Brownian Motion in the Centrifugal Field

Abstract

The combined sedimentation and diffusion process of macromolecules in the centrifugal field was considered phenomenologically. For each dissolved particle a stochastic equation is estimated composed of two independent velocities: a diffusional and a sedimentational. With the help of the ``central limit theorem with Lindeberg conditions'' the formula for the distribution of the particles in a ultracentrifugal cell was derived. A transformation has been found which converts the equations of diffusion alone in the formulas of diffusion in a centrifugal field. The expressions for concentrations in rectangular and sectorial cells can be easily tabulated; they solve the corresponding equations of continuity and fulfill the principle of conservation of amount of dissolved particles in the cell. With help of these formulas the sedimentation constant as well as the diffusion constant can be evaluated from the form of the experimental sedimentation curve.