Retention ratio and nonequilibrium bandspreading in asymmetrical flow field-flow fractionation

In asymmetrical flow field-flow fractionation (As-FlFFF), only the membrane-covered accumulation wall is permeable to fluid; the opposite channel wall is impermeable. Fluid enters the channel at the inlet and exits partly through the membrane-covered accumulation wall and partly through the channel outlet. This means that not only does the volumetric channel flow rate decrease along the channel length as fluid exits through the membrane but also the cross-channel component to fluid velocity must approach zero at the impermeable wall. This dependence of cross-channel fluid velocity on distance across the channel thickness influences the equilibrium concentration profile for the sample components introduced to the channel. The concentration profile departs from the exponential profile predicted for the ideal model of field-flow fractionation. This influences both the retention ratio and the principal contribution to bandspreading--the nonequilibrium contribution. The derivation of an equation for the nonequilibrium bandspreading parameter χ in As-FlFFF is presented, and its numerical solution graphed. At high retention, it is shown that the solutions for both retention ratio R and χ converge on those for the ideal model, as expected. At lower levels of retention, the departures from the ideal model are significant, particularly for bandspreading. For example, at a level of retention corresponding to a retention parameter λ of 0.05, R is almost 4% higher than for the ideal model (0.28047 as compared to 0.27000) but the value of χ is almost 60% higher. The equations presented for both R and χ include a first-order correction for the finite size of the particles--the steric exclusion correction. These corrections are shown to be significant for particle sizes eluting well before steric inversion. For example, particles of half the inversion diameter are predicted to elute 25% slower and to show almost 40% higher bandspreading when steric effects are not accounted for. The work presented contributes to the fundamental theory of As-FlFFF and allows quantitative prediction of both retention and bandspreading at all levels of retention.