Exact Faxén Solution for Centrifugation when Sedimentation depends linearly on Concentration

Abstract

THE solution given by Faxén to the Lamm equation has been discussed by several authors^1–3. 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 Faxén solution has so far proved to be of considerable utility in applications. It is, therefore, still of some interest to analyse the Faxén 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 Faxén 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.