Passive Sampler Exchange Kinetics in Large and Small Water Volumes Under Mixed Rate Control by Sorbent and Water Boundary Layer

Exchange kinetics of organic compounds between passive samplers and water can be partly or completely controlled by transport in the sorbent. In such cases diffusion models are needed. A model is discussed that is based on a series of cosines (space) and exponentials (time). The model applies to mixed rate control by sorbent and water boundary layer under conditions of fixed aqueous concentrations (open systems, infinite water volumes, in situ sampling) and fixed amounts (closed systems, finite water volumes, ex situ sampling). Details on the implementation of the model in computational software and spreadsheet programs are discussed, including numerical accuracy. Key parameters are Biot number (ratio of internal/external transfer resistance) and sorbent/water phase ratio. Small Biot numbers are always indicative of rate control by the water boundary layer, but for large Biot numbers this may still be the case over short time scales. Application to environmental monitoring of nonpolar compounds showed that diffusion models are rarely needed for sampling with commonly used single-phase polymers. For determining sorption coefficients in batch incubations, the model demonstrated a profound effect of sorbent/water phase ratio on time to equilibrium. Application of the model to sampling of polar organic compounds by extraction disks with or without a membrane showed that moderate to major sorbent-controlled kinetics is likely to occur. This implies that the use of sampling rate models for such samplers needs to be reconsidered. Environ Toxicol Chem 2021;00:1-14. (c) 2021 SETAC