Professor Mary Wirth and graduate students Bingchuan Wei and Benjamin Rogers from Purdue University demonstrate a quantum leap in protein column efficiency. Using colloidal silica particles of submicrometer diameters (470 nm), they obtained plate heights that were as much as 15-fold lower than the theoretical limit for Hagen-Poiseuille flow. The smallest plate height was 15 nm, 500-fold smaller than previous reports for pressure-driven protein chromatography. This remarkable achievement was attributed to "slip flow," which is explained in this installment. The authors also present a practical example using this new concept.
The plate heights of commercial liquid chromatography (LC) columns have changed little over the last 20 years, following the trend of H
min ≈ 2d
p, where d
p is the particle diameter (1). Simulations have shown that H
min ≈ d
p is the limit for nonporous particles (2). With particle sizes dropping by only a factor of about two during the last 20 years, as such plate heights have improved by the same factor. The reason is not a lack of diligence or creativity; instead, it is because of the fundamental limits of mass transport, with the ultimate limit being the velocity spread of the mobile phase across the spaces between particles. We recently used a nanofluidic phenomenon called slip flow (3–8), which greatly reduces this velocity spread, thereby reducing the plate height dramatically. We demonstrated a plate height as low as 0.03 d
p, which was 15 nm (9). This opens a new horizon for efficiency in ultrahigh-pressure liquid chromatography (UHPLC).
The concept of slip flow is illustrated in Figure 1. Imagine that the walls are the surfaces of two adjacent particles. The familiar Hagen-Poiseuille flow is depicted with its parabolic velocity profile, in which the velocity goes to zero at the walls. This is the realm of chromatography today. The figure also depicts slip flow, in which the velocity does not go to zero at the walls, thereby giving rise to a narrower distribution of velocities in the column. Slip flow occurs when the molecular interactions between fluid and the surface are weak, allowing the fluid at the interface to have a nonzero velocity. The existence of slip flow is common knowledge in the field of fluid dynamics, where it is typically a small correction factor when there are weak fluid–surface interactions, but it becomes a big factor when the channel reaches the scale of tens of nanometers (3–8). Consequently, slip flow always occurs in reversed-phase LC, but it is not distinguishable from Hagen-Poiseuille flow because the dimensions of chromatographic materials are relatively large. The nanoscale channel dimensions are achieved by using submicrometer particles.
Figure 1: Illustration of how slip flow gives a narrower velocity distribution compared to Hagen Poiseuille flow. The velocity is far from zero at the wall for slip flow.
Experimentally, the parabolic flow profile cannot be directly viewed on the nanoscale, but it can be inferred because one can measure a companion to the narrower flow profile: a faster flow rate. Because slip flow gives a nonzero velocity at the wall, the volume flow rate, Q, is enhanced relative to that for Hagen-Poiseuille flow, Q
HP. In equation 1, for a capillary of radius r, the term L
s is the slip length, which is defined as the ratio of the velocity to shear rate, each at the wall.