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1
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0346505865
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and references therein
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For an extensive review see: A. J. Bray, Adv. Phys. 43, 357 (1994), and references therein.
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(1994)
Adv. Phys.
, vol.43
, pp. 357
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Bray, A.J.1
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23
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5444261585
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Ph.D. thesis, University of Jyvakyla
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A. Koponen, Ph.D. thesis, University of Jyvakyla, 1998.
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(1998)
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Koponen, A.1
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25
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4243307948
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A. K. Gunstensen, D. H. Rothman, S. Zaleski, and G. Zaaetti, Phys. Rev. A 43, 4320 (1991).
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Phys. Rev. A
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Gunstensen, A.K.1
Rothman, D.H.2
Zaleski, S.3
Zaaetti, G.4
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28
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4644301820
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M. R. Swift, E. Orlandini, W. R. Osbom, and J. M. Yeomans, Phys. Rev. E 54, 5041 (1996).
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(1996)
Phys. Rev. E
, vol.54
, pp. 5041
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Swift, M.R.1
Orlandini, E.2
Osbom, W.R.3
Yeomans, J.M.4
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30
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0000548005
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M. San Miguel, M. Grant, and J. D. Gunton, Phys. Rev. A 31, 1001 (1985); H. Furukawa, ibid. 31, 1103 (1985).
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(1985)
Phys. Rev. A
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, pp. 1001
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Miguel, M.S.1
Grant, M.2
Gunton, J.D.3
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31
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33646988727
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M. San Miguel, M. Grant, and J. D. Gunton, Phys. Rev. A 31, 1001 (1985); H. Furukawa, ibid. 31, 1103 (1985).
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Phys. Rev. A
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32
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0035934131
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and Ref. 6 therein
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F. Qiu, G. Peng, V. Ginzburg, H. Chen, D. Jasnow, and A. C. Balazs, J. Chem. Phys. 115, 3779 (2001), and Ref. 6 therein.
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J. Chem. Phys.
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Qiu, F.1
Peng, G.2
Ginzburg, V.3
Chen, H.4
Jasnow, D.5
Balazs, A.C.6
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34
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5444258380
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note
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22 with the assumption that A and B have the same molecular weight and the molecular weight of C is twice as high. To derive the above set of equations Tong employed Reyleigh's variational method. Furthermore, the On-sager coefficients were assumed to be constants, independent of the order parameters.
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35
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5444250790
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note
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The late time behavior remains quantitatively the same whether we choose a linear or quadratic dependence of ψ in this term.
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36
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5444242964
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note
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The scaling law for the interfacial tension depends on the scaling chosen for the nonlocal coupling term, but is not completely defined by it. Interfacial tension also depends on the actual density profiles along the interfaces. The density profiles are governed by the reaction rates, the effective values of the parameters in the free energy, as well as by the hydrodynamic regimes. The analysis of the scaling for the interfacial tension is a subject of a separate study. In the current work, we only require a reduction of the interfacial tension to zero when the interface is saturated.
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37
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0035839235
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V. M. Kendon, M. E. Cates, I. Pagonabarraga, J. C. Desplat, and P. Bladon, J. Fluid Mech. 440, 147 (2001).
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(2001)
J. Fluid Mech.
, vol.440
, pp. 147
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Kendon, V.M.1
Cates, M.E.2
Pagonabarraga, I.3
Desplat, J.C.4
Bladon, P.5
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40
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0035839235
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I. M. Lifshitz and V. V. Slyozov, J. Phys. Chem. Solids 19, 35 (1961); J. Fluid Mech. 440, 147 (2001).
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(2001)
J. Fluid Mech.
, vol.440
, pp. 147
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41
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5444276142
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note
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The small negative values in the density of C near the phase boundaries in this plot, as well as in Fig. 2. are unphysical and indicate a limit of accuracy for the model. However, we can apply the same model to the case where A, B, and C are not pure components, but A-rich. B-rich, and C-rich regions, where the negative values of C have a real physical meaning.
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42
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5444240000
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note
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2terms in the free energy to zero. In the other words, for the free energy that is rewritten in terms of two order parameters we should choose an appropriate negative value of kφ. Also, in this ease, higher order gradient terms may be needed to describe the A/C (B/C) interface in order for the model to be stable. In addition, for wide regions of C, the equilibrium solution of the kinetic reaction equations (without diffusion) should correspond to the minimum of the free energy in the appropriate region.
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