting ${\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}$. However, our strong predicted decrease of ${\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}$ values at low pH and F_N,Fe suggests that applying lab-derived ${\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}$ on aerosol particles with identical composition might lead to an overestimate of HO₂ loss on atmospheric aerosol surfaces, even if all other aerosol properties (size, total iron mass, pH, etc.) are identical.