Eigenvector centrality for geometric and topological characterization of porous media

Solving flow and transport through complex geometries such as porous media is computationally difficult. Such calculations usually involve the solution of a system of discretized differential equations, which could lead to extreme computational cost depending on the size of the domain and the accuracy of the model. Geometric simplifications like pore networks, where the pores are represented by nodes and the pore throats by edges connecting pores, have been proposed. These models, despite their ability to preserve the connectivity of the medium, have difficulties capturing preferential paths (high velocity) and stagnation zones (low velocity), as they do not consider the specific relations between nodes. Nonetheless, network theory approaches, where a complex network is a graph, can help to simplify and better understand fluid dynamics and transport in porous media. Here we present an alternative method to address these issues based on eigenvector centrality, which has been corrected to overcome the centralization problem and modified to introduce a bias in the centrality distribution along a particular direction to address the flow and transport anisotropy in porous media. We compare the model predictions with millifluidic transport experiments, which shows that, albeit simple, this technique is computationally efficient and has potential for predicting preferential paths and stagnation zones for flow and transport in porous media. We propose to use the eigenvector centrality probability distribution to compute the entropy as an indicator of the "mixing capacity" of the system.