  This work is devoted to the derivation and the matematical study of a new
model for water-soluble polymers and metal ions interactions, which are used in
chemistry for their wide range of applications. First, we motivate and derive a
model that describes the evolution of the configurational distribution of
polymers. One of the novelty resides in the configuration variables which
consider both, the size of the polymers and the quantity of metal ions they
captured through sorption. The model consists in a non-linear transport
equation with a quadratic source term, the coagulation. Then, we prove the
existence of solutions for all time to the problem thanks to classical fixed
point theory. Next, we reformulate the coagulation operator under a
conservative form which allows to write a finite volume scheme. The sequence of
approximated solutions is proved to be convergent (toward a solution to the
problem) thanks to a $L^1 - weak$ stability principle. Finally, we illustrate
the behaviour of the solutions using this numerical scheme and we intend to
discuss on the long-time behaviour.
