Approximate Solutions for the Coupled Lamm Equations of Reacting Systems

The use of the weighted-average and constituent sedimentation coefficients has a long history in the analysis of sedimentation velocity of interacting systems. This chapter examines the impact of re-adjustment of species populations due to the radial dilution. The transport method provides a rigorous theoretical background for interpreting the isotherms s_w with models of mass action law and equilibrium thermodynamics. In addition to predicting the boundary pattern, the Gilbert–Jenkins theory aims at describing the boundary shapes of the reaction boundaries. Historically it preceded the ability to numerically solve the Lamm equation for reacting systems, and the restriction to a linear geometry with constant force and a diffusion-free model was essential. The work by Gilbert and Jenkins has been highly influential in many fields. It helped to achieve a general understanding of migrating systems of chemically reacting species in transport methods, including electrophoresis, chromatography, and sedimentation velocity. The chapter reviews the theory for sedimentation of self-associating systems by Gilbert.