Functional models for colloid retention in porous media at the triple line

Spectral confocal microscope visualizations of microsphere movement in unsaturated porous media showed that attachment at the Air Water Solid (AWS) interface was an important retention mechanism. These visualizations can aid in resolving the functional form of retention rates of colloids at the AWS interface. In this study, soil adsorption isotherm equations were adapted by replacing the chemical concentration in the water as independent variable by the cumulative colloids passing by. In order of increasing number of fitted parameters, the functions tested were the Langmuir adsorption isotherm, the Logistic distribution, and the Weibull distribution. The functions were fitted against colloid concentrations obtained from time series of images acquired with a spectral confocal microscope for three experiments performed where either plain or carboxylated polystyrene latex microspheres were pulsed in a small flow chamber filled with cleaned quartz sand. Both moving and retained colloids were quantified over time. In fitting the models to the data, the agreement improved with increasing number of model parameters. The Weibull distribution gave overall the best fit. The logistic distribution did not fit the initial retention of microspheres well but otherwise the fit was good. The Langmuir isotherm only fitted the longest time series well. The results can be explained that initially when colloids are first introduced the rate of retention is low. Once colloids are at the AWS interface they act as anchor point for other colloids to attach and thereby increasing the retention rate as clusters form. Once the available attachment sites diminish, the retention rate decreases.