Making Waves: Modeling bioturbation in soils - are we burrowing in the right direction?

The burrowing, feeding and foraging activities of terrestrial and benthic organisms induce displacements of soil and sediment materials, leading to a profound mixing of these media. Such particle movements, called "sediment reworking" in aquatic environments and "bioturbation" in soils, have been thoroughly studied and modeled in sediments, where they affect organic matter mineralization and contaminant fluxes. In comparison, studies characterizing the translocation, by soil burrowers, of mineral particles, organic matter and adsorbed contaminants are paradoxically fewer. Nevertheless, models borrowed from aquatic ecology are used to predict the impact of bioturbation on organic matter turnover and contaminant transport in the soil. However, these models are based on hypotheses that have not been tested with adequate observations in soils, and may not necessarily reflect the actual impact of soil burrowers on particle translocation. This paper aims to (i) highlight the possible shortcomings linked to the current use of sediment reworking models for soils, (ii) identify how recent progresses in aquatic ecology could help to circumvent these limitations, and (iii) propose key steps to ensure that soil bioturbation models are built on solid foundations: more accurate models of organic matter turnover, soil evolution and contaminant transport in the soil are at stake.

Directional Water Wicking on a Metal Surface Patterned by Microchannels.

This work focuses on the simulation and experimental study of directional wicking of water on a surface structured by open microchannels. Stainless steel was chosen as the material for the structure motivated by industrial applications as fuel cells. Inspired by nature and literature, we designed a fin type structure. Using Selective Laser Melting (SLM) the fin type structure was manufactured additively with a resolution down to about 30 µm. The geometry was manufactured with three different scalings and both the experiments and the simulation show that the efficiency of the water transport depends on dimensionless numbers such as Reynolds and Capillary numbers. Full 3D numerical simulations of the multiphase Navier-Stokes equations using Volume of Fluid (VOF) and Lattice-Boltzmann (LBM) methods reproduce qualitatively the experimental results and provide new insight into the details of dynamics at small space and time scales. The influence of the static contact angle on the directional wicking was also studied. The simulation enabled estimation of the contact angle threshold beyond which transport vanishes in addition to the optimal contact angle for transport.

Space-fractional advection-diffusion and reflective boundary condition.

Anomalous diffusive transport arises in a large diversity of disordered media. Stochastic formulations in terms of continuous time random walks (CTRWs) with transition probability densities showing space- and/or time-diverging moments were developed to account for anomalous behaviors. A broad class of CTRWs was shown to correspond, on the macroscopic scale, to advection-diffusion equations involving derivatives of noninteger order. In particular, CTRWs with Lévy distribution of jumps and finite mean waiting time lead to a space-fractional equation that accounts for superdiffusion and involves a nonlocal integral-differential operator. Within this framework, we analyze the evolution of particles performing symmetric Lévy flights with respect to a fluid moving at uniform speed . The particles are restricted to a semi-infinite domain limited by a reflective barrier. We show that the introduction of the boundary condition induces a modification in the kernel of the nonlocal operator. Thus, the macroscopic space-fractional advection-diffusion equation obtained is different from that in an infinite medium.

Model to interpret pulsed-field-gradient NMR data including memory and superdispersion effects.

We propose a versatile model specifically designed for the quantitative interpretation of NMR velocimetry data. We use the concept of mobile or immobile tracer particles applied in dispersion theory in its Lagrangian form, adding two mechanisms: (i) independent random arrests of finite average representing intermittent periods of very low velocity zones in the mean flow direction and (ii) the possibility of unexpectedly long (but rare) displacements simulating the occurrence of very high velocities in the porous medium. Based on mathematical properties related to subordinated Lévy processes, we give analytical expressions of the signals recorded in pulsed-field-gradient NMR experiments. We illustrate how to use the model for quantifying dispersion from NMR data recorded for water flowing through a homogeneous grain pack column in single- and two-phase flow conditions.

Continuous-time random-walk model of transport in variably saturated heterogeneous porous media.

We propose a unified physical framework for transport in variably saturated porous media. This approach allows fluid flow and solute migration to be treated as ensemble averages of fluid and solute particles, respectively. We consider the cases of homogeneous and heterogeneous porous materials. Within a fractal mobile-immobile continuous time random-walk framework, the heterogeneity will be characterized by algebraically decaying particle retention times. We derive the corresponding (nonlinear) continuum-limit partial differential equations and we compare their solutions to Monte Carlo simulation results. The proposed methodology is fairly general and can be used to track fluid and solutes particles trajectories for a variety of initial and boundary conditions.

Mass transport subject to time-dependent flow with nonuniform sorption in porous media.

We address the description of solutes flow with trapping processes in porous media. Starting from a small-scale model for tracer particle trajectories, we derive the corresponding governing equations for the concentration of the mobile and immobile phases within a fractal mobile-immobile model approach. We show that this formulation is fairly general and can easily take into account nonconstant coefficients and in particular space-dependent sorption rates. The transport equations are solved numerically and a comparison with Monte Carlo particle-tracking simulations of spatial contaminant profiles and breakthrough curves is proposed, so as to illustrate the obtained results.

A fractional equation for anomalous diffusion in a randomly heterogeneous porous medium.

A fractional partial differential equation is derived for the spreading of matter in a saturated porous medium starting from precise hypotheses concerning the medium itself, which is a collection of intertwisted tubes with randomly distributed slopes, filled with quiescent fluid. Examining the fundamental solution of the fractional equation indicates that the second moment is not proportional to time, which is the signature of anomalous diffusion. The equation derived preserves non-negativity and also the total mass of matter.