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(${\mathit{k}}_{\mathit{x}}$,${\mathit{k}}_{\mathit{z}}$,t) (where ${\mathit{k}}_{\mathit{x}}$ and ${\mathit{k}}_{\mathit{z}}$ are, respectively, the x and z components of the wave vector) has the generalized dynamical scaling form S(${\mathit{k}}_{\mathit{x}}$,${\mathit{k}}_{\mathit{z}}$,t) =${\mathit{l}}_{\mathit{x}}$(t)${\mathit{l}}_{\mathit{z}}$(t)F(${\mathit{k}}_{\mathit{x}}$${\mathit{l}}_{\mathit{x}}$(t),${\mathit{k}}_{\mathit{z}}$${\mathit{l}}_{\mathit{z}}$(t)), where ${\mathit{l}}_{\mathit{x}}$(t) and ${\mathit{l}}_{\mathit{z}}$(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 ${\mathit{l}}_{\mathit{z}}$(t)∼t and ${\mathit{l}}_{\mathit{x}}$(t)∼${\mathit{t}}^{1/3}$. The experimental observability of these numerical results is also discussed.

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