Insights Gained from an Approximate Analytical Solution of the Evaporation Model Used by ConsExpo Web

Evaporation of chemicals is an important source of inhalative exposure. We analyzed here the ConsExpo evaporation model, which is characterized by a set of nonlinear differential equations only solvable by numerical means. It shows qualitatively different behavior for different parameters, but the exact conditions remain unclear. This article presents an approximate analytical solution of the ConsExpo evaporation model, derived by using a specific linearization of the nonlinear equations valid for small concentrations. From this solution, three different boundary cases or regimes are found: quick release, near equilibrium, and ventilation driven regime. Depending on the evaporation regime, different parameters influence peak substance air concentration: Quick release regime: total substance amount and room volume; near equilibrium regime: vapor pressure, substance concentration in the product, and molecular weight of the product matrix; ventilation driven regime: vapor pressure, substance concentration in the product, room volume, surface area, mass transfer coefficient, ventilation rate, and molecular weight of the product matrix. A graphical method is developed to display the position of a given scenario in relation to the three regimes. Thus, the approximate analytical solution allows for a given situation to prioritize research for reducing uncertainty of the most sensitive parameters and helps to identify promising risk management measures.