Optimum centrifugal separation of particles by transient analysis and

Abstract

A process and apparatus for predicting the time and position dependent concentration of macromolecules of differing species in a gradient forming solution during centrifugation is disclosed. A mathematical model of the time dependent behavior of gradient forming solutes in a centrifugal field, based upon the underlying physical principles governing sedimentation and diffusion is formulated. The simplifying approximation is made that the wall effects may be ignored, and that the transport of solute may be treated as a one dimensional process with forces dependent only upon the radial distance. A sedimentation diffusion (Lamm) equation in one dimension is numerically integrated. The sedimentation diffusion equation (Lamm equation) for each macrosolute is solved concurrently with that for the gradient forming solute, utilizing the experimentally based density dependent sedimentation coefficient. The equations are solved for incremental time periods for the centrifuged samples in successive radial segments. The equations use concentration dependent values of sedimentation and diffusion coefficients of gradient forming solutes. There is obtained the time and position dependence of the concentration of both gradient-forming solutes and macrosolutes at a fixed temperature for an arbitrarily specified starting concentrations of the density forming solute. The distribution of the macromolecule follows from distribution of the gradient forming solute for each time period and each radial slice.