Analytical models for flow through obstructed domains

The effects of low‐ or zero‐conductivity inclusions on flow through two‐ and three‐dimensional domains are represented using an analogy to percolation theory. Here, the term flow refers to the analogous processes of fluid, electrical current, and heat conduction. Mapping functions are derived from renormalization group models as a solution to the percolation analogy. These functions relate the extent to which a domain is obstructed to the probability that the domain is conductive and to the bulk conductivity of the domain. Stochastic methods are used to define a relation between the proportion of a domain which is isolated from flow and the proportion which is obstructed. A description of the influence of the scale of the obstructions, relative to that of the domain, is inherent in the formulation. Data obtained from numerical and electrical analogues are used to verify the mapping functions and assess the limitations of the representation.