Analysis of the influence of coupled diffusion on transport in protein crystal growth for different gravity levels

Diffusion has a central role in protein crystal growth both in microgravity conditions and on ground. Recently several reports have been focused on the importance to use the generalized Fick's equations in n-component systems where crystals grow. In these equations the total flux of each component is produced by the own concentration gradient (main flow) and by the concentration gradient of the other components (cross-flow) present in the system. However in literature the latter effect is often neglected, and the so-called pseudo-binary approximation is used. Lin et al. (1995) proposed a mathematical model to evaluate the concentration profile of the species present around a growing protein crystal. Although the model is reliable, it suffers of the pseudo-binary approximation (neglecting cross term diffusion coefficients and using binary diffusion coefficients), probably because of the lack of multicomponent diffusion data. The present model is based on the experimental set-up proposed by Lin et al. (1995). Nevertheless we have included the coupled diffusion effects, according to the correct description of the matter transport through the generalized Fick's equations. The crystal growth rate is calculated for different gravity levels. The model has been applied to the ternary lysozyme-NaCl-water and quaternary lysozyme-poly(ethylene glycol) (PEG)-NaCl-water systems using recent diffusion data.