  We demonstrate how many classes of Smoluchowski-type coagulation models can
be realised as multiplicative Grassmannian flows and are therefore
linearisable, and thus integrable in this sense. First, we prove that a general
Smoluchowski-type equation with a constant frequency kernel, that encompasses a
large class of such models, is realisable as a multiplicative Grassmannian
flow. Second, we establish that several other related constant kernel models
can also be realised as such. These include: the Gallay--Mielke coarsening
model; the Derrida--Retaux depinning transition model and a general mutliple
merger coagulation model. Third, we show how the additive and multiplicative
frequency kernel cases can be realised as rank-one analytic Grassmannian flows.
