Note that such foam exhibits surface of both positive, both negative curvature. Electrons are repulsing mutually, so they're covering both surfaces of this sponge. The wet surface of sponge is responsible for good electrical and thermal conduction of common metals. At presence of hole conductivity the conductive electrons are collected inside of foam cavities preferably. The flat areas of zero curvature cannot keep the conductive electrons due the balance of electrostatic forces, and they correspond the band gap, occurring in common semiconductors. Under situation, when the motion of free electrons remains restricted to sponge cavities in continuous stripes arranged in hyperlattice, which are serving like pipes full of highly compressed electron gas, we can expect high temperature superconductivity in such system.
Another interesting situation may occur, when two pieces of sponge of different surface curvature are connected together. We can model such situation by connecting of two pieces of porous material, the hydrophilic and hydrophobic one, soaked by moderate amount of water. Because hydrophobic surface repels polar molecules of water, the water will collect inside of pores, thus emulating hole conductivity of P-type semiconductors. The hydrophilic material is attracted by water surface, so that water is forming bridges connecting convex surfaces and it represents a N-type of conductor here.
At the moment, when two pieces of such materials are connected together, the portion of fluid from hydrophobic material is soaked into the hydrophilic half of junction, thus removing water from cavities of neighboring part of hydrophobic material. This is a direct analogy of formation of space charge zone / depletion layer of semiconductor junction. Note that suction of liquid from hydrophilic part of junction doesn't improve the water transfer, it just leads to removal of additional amount of water from hydrophobic part, thus leaving it even less conductive for water molecules.
A quite different situation may appear, when we push additional amount of water in hydrophilic part. After soaking the dry portion of hydrophilic junction, the excessive water will fill up the cavities, so it can pass freely through capillary junction. Apparently, a surface tension based "diode" is formed, but we can imagine even much more complex structures analogous to transistor, thyristor and others, based on capillary forces inside of porous materials of different polarity. Nature supposedly uses these principles for controlled osmosis inside of living cells already, because surface of cell membranes is porous and it contains both hydrophilic, both hydrophobic part, formed by phospholipides.
Note that pushing of fluid into our "capillary diode" requires to overcome pressure exerted by capillary repulsion during filling of emptied cavities inside of hydrophobic part of junction. This corresponds the voltage drop in forward bias direction of semiconductor junctions. We can even met with analogy of recombination at the flat portion of porous surface, when water droplets are forced to overcame negative surface tension, so their surfaces are moving in accelerated way. At the case of liquids of extreme surface tension (like the mercury inside of porous glass), such area can even become the source of audible noise, thus mimicking the formation of photons at the recombination centers of PN junction nearly completelly. Such centers can be observed by Lorentz microscopy directly in thin layer of low temperature superconductors (compare the embedded animation bellow).