An explicit expression for the retention factor and velocity dependency of the mobile zone mass transfer band broadening in packed spheres beds used in liquid chromatography

The present study proposes a ready-to-use analytical expression to calculate the mobile zone mass transfer contribution (h(Cm)) in packed bed columns. For this purpose, first high-accuracy computations of the band broadening in a perfectly ordered sphere array (fcc-arrangement, external porosity epsilon=0.40) were made using computational fluid dynamics (CFD), covering a broad range of zone retention factors (2 <= k"<= 18) and reduced velocities (0 <=nu(i)<= 48). Subsequently, these data were used to determine the value of the geometrical constants in a number of possible analytical expressions for the h(Cm)-contribution. This fitting exercise showed the traditional literature approach, using the Wilson-Geankoplis correlation to calculate the dimensionless Sherwood (Sh) number for the mass transfer, leads to fitting errors on the h(Cm)-term as large as 150%. Instead, a new correlation for Sh is established. In addition, we also explored the difference in fitting accuracy between h(Cm)-expressions based on either a plug-flow or a laminar flow profile assumption. Surprisingly, no significant difference in fitting accuracy between both assumptions was observed. Finally, a best-fit analytical expression is proposed that can represent the CFD-computed band broadening data with an average absolute fitting error of Delta h=0.005, corresponding to a relative error of 2.5% on the h(Cm)-term and of only 0.3% on the total plate height in a perfectly ordered sphere packing. Defining the presently investigated fcc-ordered sphere array with external porosity=40% as the reference geometry for a perfect sphere packing, the established expression can be used as a new yardstick expression against which the degree of eddy-dispersion can be measured. (C) 2020 Elsevier B.V. All rights reserved.

Publication year:2020

Keywords:computational fluid dynamics, Mass transfer, Sherwood number, plate height modelling, plate height equation

CSS-citation score:1

Accessibility:Open