Flow statistics in a 2D disordered pillar array

This work investigates steady Stokes flow through a two-dimensional array of circular obstacles. We develop a minimal statistical model for the flow rate distribution based on a mapping of the pore space to a network of Poiseuille-flow tubes. Our work shows that the flow rate at the pore bodies follow a Gamma distribution, and that the flow distribution at the pore throats is fully determined in terms of it. Furthermore,  the parameters of this Gamma distribution are satisfactorily linked to the geometrical properties of the the medium. The predictions agree closely with computational fluid dynamics simulations and show better agreement than prior mean-field models, clarifying how local splitting and merging shape flow in disordered porous networks.