COMPLEX DYNAMICS OF RHYTHMIC PATTERNS AND SEDIMENTATION OF ORGANIC CRYSTALS: A NEW NUMERICAL APPROACH

Abstract

This article deals with the mathematical modeling and numerical simulation of the complex phenomena related to the crystallization of an organic macromolecular substance due to solubility modulation (lysozyme). Novel mathematical models and numerical strategies are introduced to simulate the protein nucleation and further precipitation (or resolution) according to the concentration distribution and in particular to take into account the motion of the crystals due to the combined effect of gravitational force and viscous drag if the sedimenting process is allowed (protein reactor free of gel). The numerical simulations show that gellified lysozyme reacts to produce "spaced deposits." The phenomenon is characterized by a certain degree of periodicity in time and in space (Liesegang patterns). If the gel matrix is not present, crystals settle in the growth chamber. In this case, due to solutal buoyancy forces, a very complex convection pattern arises whose dynamics depend on the nucleation phenomena occurring in the bulk of the protein chamber.