1 Functional models for colloid retention in porous media at the triple line 1 Annette Dathe 1,2,* , Yuniati Zevi 1 , Brian K. Richards 1 , Bin Gao 1,3 , J.-Yves Parlange 1 , 2 Tammo S. Steenhuis 1 3 4 Abstract 5 Spectral confocal microscope visualizations of microsphere movement in unsaturated 6 porous media showed that attachment at the Air Water Solid (AWS) interface was an 7 important retention mechanism. These visualizations can aid in resolving the functional 8 form of retention rates of colloids at the AWS interface. In this study soil adsorption 9 isotherm equations were adapted by replacing the chemical concentration in the water as 10 independent variable by the cumulative colloids passing by. In order of increasing 11 number of fitted parameters, the functions tested were the Langmuir adsorption isotherm, 12 the Logistic distribution and the Weibull distribution. The functions were fitted against 13 colloid concentrations obtained from time series of images acquired with a spectral 14 confocal microscope for three experiments performed where either plain or carboxylated 15 polystyrene latex microspheres were pulsed in a small flow chamber filled with cleaned 16 quartz sand. Both moving and retained colloids were quantified over time. In fitting the 17 models to the data, the agreement improved with increasing number of model parameters. 18 The Weibull distribution gave overall the best fit. The logistic distribution did not fit the 19 initial retention of microspheres well but otherwise the fit was good. The Langmuir 20 isotherm only fitted the longest time series well. The results can be explained that 21 initially when colloids are first introduced the rate of retention is low. Once colloids are 22 at the AWS interface they act as anchor point for other colloids to attach and thereby 23 increasing the retention rate as clusters form. Once the available attachment sites 24 diminish, the retention rate decreases. 25 26 1 Department of Biological and Environmental Engineering, Cornell University, Ithaca, New York, USA 27 2 Now at Department of Plant and Environmental Sciences, Norwegian University of Life Sciences, Ås, 28 Norway 29 3 Now at Department of Agricultural and Biological Engineering, University of Florida, Gainesville, 30 Florida, USA 31 *corresponding author: annette.dathe@umb.no, phone +47 6496 5587 32 Manuscript Click here to download Manuscript: Retention-Time_review_Aug9equ_Tammo.doc Click here to view linked References 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65