Convective diffusion in protein crystal growth

Baird, James K.; Meehan, Edward J.; Xidis, A.L.; Howard, Sandra B.

doi:10.1016/0022-0248(86)90186-7

Cited by 32 publications

(17 citation statements)

References 2 publications

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“…͑2.3͒ can be simplified by introducing the two-term Taylor series in (cϪc 0 ). 24 Define ␣ϭ(‫ץ‬ ln ‫ץ/‬ ln c) 0 and the excess concentration ͑x,y ͒ϭ͓c 0 Ϫc͑x,y ͔͒/c 0 .…”

Section: A Similarity Transformationmentioning

confidence: 99%

“…24 To avoid interferences from other edges, we assume that the plate extends to infinity in both the positive and negative z directions. By symmetry, the fluid velocity vϭ͓v x (x,y),v y (x,y)͔ and the solute concentration, cϭc(x,y), reduce to functions of the two spatial coordinates normal to z.…”

Section: A Equations Of Motionmentioning

confidence: 99%

“…A more realistic model should include the fact that the crystal surface absorbs solute at a rate proportional to a power of the supersaturation. 28 It is the purpose of this contribution to add this important sticking reaction to the flat plate model, 24 and to obtain an analytic expression for the global growth rate that can be understood in terms of the empirical hydrodynamic data correlations that have been suggested on the basis of experimental results. [4][5][6] We will show specifically how our theory can be combined with experimental data so as to evaluate not only the specific rate ͑sticking coefficient͒, but also the kinetic order of the sticking reaction.…”

Section: Introductionmentioning

confidence: 99%

“…To provide a theoretical picture of the details of the convection, there have also been presented recently analytical, 24 as well as numerical solutions, [25][26][27] of the Navier-Stokes equation and the equation of convective diffusion for the case of a crystal in the form of a vertical flat plate growing from solution. So far, these theories have dealt only with the case where solute molecules are absorbed upon every collision with the plate.…”

Section: Introductionmentioning

confidence: 99%

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Free convection and surface kinetics in crystal growth from solution

Baird

Li-hong

1998

The Journal of Chemical Physics

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As a crystal grows from solution, there is ordinarily a boundary layer depleted in solute, which forms at the crystal–solution interface. When the normal to the growing crystal surface is oriented in any direction other than parallel to gravity, the boundary layer is set into motion by the force of buoyancy. Using a similarity transformation and a boundary layer approximation, we have solved the Navier–Stokes equation and the equation for convective diffusion for a crystal in the form of a flat plate growing with normal perpendicular to gravity. Parameters in the theory include solute concentration, c0, and diffusion coefficient, D; solution shear viscosity, μ, mass density, ρ, and logarithmic density derivative with respect to concentration, α; crystal solubility, cs, height, h, and linear growth rate, kG; the specific rate, k (sticking coefficient), of the reaction which transfers molecules from the solution to the crystal and the kinetic order, n, of this reaction; and the acceleration due to gravity, g. We find these parameters to be related by the equation log[1−Sh/a (Sc) 1/4(Gr) 1/4φ s1/4]=(1/n) log[a(5/4) n(D/hkc 0n−1)(Sc) 1/4(Gr) 1/4]+[(5/4−n)/n]log φs, where a=0.9, Sh=kGh/D, Sc=μ/ρD, Gr=gαh3ρ2/4μ2, and φs=(c0−cs)/c0. Given a knowledge of the solution physical properties, if Sh is measured as a function of φs and the results plotted in accord with the above equation, both n and k can be determined.

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Section: A Similarity Transformationmentioning

confidence: 99%

Section: A Equations Of Motionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Free convection and surface kinetics in crystal growth from solution

Baird

Li-hong

1998

The Journal of Chemical Physics

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“…However, the results of space-based investigations of the protein crystal growth often showed no improvement and even more inferior to those grown on earth, in the majority of cases. Understanding how microgravity ( g) affects the crystal growth process must be preceded by an understanding of the process on ground, and much careful experimental work have to be devoted on this topic [8][9][10][11][12] .…”

Section: Introductionmentioning

confidence: 99%

Capillary convection in protein crystal growth

Li¹,

Kang²

2001

SPIE Proceedings

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An optical diagnostic system consisting of the Mach-Zehnder interferometer with the phase shift device and the image processor has been developed for the study of the kinetics of protein crystal growing process. The concentration capillary convection around growing protein crystal was investigated during the process of trichosanthin crystal growth. The observation in real time showed that the concentration capillary convection associated with the surface tension of the crystallizing solution occurs at the vicinity of the surface of the protein mother liquor and directly affects on the outcome of protein crystallization, including the process of growth and the quality of resulting crystal. So far the detailed analysis and the important role of the concentration capillary convection in protein crystallization has been overlooked in both the spaceand the ground-based crystal growth experiments. This may be one of the reasons for the majority of the results of space-based investigation shown no improvement.

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