  In recent work by L. Levine and Y. Peres, it was observed that three models
for particle aggregation on the lattice - the divisible sandpile, rotor-router
aggregation, and internal diffusion limited aggregation - share a common
scaling limit as the lattice spacing tends to zero, if they are started with
the same initial mass configuration. It is straightforward to observe that this
scaling limit is precisely the same as the potential-theoretic operation of
taking the partial balayage of this initial mass configuration to the Lebesgue
measure. However, from the theory of the partial balayage operation it is clear
that one may take the partial balayage of a mass configuration to a more
general measure than the Lebesgue measure, which one cannot do for the three
aggregation models described by Levine and Peres. In this paper we therefore
generalize one of these models, the divisible sandpile model, in mainly a
bounded setting, and show that a natural scaling limit of this generalization
is given by a general partial balayage operation.
