Intergranular mass transport in materials plays an important role in successful bonding of particles, and controls the material’s properties. This results from the processing conditions including the intergranular mass transport and interfacial reactions. The model of liquid mass transport of metals, molten salts, silicates, and molecular liquids, in capillary-like media is discussed. The model concentrates on the role of surface tension-to-viscosity ratio, gamma/eta, and volume diffusion on the liquid flow in fine pores with diameters comparable to the liquid phase above its critical thickness. We have found the following relation between two parameters : D-cap = (y/eta)L alpha, where alpha and L are a specific permeability and the mean diffusive jump length of atoms/ions/molecules, respectively. The specific permeability is related to the hydraulic permeability, taken from Darcy’s law, and depends on capillary radius and liquid/solid contact angle. It is demonstrated that the specific permeability depends on the interfacial reactions and heterogeneity of the system. The mass transport in liquid layers seems to be initiated by atoms with low interatomic distances (low atomic radii) in liquid metals or by the high non-bridging oxygen content in aluminosilicate melts.