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This chapter introduces the concept of flux of matter in the context of conservation laws—the playground of the local balance laws derived in Chap. 2. The attention moves to presenting two averaging techniques for guessing the structure of two distinct transport fluxes. First, the concern falls on the derivation of the Darcy law for two particular cases of microstructures: (i) a periodic array of cells and (ii) randomly distributed cells. Then a possible derivation for the structure of the thermodiffusion flux is given. The considerations extend immediately to the cross-diffusion case.