The Lamm equation[1] describes the sedimentation and diffusion of a solute under ultracentrifugation in traditional sector-shaped cells.
It was named after Ole Lamm, later professor of physical chemistry at the Royal Institute of Technology, who derived it during his PhD studies under Svedberg at Uppsala University.
The first and second terms on the right-hand side of the Lamm equation are proportional to D and sω2, respectively, and describe the competing processes of diffusion and sedimentation.
The diffusion constant D can be estimated from the hydrodynamic radius and shape of the solute, whereas the buoyant mass mb can be determined from the ratio of s and D where kBT is the thermal energy, i.e., the Boltzmann constant kB multiplied by the absolute temperature T. Solute molecules cannot pass through the inner and outer walls of the cell, resulting in the boundary conditions on the Lamm equation at the inner and outer radii, ra and rb, respectively.
By spinning samples at constant angular velocity ω and observing the variation in the concentration c(r, t), one may estimate the parameters s and D and, thence, the (effective or equivalent) buoyant mass of the solute.