unsaturated porous medium
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Humic acid (HA) and iron oxide (such as Fe3O4) nanoparticles are widely distributed in soil, and their complex embedded in soil might affect the transport and fate of Cu2+ in the vadose zone, while Cu2+ is a serious threat to the underlying groundwater. In this study, we synthesized a composite of Fe3O4 nanoparticles coated with HA (HA@NPs) using as an amendment a packed sand matrix in the transport column experiments. The impacts of HA content and ion strength (IS) on Cu2+ transport in the unsaturated columns were investigated. The results showed that HA exhibited a stronger inhibition effect on Cu2+ transport, and a higher IS enhanced the mobility of Cu2+ in an unsaturated porous medium in the presence of HA@NPs. The recovery ratio (Rr) of Cu2+ breakthrough in the column decreased from 66.56% to 3.94% while the mass concentration ratio CHA/CNPs increased from 0 to 50 in the HA@NPs complex. The Rr increased by 1.64 times while the IS increased from 0 to 100 mM. Batch adsorption experiments, kinetics and isotherm models, and Fourier transform infrared (FTIR) spectra analysis were implemented to elucidate the underlying mechanism. It was found that HA embedded in the sand matrix could bind Cu2+ by forming stable chelate, while the IS-dependent Cu2+ transport could be attributed to the competitive adsorption between Na+ and Cu2+. Our study demonstrates that the physicochemical environment, as well as the presence of iron oxide nanoparticles and natural organic matter, can significantly impact Cu2+ transport in unsaturated porous medium.

Boussinesq’s equation is one-dimensional nonlinear partial differential equation which represents the infiltration phenomenon. This equation is frequently used to study the infiltration phenomenon in unsaturated porous medium. Infiltration is the process in which the groundwater of the water reservoir has entered in the unsaturated soil through vertical permeable wall. An approximate analytical solution of nonlinear partial differential equation is presented by homotopy analysis method. The convergence of homotopy analysis solution is discussed by choosing proper value of convergence control parameter. The solution represents the height of free surface of infiltrated water.

Rainfall infiltration into an unsaturated region of the earth’s surface is a pervasive natural phenomenon. During the rainfall-induced seepage process, the soil skeleton can deform and the permeability can change with the water content in the unsaturated porous medium. A coupled water infiltration and deformation formulation is used to examine a problem related to the mechanics of a two-dimensional region of semi-infinite extent. The van Genuchten model is used to represent the soil-water characteristic curve. The model, incorporating coupled infiltration and deformation, was developed to resolve the coupled problem in a semi-infinite domain based on numerical methods. The numerical solution is verified by the analytical solution when the coupled effects in an unsaturated medium of semi-infinite extent are considered. The computational results show that a numerical procedure can be employed to examine the semi-infinite unsaturated seepage incorporating coupled water infiltration and deformation. The analysis indicates that the coupling effect is significantly influenced by the boundary conditions of the problem and varies with the duration of water infiltration.