Fluid-dynamic modelling of protein crystallyzers

Abstract

A fluid-dynamic model of the hanging (or sitting) drop is proposed to study the time evolution of the thermo-solutal flow fields in protein crystallyzers. An Order of Magnitude Analysis of the vapour phase surrounding the drop shows that buoyancy effects are negligible in the vaporization chamber and that the evaporation is a very fast process, so that the rate of evaporation is controlled essentially by water diffusion through the air space. The liquid drop is modelled as a mixture of water, precipitating agent and protein bounded by an undeformable interface with a surface tension depending on the concentrations. The cases considered refer to the crystallization of lysozyme in a solution of NaCl in water. Preliminary numerical results are shown corresponding to zero-g and to one-g (with and without Marangoni effect). The computations seem to indicate that in the pre-nucleation phase the Marangoni effects may be relevant at 0−g for the full drop. For the half-drop geometry Marangoni flows may plays only a role on ground. In the post-nucleation phase the comparison between 0−g and 1−g shows that in ground conditions the mass transfer is enhanced by convection and therefore the crystal growth rate increases, but the nonuniformity in the interface concentration gradients around the growing crystal may have a detrimental effect on the growth kinetics. A preliminary validation of the code is accomplished comparing the numerical results with experimental ones obtained in a facility at MARS center.