Spatial and temporal scales of variability for indoor air constituents

Historically air constituents have been assumed to be well mixed in indoor environments, with single point measurements and box modeling representing a room or a house. Here we demonstrate that this fundamental assumption needs to be revisited through advanced model simulations and extensive measurements of bleach cleaning. We show that inorganic chlorinated products, such as hypochlorous acid and chloramines generated via multiphase reactions, exhibit spatial and vertical concentration gradients in a room, with short-lived ⋅OH radicals confined to sunlit zones, close to windows. Spatial and temporal scales of indoor constituents are modulated by rates of chemical reactions, surface interactions and building ventilation, providing critical insights for better assessments of human exposure to hazardous pollutants, as well as the transport of indoor chemicals outdoors.

Reversible adsorption to the surface of the bleach and partitioning into the bleach were also treated in the model. Note that observations of chlorinated and nitrogenated compounds could not be reproduced by the model without multiphase chemical processes, as demonstrated in our previous study 1 . A full list of reactions, rate coefficients, diffusion coefficients and partitioning coefficients used in the model are summarized in a previous publication 1 .
The kinetic model provided inputs to the Computational Fluid Dynamics (CFD) model including the concentrations of HOCl, ClNO2, chloramines, and NH3 directly above the bleach surface at different times. The most important gas-phase reactions and uptake coefficients which were responsible for controlling the concentrations of species of interest were identified using the kinetic model and sensitivity tests (Supplementary Table 1). These reactions and uptake coefficients are included in the CFD simulations. Uptake coefficients to room surfaces were calculated assuming a total room surface area of 430 m 2 . In addition to the reactions and uptake coefficients included in Supplementary Table 1 an indoor NH3 production rate of 1.24 ´ 10 8 cm -3 s -1 was included in both the kinetic model and CFD simulations. A previous study has suggested primary emissions of Cl2 and ClNO2 from the bleach due to solution impurities. 5 This possibility was not considered in the model due to a lack of experimental constraints, 6 which may be one of the reasons for the difference between measurements and modeling (Supplementary Figure 2).

Computational Fluid Dynamics simulations
Spatial distributions of gas-phase bleach products and subsequent chemical reaction products were simulated under various indoor environmental conditions using a CFD model. The The model also simulated solar radiation through windows (three yellow triangular columns in Supplementary Figure 1). The areas are 2, 4, and 2 m 2 for the three windows, respectively, and the solar zenith angle was 60 degrees. The photolysis rate coefficient was considered uniform in the direct solar radiation zone while in the diffuse sunlight zone it was calculated as a 2% value of the direct sunlight zone, considering diffusions and reflections of photons in the non-sunlit zone.
A total of eleven chemical reaction equations were simulated (See Supplementary Table   1). Four species, HOCl, ClNO2, NCl3, and ClNO2, were generated directly from the cleaning surface. The concentrations directly above the bleach surface calculated from the kinetic model were inputted in the CFD model. In reaction 1 (R1), HOCl reacts with chlorine ions (Cl -) on aerosol surfaces in the ambient air of the room, producing chlorine (Cl2) and water vapor. It was assumed that aerosol particles, where HOCl uptake occurred on the surface, were distributed uniformly throughout the room, while particles were not explicitly resolved in CFD. Note that direct solar radiation in the sunlit zone photolyzed Cl2, ClNO2 and HOCl, thereby generating Cl and OH radicals (see reactions R2 -R4). OH production rates in the dark zone and the sunlit zone were The CFD model simulates surface uptake fluxes using the following equation: where Fi is uptake flux of species, γi is uptake coefficient (or reaction probability), wi is thermal velocity, and Ci is the gas-phase concentration of species i adjacent to the wall. NH3 is lost due to uptake to the bleach surface (R8). Cl2, ClNO2, and NCl3 are deposited to all indoor surfaces such as the walls, floor, and ceiling (R9 -R11).
To simulate the turbulent indoor air flow associated with the supply air jets and interior surfaces, the Menter k-ω shear stress transport turbulence model was utilized, where two turbulence variables, kinetic energy (k) and specific dissipation (ω) described turbulent eddy scales and kinetic energy. The model results were validated based on the mass and energy balance equations for gas-phase species chemical reactions as described in previous CFD studies 8,9 . In addition, the CFD model results were validated further by comparing time-varying concentrations of OH, HOCl, NCl3, and NH3 observed in the measurement campaign ( Fig. 1 Outdoor NOx, O3 and VOCs were also used to provide typical values where available. The model was then used to predict the radical concentrations to compare with measurements. The OH reactivity is defined for a chemical species X as the product of the second-order rate coefficient for the reaction of X with OH radicals with the concentration of X (k II [X]). The total OH reactivity kOH, which is the inverse of the OH lifetime, is calculated by summing the OH reactivity for each chemical species X. The INDCM contains an explicit chemical mechanism that includes all of the important OH loss routes, and the reactivity is then driven by the measured concentrations used as inputs. As well as providing an estimate of OH reactivity, the INDCM was also used to provide OH production rates as inputs for the CFD model. The production rate was calculated every minute and a 10-min running average was applied for inputting into the CFD model as shown in Supplementary Table 1.

Spatial and temporal scales
Spatial and temporal scales of indoor species are determined by loss rates due to building ventilation, surface deposition, photolysis, and chemical reactions. Supplementary Table 2 summarizes the major processes considered in evaluating spatial and temporal scales of gas-phase The spatial scale is calculated as follows:

Gas-phase species:
We calculated and summarized the spatial and temporal scales of selected indoor gas-phase species based on the present study of bleach cleaning and previous studies including ozone interactions with the human surface (8) and photochemical reaction of HONO generated from a gas stove (7). The background indoor concentrations/mixing ratios of gas-phase species were OH of 3´10 5 cm -3 , O3 of 4 ppb, VOCs of 100 ppb, NO2 of 5 ppb, and NO of 2 ppb. Reaction rate coefficients were based on the INDCM 10,12 and the MCM 11 .
Lifetimes of radicals shown in Fig. 3  Particulate matter: We report spatial and temporal scales of six different sizes of particles with particle diameters of 3 nm, 100nm, 1 µm, 5 µm, 10 µm, and 100 µm, as described in Supplementary Table   2. Nano-size particles decrease their concentrations by coagulation, deposition, and ventilation 13,14,18 , while micro-size particles decay mostly by deposition and ventilation 3,4,15,19 . The coagulation of nano-size particles contributes to 20% of the deposition rate, whereas it is negligible for micro-size particles 18 . Particle deposition to indoor sources is enhanced for nano-size particles (< 10 nm) due to Brownian and turbulent diffusion, while gravitational settling is dominant for larger particles (> 5 µm). These size-varying loss mechanisms determine the half-life and spatial transport scales.