Analysis of multi-phase systems relevant to bioengineering and materials science

In the thesis the focus is on the analysis of two multiphase systems related to biomedical engineering and materials science. The first part of the thesis is related to the long-term preservation of human Mesenchymal Stem Cells (hMSCs) from Umbilical Cord Blood (UCB) by means of cryopreservation, i.e. freezing the bio-specimens to cryogenic temperature, and drypreservation, i.e. air-drying at room temperature and atmospheric pressure. First, the peculiar osmotic behavior of hMSCs from UCB is analyzed by developing a novel mathematical model. Then, the addition and removal phases of a permeant Cryo-Protectant Agent (CPA) like dymethil-sulfoxide (DMSO) during a cryopreservation protocol is studied taking into account both the cytotoxic effect and osmotic injury (i.e. expansion lysis). Finally, a mathematical model is proposed to guide and support the development of a long-term preservation of hMSCs through air-drying. The second part of the thesis is related to the modeling of mechanical processing of powders by Ball Milling (BM). First the propagation of mechanically activated self-sustaining reactions during BM is investigated by numerical simulations. Then, a statistical description of the kinetics of processes activated by BM coupled with the mathematical description of advection cycles induced by plastic deformation is developed to model the refinement of the lamellar structure in composite Ag-Cu particles during the early stages of mechanical processing. Finally, considering the intrinsic statistical nature of this mechanical process, a kinetic model that combines a phenomenological description of the rheological behavior of molecular solids with the chemistry of interface reactions is developed.