**Faxén solutions of the Lamm equation**

The simplest approximation of the Lamm equation solution is that by Faxén (1929), which can be written as

with the meniscus position *r _{m}*, the boundary position of a
non-diffusing species

Faxén solutions according to can be calculated with the calculator function of Sedfit.

The following is sedimentation profiles simulated with finite element methods (dots), compared with the Faxén solutions (lines) in the top graph, and the residuals in the lower graph.

This is for a species with 100kDa, 7S, at 30,000 rpm:

this the same at 50,000 rpm:

this is for 800kDa, 20S, 50,000 rpm

Clearly, the precision of the Faxén solution is not sufficient for the analysis of experimental data.

A different way of using the Faxén approximation is to extract the displacement and the central slope of the sedimentation boundaries from the equation above, and to fit it to a central percentile of the sedimentation boundaries (e.g., fitting only the boundary from 10% - 90% of the plateau value). This is implemented in SEDPHAT, in the Linear Fractional Boundary model.