# Development of a New Evaporation Exposure Model: Chemical Product Evaporation Model (CPEM)
## 1 Introduction  
A volatile or semi-volatile substance can evaporate into indoor air from a chemical product with a long release time. To assess exposure due to evaporation from a consumer product, several tools have been developed [1, 2, 3]. The ConsExpo evaporation model has been used to predict the amount of a substance that will evaporate from a chemical product into indoor air [3]. In the ConsExpo model, the inhalation exposure to vapor is divided into three scenarios: instantaneous release, constant rate, and evaporation emission modes. The instantaneous release scenario assumes that all substances are released from a product into the air at once. The constant rate scenario describes the release of a substance at a constant rate over the period that a product is used. The evaporation mode describes the release of a substance from the surface of a liquid or gel product by evaporation, which is driven by the difference between the vapor pressure and saturated vapor pressure of a substance in the air. The ConsExpo evaporation model could successfully predict the measured air concentration of glutaraldehyde when a cleaner/sanitizer product was applied [4], as well as the n-alkane concentration in the air from paint use [5]. In these two cases, the release areas of both products increased when the products were applied. Conversely, another case reported a decrease in product volume over time, such that 5-chloro-2-methylisothiazol-3(2H)-one (CMIT) and 2-methylisothiazol-3(2H)-one (MIT) concentrations in the air freshener studied increased over 7 days [6]. From these studies, the volume of a product can change and affect the air concentrations of volatile substances in that product. Because both the massof the product and the amount of substance in the product decrease over time, the concentration of substances in the product can change. However, for non-applied products such as passive air fresheners, the mass of the product generally decreases over time. Therefore, the constant rate mode and evaporation mode in the ConsExpo model can lead to underestimation of the real exposure level of non-applied chemical products because both modes exclude the possibility that the target substance concentration in the product increases over time. According to [PERSON] et al. (2016) [6], because the ConsExpo evaporation model assumes that the volume of a given air freshener does not change, it is not able to account for the increasing concentrations of target substances in the product. Therefore, [PERSON] et al. (2016) developed a new evaporation exposure model incorporating the target substance concentration in the product as a state variable, which made it possible to predict increasing concentrations of target substances in a product that matched the experimental data. They described the evaporation process of a chemical in a product as an inter-phase mass transfer of volatile compounds. They also predicted fluxes from the product into the air assuming that the target substance concentrations in the product were negligible compared with other materials in the product and omitted the possibility of in-air saturation of the target substances. This assumption limited the application domain of the new model into the minor compounds, such as biocides with very low concentration in the product. In our study, we attempt to broaden the applicability of this new evaporation model, such that it can be used to analyze volatile major ingredients as well as minor compounds in a chemical product. This study developed a new evaporation model, the chemical product evaporation model (CPEM), to estimate the air concentration of a target substance when using non-applied products containing volatile solvents while accounting for the saturation kinetics of the target substance in air. The CPEM includes the concentration of the target substance in a product as a state variable with the rate of mass reduction of liquid or gel products set as a parameter to predict the substance concentration in the air.