  We study a model of mass-bearing coagulating planar Brownian particles.
Coagulation is prone to occur when two particles become within a distance of
order $\epsilon$. We assume that the initial number of particles is of the
order of $| \log \epsilon |. Under suitable assumptions on the initial
distribution of particles and the microscopic coagulation propensities, we show
that the macroscopic particle densities satisfy a Smoluchowski-type equation.
