Abstract
Although under normal circumstances the classical Fick law gives an excellent description of mass diffusion, it is however not appropriate for describing some particular features, like those concerned with inertial effects or couplings between mass transport and viscous pressure. Inertial effects are of importance in some applications which have been studied in the framework of stochastic processes, as correlated random walks, a topic to be discussed in Sect. 13.2.
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References
M.S. Boukary and G. Lebon, Physica A 137 (1986) 546; R.F. Rodríguez, L.S. García-Colín, and M. López de Haro, J. Chem. Phys. 83 (1985) 4099; R. E. Nettleton, J. Phys. A 21 (1988) 1079.
D. Lhuillier, Physica A 165 (1990) 303; N. Depireux and G. Lebon, J. Non-Newtonian Fluid Mech. 96 (2000) 105.
S. Goldstein, Q.J. Mech. Appl. Math. 4 (1951) 129; H.D. Weyman, Am. J. Phys. 35 (1965) 488; M.O. Hongler and L. Streit, Physica A 165 (1990) 196.
J. Masoliver, J.M. Porrà, and G.H. Weiss, Phys. Rev. A 45 (1992) 2222; J. Masoliver and G.H. Weiss, Physica A 183 (1992) 537; J.Masoliver, K. Lindenberg, and G.H. Weiss, Physica A 157 (1989) 593; W. Horthemske and R. Lefever, Noise-induced Phase Transitions, Springer, Berlin, 1983.
P. Rosenau, Phys. Rev. E 48 (1993) R 655.
J. Camacho and D. Jou, Phys. Lett. A 171 (1992) 26; M. Grmela and D. Jou, J. Math. Phys. 34 (1993) 2290; H. Vlad and J. Ross, Phys. Lett. A 184 (1993) 403.
M.A. Schweizer, Can. J. Phys. 63 (1985) 956.
G.I. Taylor, Proc. Roy. Soc. London, Ser A 219 (1953) 186, 223 (1954) 446; R. Aris, Proc. R. Soc. London, Ser A 235 (1956) 67.
P.C. Chatwin, J. Fluid Mech 43 (1970) 321; W.N. Gill and R. Sankasubramanian, Proc. Roy. Soc. London, Ser. A 316 (1970) 341, 322 (1971) 101; V.l. Maron, Int. J. Multiphase Flow 4 (1977) 339; R. Smith, J. Fluid Mech. 105 (1981) 469; 175 (1987) 201; 182 (1987) 447; W.R. Young and S. Jones, Phys. Fluids A 3 (1991) 1087.
J. Camacho, Phys. Rev. E 47,1049 (1993); 48 (1993) 310, 1844.
P. Rigord, Ph. D Thesis, Université de Paris 6, 1990.
H.L. Frisch, Polym. Engn. Sci. 20 (1980) 1; H.B. Hopfenberg and V. Stannett in The Physics of Glassy Polymers (R. N. Howard, ed.), Appl. Sci. Publish., London, 1973.
J. Crank, The Mathematics of Diffusion, Clarendon, Oxford, 1975.
H.B. Hopfenberg, R.M. Holley, and V. Stannett, Polym. Engn. Sci. 9 (1969) 242; T.K. Kwei and H.M. Zupko, J. Polym. Sci. A 2,7 (1969) 867; P. Neogi, AIChE J. 29 (1983) 829.
N.L. Thomas and A.H. Windle, Polymer 23 (1982) 529; C.J. Durning and M. Tabor, Macromolecules 19 (1986) 2220.
V. Méndez, J. Fort and J. Farjas, Phys. Rev. E 60 (1999) 5231; V. Méndez and J.E. Llebot, Phys. Rev. E 56 (1997) 6557.
J. Fort and V. Méndez, Phys. Rev. Lett. 82 (1999) 867; L.L. Cavalli-Sforza, P. Menozzi and A. Piazza, Science 259 (1993) 693.
S. Fedotov, Phys. Rev. E 58 (1998) 5143.
V. Méndez and J. Fort, Phys. Rev. E 60 (1999) 6168; H.G. Ohtmer, S.R. Dunbar and W. Alt, J. Math. Biol. 26 (1988) 263.
V. Méndez and A. Compte, Physica A 260 (1998) 90.
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Jou, D., Casas-Vázquez, J., Lebon, G. (2001). Non-classical Diffusion. In: Extended Irreversible Thermodynamics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56565-6_13
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DOI: https://doi.org/10.1007/978-3-642-56565-6_13
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