Height Equivalent to a Theoretical Plate Theory for Rectangular GC Columns

Abstract

The theory for the height equivalent to a theoretical plate (HETP) of a miniature rectangular gas chromatographic (GC) column is developed in analogy to Golay's theory for an open tubular GC column. The HETP is similar to that for an open tubular column except for the nonequilibrium or mass-transfer term. Unlike prior theories, the nonequilibrium or mass-transfer term is complexly related to column geometry. The theory successfully predicts the performance of fast chromatography, in the form of both short microbore and micromachined columns. For a given column length, rectangular columns have lower HETPs than conventional capillary columns and higher volumetric flow rates. A good rule of thumb is that the resolution can be adjusted by selecting the column height (provided it is much less than the column width), and the volumetric flow of carrier gas can be adjusted by selecting the column width (or cross-sectional area). A satisfactory compromise is to use a low inlet pressure that also provides an HETP that remains nearly constant over a range of pressures.

Development of µGC (micro gas chromatography) with high performance micromachined chip column

“…Theories [14,15] for determining the HETP of a chip column have been developed. Spangler reported HETP of rectangular channel [11], as shown in (3).…”

“…Theory of height equivalent to a theoretical plate (HETP) of rectangular channel of chip columns was reported by Spangler. [11] His model of chip columns is compared with experimental results obtained by the chip columns.…”

Computer simulation and theory of the diffusion- and flow-induced concentration dispersion in microfluidic devices and HPLC systems based on rectangular microchannels

“…For simplicity, a parallel-plate geometry with w h is assumed, which implies that the velocity profile in the mobile phase becomes completely flat along the y-axis, except for the two boundary layers near the walls at y = −w/2 and y = w/2 [27,38,39]. In fact, the average flow velocity in a rectangular channel of the width w = 10h differs by only 6% from that in an infinitely wide channel of the same height h at the same pressure [40].…”

“…(11) have been reported that rely on different approximations or boundary conditions [25][26][27][28][29][30][31][32][33]. It has been shown that additional contributions to HETP are generated at the side-walls of rectangular channels when these channels have a finite width [25][26][27][28][29][30][31][32][33].…”

“…Microfabricated devices usually incorporate channels that roughly have a rectangular cross-section. The performance of rectangular chromatographic columns has been analyzed first by Golay [16] (see also [21]), and was studied extensively in recent contributions [25][26][27][28][29][30][31][32][33]. In addition to theoretical treatments, numerical modeling of mass transfer has proved to be successful in tracing down the performance of such columns [33][34][35][36][37].…”