Invasion of a porous domain by a fluid network, a constructal perspective

Abstract

This paper presents a methodology to predict the growth of fluid networks within a porous domain. Tree-shaped networks are generated for minimum volume and constant volumetric flow rate, maximum flow rate at constant volume and minimum walls-fluid contact surface at constant volumetric flow rate. The constructal methodology relies on the development of an algorithm inspired by the Constrained Constructive Optimization technique combined to the Hess-Murray's law. It is shown that the fluid network reconfigures itself entirely while growing, but its average bifurcation angle remains constant regardless the number of outlets connected. Furthermore, our results show that the fluid networks tend to invade the entire space regardless the shape of the domain.