Showing papers on "Lamm equation published in 1964"
TL;DR: In this article, the exact Faxen solution of the Lamm equation has been found, that is, a solution assuming that the cell is an infinite wedge, but no one has succeeded in solving equation (1) with this form for s.
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 Faxen solution has been found, that is, a solution assuming that the cell is an infinite wedge4.
6 citations
TL;DR: In this article, an exact Faxen solution for the Lamm equation is presented for the Fujita model with the assumption that the diffusion constant is independent of concentration but the sedimentation coefficient depends linearly on concentration.
Abstract: THE solution given by Faxen to the Lamm equation has been discussed by several authors1–3. It contains two types of approximation, the first of which assumes that the ultra-centrifuge is infinitely long, and the second assumes that both the sedimentation and diffusion coefficients are independent of concentration. Although an exact solution is available for realistic boundary conditions4, the Faxen solution has so far proved to be of considerable utility in applications. It is, therefore, still of some interest to analyse the Faxen type models. Fujita has proposed a model for the ultracentrifuge in which the diffusion constant is independent of concentration but the sedimentation coefficient depends linearly on concentration: where s is the sedimentation coefficient and c is the concentration5. The original paper by Fujita contained an approximate solution to this modified Faxen problem. It is the purpose of this communication to point out that an exact solution is available for the Fujita model. The basic solution is given here and is in a form which can be treated easily by numerical methods.
2 citations
TL;DR: In this paper, a Hankel transform technique is used to derive the Faxen solution to the Lamm equation when the sedimentation coefficient is constant and when it varies linearly with concentration.
Abstract: In this paper a Hankel transform technique is used to derive the Faxen solution to the Lamm equation when the sedimentation coefficient is constant and when it varies linearly with concentration.
1 citations