In the vadose zone, preferential flow and transport are much more common than uniform water flow and solute transport. In recent decades, several models have been developed for preferential water flow and physical nonequilibrium solute transport. Among these models, the dual-permeability approach is an interesting tool for the conceptualization and modeling of preferential flow. However, this approach has been mainly studied from a numerical point of view. In this study, we developed a new analytical model for water infiltration into dual-permeability soils. The model is based on the analytical model originally proposed for single-permeability soils. The proposed model relies on the assumption that the water exchange rate at the interface between the matrix and fast-flow regions does not change cumulative infiltration at the soil surface, so that the total cumulative infiltration can be set equal to the sum of independent cumulative infiltrations into each region. This assumption was investigated using numerically generated data. The proposed analytical model was then used to evaluate the effects of fast-flow region hydraulic properties and hydraulic conditions on total cumulative infiltration for the case of single-and multi-tension water infiltration experiments. Finally, both single-and dual-permeability models were evaluated with respect to their ability to fit experimental data and associated problems of non-uniqueness in optimized parameters. The proposed model could serve as a new tool for modeling and characterizing preferential flow in the vadose zone.Abbreviations: BOF, basic oxygen furnace; CVRMSE, coefficient of variation of the root mean square error;

The time scan measured when a dispersion of nanoparticles is analyzed by single particle inductively coupled plasma -mass spectrometry (sp-ICP-MS) is typically made of many intense short-lived spikes. On the basis of theoretical arguments backed by experimental data and statistical tests, I show that, in the very dilute limit, there is a one-to-one correspondence between the spikes present in a time scan and the points of discontinuity of the outcome of a homogeneous Poisson process. This relationship underlies the random nature of the sp-ICP-MS time scan. Furthermore, I establish that the stochastic processes describing the nanoparticle arrivals in the plasma and the time sequence of spikes in the time scan are fully identical, thus helping to place on firmer grounds a frequently made hypothesis regarding the Poissonian character of the sp-ICP-MS time scan.