  We consider two different models for colloidal particles. In the first model,
we consider their free motion to be diffusion while in the second model we take
it to be integrated Ornstein-Uhlenbeck process. In both models, we derived
collision estimates for pairs of particles. In particular, we found that these
estimates would be different to the Brownian case even when the particles' free
motion is Brownian at macroscopic scales. As a consequence, the coagulation
kernel and diffusivity in the coagulation-diffusion equations would also be
affected accordingly. We then proved that there exists a unique solution to the
coagulation-diffusion equations in these cases under physically reasonable
assumptions.
