Inferring experimental colloid removal with an inverse two-population model linking continuum scale data to nanoscale features

Abstract

Models of colloid transport in porous media that assume constant fractional loss per grain passed fail in the presence of repulsive barriers to attachment, under which condition experiments produce profiles of colloid concentrations with distance from source that are nonexponential. Nonexponential removal is hypothesized to arise from variable likelihood of encountering nanoscale regions of attraction (heterodomains) on grain surfaces that allow attachment. Implementing heterodomains in mechanistic simulations of pore scale trajectories generates continuum-scale rate coefficients that produce experimentally-observed breakthrough-elution curves (BTEC) and retention profiles (RP). However, current one-directional simulation across scales is inefficient in finding a heterodomain surface coverage that yields observed RP and BTEC. In this work, we develop an inverse two-population model approach that not only estimates colloid rate coefficients from experimental BTEC and RP data but also quantifies the associated uncertainty, thereby allowing the problem to be worked from both ends via comparison of (1) rate coefficients upscaled from mechanistic pore scale simulations incorporating heterodomains with (2) rate coefficients inverted from continuum-scale BTEC and RP. We validate our inverse model using synthetic data with known removal rates and subsequently demonstrate its applicability to experimental data with multiexponential and nonmonotonic RPs. We moreover derive what is likely the first analytical expression for the RP under repulsive conditions, revealing that the hypoexponential distribution can be used to reproduce multiexponential and non-monotonic shapes. By addressing key limitations in present models, our inverse approach offers a valuable tool for advancing colloidal transport predictions in natural environments.