Emission of SVOCs from a product into air is generally understood to result from two subsequent processes: first, the partitioning of the substance between the product material and the air in direct contact with the product (evaporation). Second, the substance’s transfer over a stagnant boundary layer of air over the product surface into bulk indoor air by diffusion (Xu and Little 2006).

The concentration in the air in direct contact with the product (y_o) is assumed to be determined by the material/air partition coefficient K_ma (unitless) and the concentration in the product C_prod (mass/volume) as:

The transfer of the substance into bulk air is characterized by the mass transfer coefficient h_m (distance per time) times the concentration gradient overthe boundary layer. Combined, the rate of change in the air concentration C_air due to evaporation is given by:

where V_room is the volume of the room, and S_prod the surface area of the product in contact with air.

This description is valid only for SVOCs, since for these substances the slowest, rate-determining step is the transfer from the product to air. For more volatile substances, the emission is also determined by diffusion of the substance within the product matrix (Xu and Little 2006).

Weschler and Nazaroff (2008) demonstrate that the transfer of a substance into house dust can largely be explained by the emission of the substance into air and subsequent partitioning of the substance between air and dust. The partitioning of a substance between the gas phase and dust can be described using the dust/air partition coefficient K_da. According to Weschler and Nazaroff (2008) K_da depends on the organic material content of house dust, f_om,dust and the octanol-air partition coefficient K_oa according to:

The rate of transfer between dust and bulk air is described by the mass transfer rate h_m. Weschler and Nazaroff (2008) assume h_m to be the same as for the transfer from the product to air (see equation (2)).

The concentration of the substance in dust C_dust (mass of substance/volume of dust) is reduced by the removal of substance contaminated dust by vacuum cleaning and track out of dust and the replacement by clean dust, maintaining a fixed amount of dust indoors. The removal of substance with dust is modelled with a dust elimination rate coefficient k_el,dust (per time) that summarises these elimination processes into a single parameter:

Combining the two processes (transfer between air and dust and the removal with dust) gives

with S_d and V_d the total surface area and the volume of indoor surface dust, respectively. The volume of dust is estimated from the surface area of dust-loaded surfaces, the dust surface loading and the density of dust.

Following Weschler and Nazaroff (2008), sorption to surfaces such as furniture, flooring and windows is conceptualized as transfer to and partitioning into a thin film of organic material on these surfaces. Sorption is determined by the affinity of the substance for the organic material in the surface film. The partitioning between air and the organic film can be approximated by the K_oa. The rate of transfer of the substance from air to the surface film is furthermore determined by the mass transfer rate h_m. Weschler and Nazaroff (2008) assume h_m to be the same as for mass transfer of the substance from the product into air.

Combined, these factors determine the sorption of the substance to surfaces as:

In this equation, C_surf is the concentration of substance in the film on the surface (mass/volume), V_surf, S_surf and d_surf are the volume, surface area and thickness of the film, respectively.

In analogy with the sorption of substances to surfaces, sorption to airborne particulate matter can be described by partitioning between air and the organic matter content of airborne particles (Weschler and Nazaroff 2008). The particle/air partition coefficient K_part is then proportional to the K_oa, i.e.

where f_om,part is the fraction of organic matter in the particles.

Sorption of SVOCs to airborne particles is usually fast compared to the other transfer processes considered. Little et al. 2012 assume instantaneous equilibration between the gas phase SVOC concentration and the concentration in airborne particles. The concentration of SVOC bound to airborne particles C_ap is then given by

C_ap is the concentration of the substance (mass/volume) in the particles themselves. If equilibrium between air and particle concentrations cannot be regarded as established instantaneously, the dynamic exchange between material in the gas phase and airborne particles is described by the mass transfer coefficient for airborne particles h_mp. The rate of change in the concentration of particle-bound substance is given by

where S_ap is the total surface area of the airborne particulate matter and V_ap is their total volume.

From the concentration of substance in airborne particles (C_ap), the concentration of particle-bound substance in air C_air,p, is derived as:

where TSP (total suspended particles) is the air concentration of airborne particulate matter (mass/volume) and ρ_ap is the mass density of the airborne particulate matter.

The gas phase concentration of the substance is the result of competing processes of emission, exchange between dust, surfaces and airborne particles and removal by ventilation. The latter is modelled using the ventilation rate q (air changes per time) as

The total rate of change of the indoor air concentration follows from combining equations 2), 5), 6), 8) and, 10):

Taken together, equations 2), 5), 6), 8), and 10) define a system of coupled differential equations. Integration of this system of equations using suitable boundary and initial conditions (i.e. reflecting the specific exposure scenario), gives the concentrations of substance in all different compartments (air, product, dust, airborne particles, indoor surfaces) as a function of time.  In the DustEx tool, it is assumed that emission starts at t=0, when the product is brought into the indoor environment. It is further assumed that no other sources of emission of the substance are present.