Abstract
We present an order-of-magnitude analysis of the Navier-Stokes equations in a time-dependent, incompressible and Boussinesq formulation. The hypothesis employed of two different length scales allows one to determine the different flow regimes on the basis of the geometrical and thermodynamical parameters alone, without solving the Navier-Stokes equations. The order-of-magnitude analysis is then applied to the field of protein crystallization, and to the flow field around a crystal, where the driving forces are solutal buoyancy-driven convection, from density dependence on species concentration, and sedimentation caused by the different densities of the crystal and the protein solution. The main result of this paper is to provide predictions of the conditions in which a crystal is growing in a convective regime, rather than in the ideal diffusive state, even under the typical microgravity conditions of space platforms.
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References
J. R. Helliwell: Macromolecular crystallography with synchrotron radiation, Cambridge University Press (1992).
A. McPherson: Preparation and analysis of protein crystals, Krieger Publishing (1982); A. Ducruix and R. Giegé, editors, Crystallization of nucleic acids and proteins, Oxford University Press (1999).
F. Otálora, M. L. Novella, J. A. Gavira, V. R. Thomas andJ. M. García Ruiz: Experimental evidence for the stability of the depletion zone around growing protein crystal under microgravity, Acta Cryst D 57, 412–417 (2001).
L. G. Napolitano: Surface and buoyancy driven free convection, Acta Astronautica 9, 199–215 (1982).
G. Russo and L. G. Napolitano: Order of magnitude analysis of unsteady Marangoni and buoyancy free convection, IAF-84-150, 35th Congress, Switzerland, (1984).
L. D. Landau and E. M. Lifshitz: Fluid Mechanics, 2nd Ed., Pergamon (1987).
L. K. Steinrauf: Preliminary X-ray data for some new crystalline forms of β-lactoglobulin and hen-egg-white lysozyme, Acta Cryst. 12, 77 (1959); S. B. Dubin, G. Feher, and G. B. Benedek, Study of the chemical denaturation of lysozyme by optical mixing spectroscopy Biochem. 12, 714–719 (1973); W. J. Fredericks, M. C. Hammonds, S. B. Howard, and F. Rosenberger, Density, thermal expansivity, viscosity and refractive index of lysozyme solutions at crystal growth concentrations, J. Cryst. Growth 141, 183–192 (1994).
D. N. Petsev, B. R. Thomas, S.-T. Yau, andP. G. Vekilov: Interactions and aggregation of apoferritin molecules in solution: Effects of added electrolytes, Biophys. J. 78, 2060–2069 (2000).
A. J. Fletcher: Computational Techniques for Fluid Dynamics, vol 2, Springer (1991).
R. De Lombard: Compendium of Information for Interpreting the Microgravity Environment of the Orbiter Spacecraft, NASA Tech. Memorandum, 107032, 1–40, (1996).
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Carotenuto, L., Cartwright, J.H.E., Castagnolo, D. et al. Theory and simulation of buoyancy-driven convection around growing protein crystals in microgravity. Microgravity sci. Technol. 13, 14 (2002). https://doi.org/10.1007/BF02872072
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DOI: https://doi.org/10.1007/BF02872072