Relative velocity profile and flow‐rate in sedimentation field‐flow fractionation

Abstract

SummaryAlthough the classical retention theory is used for interpreting data or optimizing separations in sedimentation field-flow fractionation (SedFFF), as in most other field-flow fractionation techniques, the assumption of a parabolic flow profile on which this theory is based is not rigorously correct in SedFFF because of the curvature of the channel walls. In order to examine quantitatively the influence of this effect, the relative velocity profile in SedFFF is obtained by solving the Navier-Stokes equation in cylindrical coordinates. Discrepancies found in the literature about the definition of the mean velocity in such channels are discussed. Relationships between mean velocity, flow-rate and pressure gradient are given. Approximating the velocity profile by a third-degree polynomial of the radial coordinate which provides the same slope as the exact profile at a reference wall, for small values of 6, the curvature ratio (ratio of the channel thickness to the mean curvature radius), shows that the adjustable parameter of the approximate profile, v, is equal to f 6/3, the sign depending on whether the reference wall is the inner or outer wall. The curvature ratio appears to be a good indicator of the error made on retention when using the straight channel approximation in retention theory. The error is quite small for typical SedFFF channels. It may have to be taken into account for precise determinations if thicker channels and/or miniaturized systems are used.

Retention in Field-Flow Fractionation with a Moderate Nonuniformity in the Field Force

“…The implementation of the proposed approach is relatively simple and is summarized as follows. First, the flow distortion parameter, ν, is computed or estimated (see refs and for estimation of ν in thermal FFF and sedimentation FFF, respectively). With this value of ν and the experimentally determined retention ratio, R , λ app is computed from eq 3.…”

“…In sedimentation FFF, deviations from the parabolic flow profile are due to the curvature of the flow streamlines. It can be shown that the ν parameter of the approximate third-degree polynomial velocity profile is equal to plus or minus one-third of the curvature ratio, i.e., of the ratio of w to the average radius of curvature of the two channel walls, R c , the sign depending on whether the accumulation wall is the inner or outer wall . In present-day sedimentation FFF systems, the curvature ratio is very small, and the deviation of the flow profile is not significant.…”

Precision in differential field‐flow fractionation: A chemometric study

“…Nevertheless, when the ratio of the channel thickness to the curvature radius is as low as that of the channel used in the present study, the correction to be brought to Eq. (8) can be safely neglected [15]. Experimentally, R allows to calculate the value of the k parameter, which gives information on particle effective mass or size using Eqs.…”