  We consider coagulation equations of Smoluchowski or Flory type where the
total merge rate has a bilinear form $\pi(y)\cdot A\pi(x)$ for a vector of
conserved quantities $\pi$, generalising the multiplicative kernel. For these
kernels, a gelation transition occurs at a finite time $t_\mathrm{g}\in
(0,\infty)$, which can be given exactly in terms of an eigenvalue problem in
finite dimensions. We prove a hydrodynamic limit for a stochastic coagulant,
including a corresponding phase transition for the largest particle, and
exploit a coupling to random graphs to extend analysis of the limiting process
beyond the gelation time.
