Diffusion in porous layers with memory

摘要: SUMMARY The process of diffusion fluid in porous media and biological membranes has usually been modelled with Darcy's constitutive equation, which states that the flux is proportional to pressure gradient. However, when permeability matrix changes during process, solution equations governing presents severe analytical difficulties because variation not known a priori. A diverse formulation law therefore needed many authors have studied this problem using various methods solutions. In paper equation modified introduction memory formalism. We also second relates density variations pressure, introducing rheology represented by formalisms operating on as well variations. The are then specified derivatives fractional order, solving case layer constant pressures applied its sides. For technical reasons studies devoted rather than pressure; work we shall devote our attention studying compute Green's function boundary (Case A) for found closed-form formulae. described already considered half space (Caputo 2000); however, results mostly qualitative since most practical problems occurs layers. The readily extended periodic one planes while other B) mimics effect tides sea coasts. skin limits surface whose thickness decreases increasing frequency. Regarding due tidal waters coast, it observed medium sand water, sinusoidal 2 × 104 Pa period 24 hr at boundaries zero boundary, same amplitude decaying exponentially distance become negligible few hundred metres. A brief discussion given concerning mode determination parameters several frequencies. see that, classic pure behaviour, resulting through pressure.