Convective instability in protein crystal growth.

The conditions for the onset of convection during protein crystalization from a solution are studied theoretically on the basis of diffusion-convection evolution equations for the concentrations coupled to the Navier-Stokes equation describing the flow velocity. We consider that the density of the solution depends on the concentration of two species, namely, a protein and a precipitating agent, a salt. While the protein is crystallized at the crystal/solution interface, the salt is rejected, and these mechanisms are described by means of boundary conditions for the interface. We find the base profiles for both protein and salt concentrations and perform a linear stability analysis of this basic state with regard to buoyancy induced perturbations. This gives information on the critical diameter of capillaries above which convection may be observed, as well as on the influence of the speed of growth V of the crystal interface on the stability of the system. Numerical integration of the model shows good agreement with the predictions of the linear stability analysis.