Scaling rules for isocratic elution chromatography

Scaling rules for both linear and nonlinear elution chromatography with independent solutes are discussed. The scaling method utilizes smaller diameter particles with high mass transfer rates. The column length, diameter, and cycle time are then scaled so that pressure drop, separation, and throughput are the same or better than in the old design. The new design uses much less packing and cycles more rapidly than the old design. Mathematical derivation shows that the scaling rules for systems with linear and nonlinear isotherms are the same in certain circumstances. Gaussian solutions are used for studying linear systems. Mass transfer zone and diffusive wave analyses are used for constant and proportional patterns, respectively, to describe elution when plateaus form at the feed concentration. Numerical examination of the constant‐pattern elution curve using the Thomas solution shows that the scaling rules are applicable to short columns, which means that there is a negligible entrance effect on the scaling rules. The Thomas solution also shows that the mass transfer resistance has little effect on the scaling rules for the proportional‐pattern wave of a nonlinear solute. Shock and diffusive wave analyses based on the local equilibrium model are employed to describe the separation when the elution curves do not have plateaus. The calculated results show that the scaling rules are followed exactly when pore diffusion controls. Separation of two noninteracting nonlinear components and of a linear and a nonlinear component remains constant when these scaling rules are followed. Several example calculations are used to demonstrate the method.