Non-linear waves in chromatography: I. Waves, shocks, and shapes

Cause and effect in non-linear chromatography are examined from the point of view of wave theory. This first of four instalments is restricted to single-component systems and examines monotonic concentration variations and chromatographic peaks and bands. It uses the wave equation, which states the velocity at which a given concentration advances, to establish the properties of “waves,” that is, monotonic concentration variations. Depending on the sense of curvature of the isotherm, a wave may be self-sharpening or nonsharpening. A self-sharpening wave remains, or sharpens to become, a shock layer; a nonsharpening wave spreads indefinitely, eventually in proportion to traveled distance. The concentration profile of a shock layer depends on the shape of the isotherm and on the dispersive effect of non-idealities, of which resistance to mass transfer usually is the most important. Mass-transfer resistance in the moving phase causes “fronting:” mass-transfer resistance within the stationary sorbent causes “tailing.” It is therefore in general not possible to model shock layers with only a single, lumped mass-transfer parameter. The concentration profile of a nonsharpening wave depends almost exclusively on the shape of the isotherm. The knowledge of wave behavior is used to examine peak shapes in elution under overload conditions and bands in displacement. The peak shape in elution is almost entirely determined by the degree of overload and the shape of the isotherm. Wave theory confirms a rule previously stated by Knox that, in columns exceeding a certain length, samples containing the same amount of solute give peaks of essentially the same shape under conditions of predominant concentration overload, predominant volume overload, or any combination of the two. In displacement development, the final pattern can be established by determination of the lengths of the bands of the individual components according to Tiselius and separate calculation of the shock-layer profiles.