COARSENING OF 3-DIMENSIONAL DROPLETS BY 2-DIMENSIONAL DIFFUSION .2. THEORY

Theoretical modeling of coarsening among a finite cluster of precipita tes is implemented, using the multipole expansion method. This method requires the diffusion field to behave quasi-statically. Two approxima te solutions were developed, one to monopolar order, and other to the dipolar order. The conventional Gibbs-Thomson equilibrium relationship was used as the boundary condition at the precipitate-matrix interfac e. Part I of this paper considers a liquid-liquid system in a mixed-di mensional geometrical configuration, wherein three-dimensional precipi tates interact via a diffusion field constrained in two dimensions. Th is kind of geometric configuration is often encountered in island evol ution dynamics and phase segregation in thin films. The initial experi mental configuration of droplets provides the initial condition for th e simulation. Both monopole and dipole approximations closely follow t he experimentally observed scaling laws, characteristic for the mixed- dimensional coarsening (N-4/3 and R4BAR, varied linearly with time, wh ere N is the number of droplets in the experimental field of view, and RBAR is the average droplet radius). Good agreement is observed for t ime evolution of radii of some individual precipitates. Certain deviat ions appearing among the two approximate solutions and the experimenta l data are discussed.