  A multiscale mathematical model is presented to describe the de novo
granulation and the evolution of multispecies granular biofilms within a
continuous reactor. The granule is modelled as a spherical free boundary domain
with radial symmetry. The equation which governs the free boundary is derived
from global mass balance considerations and takes into account the growth of
sessile biomass and the exchange fluxes with the bulk liquid. Starting from a
vanishing initial value, the expansion of the free boundary is initiated by the
attachment process, which depends on the microbial species concentrations
within the bulk liquid and their specific attachment velocity. Nonlinear
hyperbolic PDEs model the growth of the sessile microbial species, while
quasi-linear parabolic PDEs govern the dynamics of substrates and invading
species within the granular biofilm. Nonlinear ODEs govern the evolution of
soluble substrates and planktonic biomass within the bulk liquid. The model is
applied to an anaerobic granular-based system and solved numerically to test
its qualitative behaviour and explore the main aspects of de novo anaerobic
granulation: ecology, biomass distribution, relative abundance, dimensional
evolution of the granules and soluble substrates and planktonic biomass
dynamics within the reactor. The numerical results confirm that the model
accurately describes the ecology and the concentrically-layered structure of
anaerobic granules observed experimentally, and is able to predict the effects
of some significant factors, such as influent wastewater composition,
granulation properties of planktonic biomass, biomass density and hydrodynamic
and shear stress conditions, on the process performance.
