Determination of sorption isotherm based on the measurements of contaminant outflow

Abstract

In this paper, we present a method for determining the sorption isotherm from experimental measurements. The sorption isotherm is not assumed to be a member of any specific finite dimensional class (e.g. Freundlich isotherm, Langmuir isotherm). Instead, an infinite-dimensional space of functions is considered with limited a priori assumptions (e.g. smoothness, monotonicity). Consequently, we face a more challenging problem compared to the finite-dimensional case, in which only few tuning parameters need to be determined. We consider the case of flow of the contaminated water into the unsaturated porous media sample; we assume that the data are collected at the outflow. The sorption isotherm is determined in an iterative way. We minimize the cost functional reflecting the discrepancy between measured and computed data. In doing so, we use the Gateaux differential to obtain the direction of descent.