  We study hydrodynamic limits of the cluster coagulation model; a coagulation
model introduced by Norris [$\textit{Comm. Math. Phys.}$, 209(2):407-435
(2000)]. In this process, pairs of particles $x,y$ in a measure space $E$,
merge to form a single new particle $z$ according to a transition kernel $K(x,
y, \mathrm{d} z)$, in such a manner that a quantity, one may regard as the
total mass of the system, is conserved. This model is general enough to
incorporate various inhomogeneities in the evolution of clusters, for example,
their shape, or their location in space. We derive sufficient criteria for
trajectories associated with this process to concentrate among solutions of a
generalisation of the $\textit{Flory equation}$, and, in some special cases, by
means of a uniqueness result for solutions of this equation, prove a weak law
of large numbers. This multi-type Flory equation is associated with
$\textit{conserved quantities}$ associated with the process, which may encode
different information to conservation of mass (for example, conservation of
centre of mass in spatial models). We also apply criteria for gelation in this
process to derive sufficient criteria for this equation to exhibit gelling
solutions. When this occurs, this multi-type Flory equation encodes, via the
associated conserved property, the interaction between the gel and the finite
size sol particles.
