Using a local thermal equilibrium model required that the averaged heat exchange between each phase of a porous medium is equal to zero. However, locally it could be very high. Effective conductivity will, thus depends on ratio of thermal conductivity and specific surface (exchange surface between each phases). It means that in a case of close thermal conductivity, the effective conductivity will not be the sum of separate phase effective thermal conductivity.
Yes, it has the impact and it will be directly proportional to the magnitude of the ratio. It also depends on the magnitude of the porosity. The larger is the porosity the greater is the impact.
Because of the continuous path for heat flow in the metallic part of Metal Foams, it can be approximately treated as resistances in parallel. Therefore you will find that the effective conductivity depends more strongly on the thermal conductivity of the metal and the porosity. The interstitial medium, if it is poor conducting (as should be the case in most systems), will impact the effective conductivity only weakly.
As for additivity of thermal conductances (not conductivities), it is correct for resistances in parallel. As the conductivity ratio approaches unity, all systems, irrespective of how the phases are distributed, collapse to a single point.
The ratio has very strong impact on ETC but it is NEVER a function of porosity. It completely depends on the shape and nature of the metallic foam which is indirect form of porosity but greatly influenced by geometry. It is basically coupled with ratios of solid and fluid phase conductivities and geometrical parameters of metallic foam.
Those interested at this question may possibly find interesting to check also answers to the following related discussion: https://www.researchgate.net/post/Is_the_formula_for_thermal_conductivity_of_metal_foam_correct2
We have to remember about convective heat transfer in fluid phase as well - if LTE consists of a sum of NLTE equations, convective part concerning fluid remains in LTE equation - so as fluid flows through the foam, heat transfer between phases occurs, so yes, ratio of thermal conductivity have impact
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