Coagulation-flocculation process on a lattice: Monte Carlo simulations

Coagulation-flocculation, the physicochemical process widely used for purification a wastewater, is affected both by chemical details of involved polymers and by the statistics of their conformations on a large scale. The latter aspect is covered in this study by employing a coarse-grained modelling approach based on a combination of two paradigms of statistical mechanics. One is the self-avoiding walk (SAW) which generates a range of conformations for a linear polymer of $N_{{\rm SAW}}$ monomers. Another one is a non-trivial diffusion limited aggregation (DLA) process of $N_{{\rm DLA}}$ impurities (referred thereafter as "particles") which describes their coagulation occurring with the probability $0< p \leq 1$ ($p=1$ recovers a standard DLA). DLA of diffusive particles is complemented by their irreversible adsorption on the SAW monomers occurring with the probability equal to one, both processes resulting in formation of the DLA-SAW agglomerates. The dynamics of formation of such agglomerates, as well as their fractal dimensions and internal structure are of practical interest. We consider a range of related characteristics, such as: (i) absolute $N_a$ and relative $n_a$ adsorbing efficiencies of SAW; (ii) effective gyration radius $R_{g {\rm DLA-SAW}}$ of the DLA-SAW agglomerates; and (iii) the fractal dimension $D_{{\rm DLA-SAW}}$ of these aggregates. These are studied within a wide range for each parameter from a set $\{p,N_{{\rm DLA}},N_{{\rm SAW}}\}$.