Asymptotic kinetics of phase coarsening in dilute systems

A detailed discussion is presented of the monopole approximation commonly used to model coarsening systems, whereby each particle is represented by an equivalent point source or sink of solute located at the particle center. This approach applies the interfacial boundary condition only in an average sense for each particle and does not exclude the interior volume of the particles from the field domain. These approximations introduce an error in the derived coarsening rate that scales as >πf13 to first order, where φ is the volume fraction of the dispersed phase. This error is larger than the Φ12 correction to infinitely dilute systems (φ = 0) that resultsfrom analyses of electrostatic monopole interactions.