Dilute aqueous suspensions of silicon nanoparticles and sodium carboxymethylcellulose salt (CMC) are studied experimentally and numerically by Brownian dynamics simulations. The study focuses on the adsorption of CMC on silicon and on the aggregation state as a function of the suspension composition. To perform simulations, a coarse-grained model has first been developed for the CMC Molecules. Then, this model has been applied to study numerically the behavior of suspensions of silicon and CMC. Simulation parameters have been fixed on the basis of experimental characterizations. Results of Brownian dynamics simulations performed with our model are found in qualitative good agreement with experiments and allow a good description of the main features of the experimental behavior.