New mathematical models and CFD numerical tools for the investigation of macromolecular crystal growth at macroscopic and microscopic length scales

This analysis deals with advances in computational methods for the investigation of macromolecular crystal growth. The modelling of these processes leads to the introduction of a group of equations, strictly related, from a mathematical point of view, to the ‘kinetic conditions’ used to model mass transfer at the crystal surface as well as to the level of detail required by the analysis ('local' or 'global'); i.e. diversification of the model occurs according to the desired scale length. If the "local" evolution of the crystal surface is the subject of the investigation (distribution of the local growth rate along crystal face, shape instabilities, onset of surface depressions due to diffusive and/or convective effects, etc, i.e. all those factors dealing with the "local" history of the shape) the method must provide "microscopic" and "morphological" details. For this case a ‘kinetic-coefficient-based’ Volume of Fluid Method is specifically and carefully developed taking into account the possibility of anisotropic (faceted) surface-orientation-dependent growth. On the contrary, if the size of the crystals is negligible with respect to the size of the reactor (i.e. if they are small and undergo only small dimensional changes with respect to the overall dimensions of the cell containing the feeding solution), the shape of the crystals is ignored and the proposed approach relies directly on an algebraic formulation of the nucleation events and on the application of an integral form of the mass balance kinetics for each protein crystal. The applicability and the suitability of the different models are discussed according to some worked examples dealing with microgravity conditions.