The Lamm equation (O. Lamm, 1928) describes the time evolution of the sedimenting boundary:
$$\left(\frac{\partial c}{\partial t} \right)_r =-\frac{\partial}{r\partial r}\left[ \omega^2r^2s(c)c – rD(c) \left( \frac{\partial c}{\partial r} \right)_t \right]$$
The sedimentation coefficient, s, is defined operationally as: $$s \equiv \frac{1}{\omega^2 r}\frac{dr}{dt}$$