  We study the weak solvability of a quasilinear reaction-diffusion system
nonlinearly coupled with an linear elliptic system posed in a domain with
distributed microscopic balls in $2D$.
  The size of these balls are governed by an ODE with direct feedback on the
overall problem. The system describes the diffusion, aggregation,
fragmentation, and deposition of populations of colloidal particles of various
sizes inside a porous media made of prescribed arrangement of balls.
  The mathematical analysis of the problem relies on a suitable application of
Schauder's fixed point theorem which also provides a convergent algorithm for
an iteration method to compute finite difference approximations of smooth
solutions to our multiscale model.
  Numerical simulations illustrate the behavior of the local concentration of
the colloidal populations close to clogging situations.
