When a constitute material in a structure is pure solid or fluid, the intrinsic thermal or electrical conductivity of the material is needed to compute the effective conductivity of the structure. However, when the material is unresolved and is composed of both solid and fluid, the effective conductivity should be given. You can obtain it from laboratory measurements, or by simulating a resolved structure by using higher resolution. Besides those, mixing rules are widely used to express the effective properties of porous media.

Since GeoDict 2025, the following mixing rules are possible in Constituent Materials for porous media to find the effective thermal / electrical conductivity that can take porosity and tortuosity factors into account.

• Single Phase: is applicable for pure material of solid, fluid or porous. Also if you have known the effective property of the porous medium and do not need the mixing rules, you can just give the value for the porous medium by choosing Single Phase.

• Parallel Model (Upper Bound or Voigt modulus): in general there are two models for a rule of mixtures, one for axial loading (Voigt model), and one for transverse loading (Reuss model). For parallel model, solid and fluid are assumed to be distributed parallel in the conduction direction and the effective conductivity is the weighted arithmetic mean of the conductivity of the solid and fluid

where and are the conductivity for solid and fluid, respectively. is the solid volume fraction.

• Series Model (Lower Bound or Reuss modulus): for series model, solid and fluid are connected in series and the effective conductivity is the weighted harmonic mean of the conductivity of the two substances.

• Hill's Average: the parallel and series model represent the upper and lower bound, respectively, of the quantity of the effective properties. Hill's average is the middle value of them.
• Tortuosity Model: the tortuosity model finds the effective conductivity based on the increased path length

where and are the tortuosity factor for solid and fluid, and is interfacial conductance, which is zero as the default at the moment in ConductoDict.