Abstract
AN exact solution of the Lamm equation: is of considerable utility in ultracentrifugal analysis1. In this equation c(r, t) is the concentration of solute in a two-component system, D is the diffusion constant, s is the sedimentation coefficient, and ω2 is the square of the frequency. Archibald has calculated an exact solution for s and D independent of concentration, with the boundary conditions2: The experimental dependence of s on c is : but no one has succeeded in solving equation (1) with this form for s. In 1956 Fujita showed that if equation (3) is approximated by: that is, the concentration is low enough, then the resulting non-linear equation can rigorously be linearized3. Recently the exact Faxén solution has been found, that is, a solution assuming that the cell is an infinite wedge4.
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References
Fujita, H., Mathematical Theory of Sedimentation Analysis (Academic Press, New York, 1962).
Archibald, W. J., Ann. N.Y. Acad. Sci., 43, 211 (1942).
Fujita, H., J. Chem. Phys., 24, 1084 (1956).
Weiss, G. H., J. Math. Phys. (in the press).
Billick, I., and Weiss, G. H., J. Res. Nat. Bur. Stand., A (in the press).
Weiss, G. H., and Yphantis, D. A. (in preparation).
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WEISS, G. An Archibald-type Solution to a Non-linear Lamm Equation. Nature 202, 792–793 (1964). https://doi.org/10.1038/202792a0
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DOI: https://doi.org/10.1038/202792a0
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