Molecular dispersion in pre-turbulent and sustained turbulent flow of carbon dioxide

The average dispersion coefficients, D_a¯, of two small molecules (acetonitrile and coronene) were measured under laminar, transient, and sustained turbulent flow regimes along fused silica open tubular capillary (OTC) columns (180 μm inner diameter by 20 m length). Carbon dioxide was used as the mobile phase at room temperature (296 K) and at average pressures in the range from 1500 to 2700 psi. The Reynolds number (Re) was increased from 600 to 5000. The measurement of D_a¯ is based on the observed plate height of the non-retained analytes as a function of the applied Reynolds number. D_a¯ values are directly estimated from the best fit of the general Golay HETP equation to the experimental plate height curves. The experimental data revealed that under a pre-turbulent flow regime (Re < 2000), D_a¯ is 2-6 times larger (3.5 × 10^-4 cm²/s) than the bulk diffusion coefficients D_m of the analyte (1.6 × 10^-4 and 5.8 × 10^-5 cm²/s for acetonitrile and coronene, respectively). This result was explained by the random formation of decaying or vanishing turbulent puffs under pre-turbulent flow regime. Yet, the peak width remains controlled exclusively by the slow mass transfer in the mobile phase across the inner diameter (i.d.) of the OTC. Under sustained turbulent flow regime (Re > 2500), D_a¯ is about four to five orders of magnitude larger than D_m. The experimental data slightly overestimated the turbulent dispersion coefficients predicted by Flint-Eisenklam model (D_a¯=4 cm²/s). The discrepancy is explained by the approximate nature of the general Golay equation, which assumes that D_a¯ is strictly uniform across the entire i.d. of the OTC. In fact, both the viscous and buffer wall layers, in which viscous effects dominate inertial effects, cannot be considered as fully developed turbulent regions. Remarkably, the mass transfer mechanism in OTC under sustained turbulent flow regime is not only controlled by longitudinal dispersion but also by a slow mass transfer in the mobile phase across the thick buffer layer and the thin viscous layer. Altogether, these layers occupy as much as 35% of the OTC volume at Re = 4000. From a theoretical viewpoint, the general Golay HETP equation is only an approximate model which should be refined based on the actual profile of the analyte dispersion coefficient across the OTC i.d. In practice, the measured plate height of non-retained analytes under sustained turbulent flow of carbon dioxide are two orders of magnitude smaller than those expected under hypothetical laminar flow regime.