  We introduce a two-type internal DLA model which is an example of a non-unary
abelian network. Starting with n "oil" and n "water" particles at the origin,
the particles diffuse in Z according to the following rule: whenever some site
x has at least 1 oil and at least 1 water particle present, it "fires" by
sending 1 oil particle and 1 water particle each to an independent random
neighbor x+1 or x-1. Firing continues until every site has at most one type of
particles. We establish the correct order for several statistics of this model
and identify the scaling limit under assumption of existence.
