Making sense of complex systems through resolution, relevance, and mapping entropy.

Complex systems are characterized by a tight, nontrivial interplay of their constituents, which gives rise to a multiscale spectrum of emergent properties. In this scenario, it is practically and conceptually difficult to identify those degrees of freedom that mostly determine the behavior of the system and separate them from less prominent players. Here, we tackle this problem making use of three measures of statistical information: Resolution, relevance, and mapping entropy.

Comprehensive comparison of pore-scale models for multiphase flow in porous media.

Multiphase flows in porous media are important in many natural and industrial processes. Pore-scale models for multiphase flows have seen rapid development in recent years and are becoming increasingly useful as predictive tools in both academic and industrial applications. However, quantitative comparisons between different pore-scale models, and between these models and experimental data, are lacking.

Drying in a microfluidic chip: experiments and simulations.

We present an experimental micro-model of drying porous media, based on microfluidic cells made of arrays of pillars on a regular grid, and complement these experiments with a matching two-dimensional pore-network model of drying. Disorder, or small-scale heterogeneity, was introduced into the cells by randomly varying the radii of the pillars. The microfluidic chips were filled with a volatile oil and then dried horizontally, such that gravitational effects were excluded.

Dispersive transport and symmetry of the dispersion tensor in porous media.

The macroscopic laws controlling the advection and diffusion of solute at the scale of the porous continuum are derived in a general manner that does not place limitations on the geometry and time evolution of the pore space. Special focus is given to the definition and symmetry of the dispersion tensor that is controlling how a solute plume spreads out. We show that the dispersion tensor is not symmetric and that the asymmetry derives from the advective derivative in the pore-scale advection-diffusion equation.