Prog. Theor. Phys. Vol. 90 No. 3 (1993) pp. 521-528
A New Phenomenological Equation of the Interface Dynamics
Department of Fundamental Sciences, Faculty of Integrated,
Human Studies, Kyoto University, Kyoto 606-01
(Received May 6, 1993)
A new type of the interface dynamics in the late stage of the phase separation process at the critical quench is derived with use of an intuitive solution for the Dirichlet problem of the diffusion equation with the Gibbs-Thomson boundary condition. A quasistatic approximation is used. In the well-known Green formula a mean shielding length is introduced phenomenologically for the charge induction on the earthed random interface. A smoothing process through the diffusion current along the random interface is incorporated in a unified equation with the usual evaporation-condensation process. Both processes are consistent with the t1/3-evolution law.
DOI : 10.1143/PTP.90.521
- I. M. Lifshitz and V. V. Slyozov, J. Phys. Chem. Solid. 19 (1961), 35.
- K. Kawasaki and T. Ohta, Physica A118 (1983), 175.
A. Chakrabarti, R. Toral and J. D. Gunton, Phys. Rev. B39 (1989), 4386[APS].
- Y. Oono, IEICE Trans. E74 (1991), 1379.
- T. Ohta and H. Nozaki, in Space-Time Organization in Macromolecular Fluids, ed. F. Tanaka et al. (Springer-Verlag, 1989).
A. Shinozaki and Y. Oono, Phys. Rev. Lett. 66 (1991), 173[APS].
- T. Hashimoto, M. Takenaka and T. Izumitani, Polymer Commun. 30 (1989), 45.
M. Takenaka, T. Izumitani and T. Hashimoto, J. Chem. Phys. 92 (1990), 4566[CrossRef].
T. Ohta, D. Jasnow and K. Kawasaki, Phys. Rev. Lett. 49 (1982), 1223[APS].
- H. Furukawa, Adv. Phys. 34 (1985), 703.
A. Shinozaki and Y. Oono, Phys. Rev. E47 (1993), 804[APS].
- H. Orihara and Y. Ishibashi, in Dynamics of Ordering Processes in Condensed Matter, ed. S. Komura and H. Furukawa (Plenum Publishing, 1988);
J. Phys. Soc. Jpn. 59 (1990), 2355[JPSJ].
- For example, C. E. Weatherburn, Differential Geometry (Cambridge Univ. Press, 1927).
- T. Ohta, Ann. of Phys. 158 (1984), 33.
- After submittance of the present paper, a similar formula is found in a preprint by C. Yeung, Y. Oono and A. Shinozaki. They also discuss the violation of the order parameter conservation in the Gaussian u-field.
- H. Tomita, Prog. Theor. Phys. 59 (1978), 1116[PTP].
Citing Article(s) :
Progress of Theoretical Physics Vol. 104 No. 2 (2000) pp. 307-324
An Explicit Form of the Equation of Motion of the Interface in Bicontinuous Phases