Dynamical scaling in anisotropic phase-separating systems in a gravitational field

Puri, Sanjay ; Binder, Kurt ; Dattagupta, S. (1992) Dynamical scaling in anisotropic phase-separating systems in a gravitational field Physical Review B, 46 (1). pp. 98-105. ISSN 0163-1829

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Official URL: http://prb.aps.org/abstract/PRB/v46/i1/p98_1

Related URL: http://dx.doi.org/10.1103/PhysRevB.46.98


We derive a generalization of the Cahn-Hilliard equation for phase separation in the presence of a field that varies linearly in (say) the z direction, e.g., gravity. The starting point of our derivation is the master-equation description for a spin-exchange kinetic Ising model in the presence of such a field. We neglect thermal fluctuations and the effect of hydrodynamic interactions. We also mptivate the concept of generalized dynamical scaling as a means of characterizing anisotropic domain growth. We present numerical results from a two-dimensional (2D) simulation of this equation. Our results indicate that the 2D time-dependent structure factor S(kx,kz,t) (where kx and kz are, respectively, the x and z components of the wave vector) has the generalized dynamical scaling form S(kx,kz,t) =lx(t)lz(t)F(kxlx(t),kzlz(t)), where lx(t) and lz(t) are time-dependent length scales in the x direction (perpendicular to direction of gravity) and in the z direction (in the direction of gravity), respectively; and F(x,y) is a universal function of its arguments. The temporal behavior of these length scales is lz(t)~t and lx(t)~t1/3. The experimental observability of these numerical results is also discussed.

Item Type:Article
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ID Code:9137
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