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Nonlinear diffusion equations in fluid mixtures
1. | DIBRIS, University of Genoa, Via Opera Pia 11A, 16145 Genoa, Italy |
References:
[1] |
W. J. Boettinger, J. E. Guyer, C. E. Campbell and G. B. McFadden, Computation of the Kirkendall velocity and displacement field in a one-dimensional binary diffusion couple with a moving interface, Proc. Royal Soc. A, 463 (2007), 3347-3373.
doi: 10.1098/rspa.2007.1904. |
[2] |
J. O'M. Bokris and A. K. N. Reddy, Modern Electrochemistry,, Plenum, ().
|
[3] |
R. M. Bowen and J. C. Wiese, Diffusion in mixtures of elastic materials, Int. J. Engng Sci., 7 (1969), 689-722.
doi: 10.1016/0020-7225(69)90048-2. |
[4] |
M. F. Mc Carthy, Singular Surfaces and Waves,, in Continuum Physics II (ed. A.C. Eringen), (): 449.
|
[5] |
J. Crank, The Mathematics of Diffusion, Oxford, at the Clarendon Press, 1956. |
[6] |
J. A. Dantzig, W. J. Boettinger, J. A. Warren, G. B. McFadden, S. R. Coriell and R. F. Sekerka, Numerical modeling of diffusion-induced deformation, Metall. Mat. Trans. A, 37 (2006), 2701-2714.
doi: 10.1007/BF02586104. |
[7] |
L. S. Darken, Diffusion, mobility and their interrelation through free energy in binary metallic systems, Trans. AIME, 175 (1948), 184-201. |
[8] |
M. Fabrizio, C. Giorgi and A.Morro, A thermodynamic approach to non-isothermal phase-field evolution in continuum physics, Physica D, 214 (2006), 144-156.
doi: 10.1016/j.physd.2006.01.002. |
[9] |
M. E. Gurtin, Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance, Physica D, 92 (1996), 178-192.
doi: 10.1016/0167-2789(95)00173-5. |
[10] |
J. B. Haddow and J. L. Wegner, Plane harmonic waves for three thermoelastic theories, Math. Mech. Solids, 1 (1996), 111-127. |
[11] |
P. M. Jordan, Second-sound propagation in rigid, nonlinear conductors, Mech. Res. Comm., 68 (2015), 52-59.
doi: 10.1016/j.mechrescom.2015.04.005. |
[12] |
P. J. A. M. Kerkhof and M. A. M. Geboers, Analysis and extension of the tehory of multicomponent fluid diffusion, Chem. Engng Sci., 60 (2005), 3129-3167. |
[13] |
B. J. Kirby, Micro- and Nanoscale Fluid Mechanics, Transport in microfluidic devices. Paperback reprint of the 2010 original. Cambridge University Press, Cambridge, 2013. |
[14] |
J. C. Maxwell, On the dynamical theory of gases, The Scientific Papers of J.C. Maxwell, 2 (1965), 26-78. |
[15] |
A. Morro, Governing equations in non-isothermal diffusion, Int. J. Non-Linear Mech., 55 (2013), 90-97.
doi: 10.1016/j.ijnonlinmec.2013.04.010. |
[16] |
A. Morro, Evolution equations for non-simple viscoelastic solids, J. Elasticity, 105 (2011), 93-105.
doi: 10.1007/s10659-010-9292-3. |
[17] |
I. Müller, Thermodynamics of mixtures of fluids, J. Mécanique, 14 (1975), 267-303. |
[18] | |
[19] |
I. Müller, Thermodynamics of mixtures and phase field theory, Int. J. Solids Structures, 38 (2001), 1105-1113. |
[20] |
I. Müller and T. Ruggeri, Extended Thermodynamics, Springer, New York 1993, ξ 2.5.
doi: 10.1007/978-1-4684-0447-0. |
[21] |
S. Rehfeldt and J. Stichlmair, Measurement and calculation of multicomponent diffusion coefficients in liquids, Fluid Phase Equilibria, 256 (2007), 99-104.
doi: 10.1016/j.fluid.2006.10.008. |
[22] |
R. F. Sekerka, Similarity solutions for a binary diffusion couple with diffusivity and density dependent on composition, Prog. Mat. Sci, 49 (2004), 511-536.
doi: 10.1016/S0079-6425(03)00033-1. |
[23] |
J. Stefan, Über das Gleichgewicht und Bewegung, insbesondere die Diffusion von Gemishen, Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften Wien, 63 (1871), 63-124. |
[24] |
I. Steinbach and M. Apel, Multi phase field model for solid state transformation with elastic strain, Physica D, 217 (2006), 153-160.
doi: 10.1016/j.physd.2006.04.001. |
[25] |
B. Straughan, Heat Waves, Springer, New York, 2011.
doi: 10.1007/978-1-4614-0493-4. |
[26] |
C. Truesdell, Rational Thermodynamics, Springer, New York, 1984.
doi: 10.1007/978-1-4612-5206-1. |
[27] |
C. Truesdell and R. Toupin, The classical field theories, Handbuch der Physik, Bd. III/1, Springer, Berlin, (1960), 226-793; appendix, 794-858. |
show all references
References:
[1] |
W. J. Boettinger, J. E. Guyer, C. E. Campbell and G. B. McFadden, Computation of the Kirkendall velocity and displacement field in a one-dimensional binary diffusion couple with a moving interface, Proc. Royal Soc. A, 463 (2007), 3347-3373.
doi: 10.1098/rspa.2007.1904. |
[2] |
J. O'M. Bokris and A. K. N. Reddy, Modern Electrochemistry,, Plenum, ().
|
[3] |
R. M. Bowen and J. C. Wiese, Diffusion in mixtures of elastic materials, Int. J. Engng Sci., 7 (1969), 689-722.
doi: 10.1016/0020-7225(69)90048-2. |
[4] |
M. F. Mc Carthy, Singular Surfaces and Waves,, in Continuum Physics II (ed. A.C. Eringen), (): 449.
|
[5] |
J. Crank, The Mathematics of Diffusion, Oxford, at the Clarendon Press, 1956. |
[6] |
J. A. Dantzig, W. J. Boettinger, J. A. Warren, G. B. McFadden, S. R. Coriell and R. F. Sekerka, Numerical modeling of diffusion-induced deformation, Metall. Mat. Trans. A, 37 (2006), 2701-2714.
doi: 10.1007/BF02586104. |
[7] |
L. S. Darken, Diffusion, mobility and their interrelation through free energy in binary metallic systems, Trans. AIME, 175 (1948), 184-201. |
[8] |
M. Fabrizio, C. Giorgi and A.Morro, A thermodynamic approach to non-isothermal phase-field evolution in continuum physics, Physica D, 214 (2006), 144-156.
doi: 10.1016/j.physd.2006.01.002. |
[9] |
M. E. Gurtin, Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance, Physica D, 92 (1996), 178-192.
doi: 10.1016/0167-2789(95)00173-5. |
[10] |
J. B. Haddow and J. L. Wegner, Plane harmonic waves for three thermoelastic theories, Math. Mech. Solids, 1 (1996), 111-127. |
[11] |
P. M. Jordan, Second-sound propagation in rigid, nonlinear conductors, Mech. Res. Comm., 68 (2015), 52-59.
doi: 10.1016/j.mechrescom.2015.04.005. |
[12] |
P. J. A. M. Kerkhof and M. A. M. Geboers, Analysis and extension of the tehory of multicomponent fluid diffusion, Chem. Engng Sci., 60 (2005), 3129-3167. |
[13] |
B. J. Kirby, Micro- and Nanoscale Fluid Mechanics, Transport in microfluidic devices. Paperback reprint of the 2010 original. Cambridge University Press, Cambridge, 2013. |
[14] |
J. C. Maxwell, On the dynamical theory of gases, The Scientific Papers of J.C. Maxwell, 2 (1965), 26-78. |
[15] |
A. Morro, Governing equations in non-isothermal diffusion, Int. J. Non-Linear Mech., 55 (2013), 90-97.
doi: 10.1016/j.ijnonlinmec.2013.04.010. |
[16] |
A. Morro, Evolution equations for non-simple viscoelastic solids, J. Elasticity, 105 (2011), 93-105.
doi: 10.1007/s10659-010-9292-3. |
[17] |
I. Müller, Thermodynamics of mixtures of fluids, J. Mécanique, 14 (1975), 267-303. |
[18] | |
[19] |
I. Müller, Thermodynamics of mixtures and phase field theory, Int. J. Solids Structures, 38 (2001), 1105-1113. |
[20] |
I. Müller and T. Ruggeri, Extended Thermodynamics, Springer, New York 1993, ξ 2.5.
doi: 10.1007/978-1-4684-0447-0. |
[21] |
S. Rehfeldt and J. Stichlmair, Measurement and calculation of multicomponent diffusion coefficients in liquids, Fluid Phase Equilibria, 256 (2007), 99-104.
doi: 10.1016/j.fluid.2006.10.008. |
[22] |
R. F. Sekerka, Similarity solutions for a binary diffusion couple with diffusivity and density dependent on composition, Prog. Mat. Sci, 49 (2004), 511-536.
doi: 10.1016/S0079-6425(03)00033-1. |
[23] |
J. Stefan, Über das Gleichgewicht und Bewegung, insbesondere die Diffusion von Gemishen, Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften Wien, 63 (1871), 63-124. |
[24] |
I. Steinbach and M. Apel, Multi phase field model for solid state transformation with elastic strain, Physica D, 217 (2006), 153-160.
doi: 10.1016/j.physd.2006.04.001. |
[25] |
B. Straughan, Heat Waves, Springer, New York, 2011.
doi: 10.1007/978-1-4614-0493-4. |
[26] |
C. Truesdell, Rational Thermodynamics, Springer, New York, 1984.
doi: 10.1007/978-1-4612-5206-1. |
[27] |
C. Truesdell and R. Toupin, The classical field theories, Handbuch der Physik, Bd. III/1, Springer, Berlin, (1960), 226-793; appendix, 794-858. |
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