Packed columns velocity gradients

FIG U RE 1.13 Gradient separation of polypeptides on silica rod column and particle-packed columns. Mobile phase velocity 4mm/s, gradient 5%-60% ACN in the presence of TFA, gradient time 5min, columns (a) silica rod column, (b) Capcellpak SG (5 pm), (c) LiChrospher WP 300 RP-18e (5 pm), (d) nonporous NPS-ODS-1 HPLC column (1.5pm) (e) polymer-based TSKgel Octadecyl-NPR (2.5pm). (Reprinted from Minakuchi, H. et al., J. Chromatogr. A, 828, 83, 1998. Copyright 1998, with permission from Elsevier.)... 

A considerable difference exists between flow through an open column and packed column as illustrated by Figure 2.11. Darcy s law, which governs flow through packed columns, states that flow velocity is proportional to the pressure gradient. 

To determine the pressure and velocity distributions, we must relate mean cross-sectional flow velocity (v) to the pressure gradient. This is done by means of Eq. 4.11 for capillary tubes and Eq. 4.22 for packed columns. To work with these equations, we must replace the overall pressure gradient Ap/L by the local pressure gradient - dpldx, where the negative sign arises because pressure decreases as one moves along the positive flow coordinate x. With this substitution, Eq. 4.11 can be rearranged to... 

Darcy s law Describes the relationship between mobile phase velocity, v, and the pressure gradient in a packed column, dP/dr ... 

---