A mathematical approach for the analysis of data obtained from the monitoring of biocides leached from treated materials exposed to outdoor conditions

Leaching processes are responsible for the release of biocides from treated materials into the environment. Adequate modeling of emission processes is required in order to predict emission values in the framework of the risk assessment of biocidal products intended for long-term service life. Regression approaches have been applied to data obtained from the long-term monitoring of biocide emissions in experiments involving semi-field conditions. Due to the complex interaction of different underlying mechanisms such as water and biocide diffusion and desorption, however, these attempts have proven to be of limited usefulness – at least, for the available biocide emission data. It seems that the behavior of the biocide emission curve depends to a considerable extent on whichever underlying mechanism is slowest at a given point in time, thus limiting the amount of biocide available for release. Building on results obtained in the past few years, the authors propose a criterion for determining which mechanism controls the leaching process at a given point in time based on the slope of the log-log emission curve. In addition, a first-order approximation of this slope value is presented which displays advantages both in terms of computability and interpretability. Finally, an algorithm for the determination of breakpoints in the slope of the log-log emission curve is presented for the demarcation of phases within which one mechanism acts as a limiting factor. [Display omitted] •The usefulness of regression approaches to model leaching processes is limited.•Controlling mechanisms are identified via slope values of log-log emission curves.•A promising expression for these slope values is derived.•Breakpoints in emission curves can be identified by maximum likelihood estimation.