In the present dissertation the mathematical modelling of particle deposition is studied and the solution algorithms for particle tracking, deposition and deposit growth are developed. Particle deposition is modelled according to mechanical impact and contact mechanics taking into account the dependency on time, temperature and particle-deposit composition explicitly. Indeed, such a model lies in the field of the rheology of visco-elastic solids which the author of this dissertation refers to in the following chapters. Particle adhesion is calculated by imposing an energy balance between kinetic energy, energy loss and the work of adhesion at the impact while the hard sphere approach is applied to model particle to particle collision. These calculations eventually return as result the particle tangential and normal to impact surface (energy) restitution coefficients. Particular attention was given to the implementation of the solution algorithms and the development of a computational strategy to investigate in detail both particle trajectories, properties and deposit locations. The development of the solution algorithms is twofold, to investigate both particle deposition and the deposit growth applying different computational strategies and algorithms which are usually employed separately (competitor algorithm solution). In the "integrated" approach proposed here, these strategies are coupled (staged partner algorithm solution) according to a sequential use (staged procedure), to provide detailed and time dependent result data. A novel computer program for Lagrangian particle tracking on unstructured meshes, was developed to investigate particle deposition in Computational Fluid Dynamics (CFD) data post-processing. Developing a particle tracker program as a separate and CFD independent computer code has overcome several limitations in particle modelling which are present in commercial CFD code (i.e. non-open source) even though, on the other hand, it required to develop a robust in-cell particle location algorithm as well as an accurate and efficient particle interpolation and integration time scheme. All these characteristics and requirements have driven the author in the development of the Particle Post-Processor software, nicknamed P³, which is capable of calculating particle trajectories and deposition, deposit growth and particle-particle interaction (hard spheres model). A specific particle in-cell detection algorithm, to locate the cell hosting the particle, was developed to upload and elaborate results from commercial CFD codes for hybrid-unstructured meshes. Three commercial CFD codes have been tested. Particle tracking on both Reynolds Averaged Navier-Stokes (RANS) and Large Eddy Simulation (LES) results was successfully performed and compared. Numerical results are substantially in good agreement with the experimentals.