Gas/particle partitioning of semi-volatile organic compounds in the atmosphere: Transition from unsteady to steady state

We derive differential equations to determine the kinetics of gas/particle partitioning of semi-volatile organic compounds (SVOCs). These equations model the transient states from initiation of sorption to particles (non-steady state) through the establishment of steady state. Two hypothetical scenarios are examined: (1) exchange of SVOCs between gas- and particle-phases alone; and (2) both gas/particle partitioning and wet and dry deposition of particles. The differential equations show that, under Scenario 1, a steady state is reached as an equilibrium between gas- and particle-phases, whereas under Scenario 2, the attained steady state is not in equilibrium. Our model shows that SVOCs in atmosphere where particle deposition is occurring reach a steady non-equilibrium state sooner than they would reach equilibrium under Scenario 1. We infer that SVOCs in the atmosphere will reach steady state instead of equilibrium between gaseous and particulate phases in circumstances where wet and dry deposition of particles cannot be neglected. In addition, our study indicates that the time for SVOCs to reach steady state in the atmosphere is fast, most likely within minutes or hours, suggesting that SVOCs are in steady or quasi-steady state in the atmosphere. Our analysis also reveals that gas/particle partitioning and particle deposition of SVOCs are dependent on each other.