Numerical simulation of FID hydrodynamics of protein crystallization

Recently, some of us have proposed predictive equations for the four diffusion coefficients, Dij, in a ternary system of hard spheres. These equations have been tested successfully for some ternary systems of interest in protein crystallization: mixture of PEGs in aqueous solution, and the system lysozyme-NaCl-H2O. These equations supply the tools for a correct coupled analysis of the diffusion phenomena occurring in crystallization processes. Using the previous approach for the dependence of the four diffusion coefficients on the solute concentrations, a numerical analysis of transport phenomena in a model system that can simulate protein crystal growth has been carried out. The set of equations is based on the incompressible form of the two-dimensional and time dependent Navier-Stokes equations. The hypothesis of variable thermodynamic properties (diffusion and dynamical viscosity) and the Bousinnesq approximation for the momentum equation have been considered. The study has been performed by means of a numerical code based on a finite difference method. The influence of the coupled diffusion has been evaluated at different gravity levels.