The resolution power of turbulent flow chromatography using carbon dioxide as the mobile phase and coated (crosslinked methyl phenyl polysiloxane) open tube columns (OTCs) as the stationary phase was investigated under retentive conditions (0 < k < 1). The improvement in column efficiency from a laminar to a turbulent flow regime was accurately measured for small molecules (coronene and benzo[a]anthracene). This relative increase in column performance decreased from 9 to 5, 3, and to 3 with increasing the retention factor from 0 to 0.2, 0.5, and to 1.0, respectively. Despite a four to five orders of magnitude larger sample dispersion coefficient in turbulent than in laminar flow, the mass transfer in turbulent flow chromatography is still 12controlled and limited by the slow sample transport across the viscous layer at the column wall. The benefit of turbulent flow chromatography is then restricted to small retention factor (k < 0.2). From a practical viewpoint, turbulent flow chromatography using carbon dioxide as the mobile phase and 20 m long × ۱۸۰ µm i.d. × ۰٫۲ µm film thickness OTCs provides ultra-fast (analysis time < 10 s) and high-resolution (plate counts of 33,000) separations of weakly retained compounds (k ∼۰٫۱) at Reynolds number around 5000 (3.75 mL/min, 3000 psi back pressure).

Introduction

It has been sixty years since Golay invented open tubular columns (OTCs) for gas chromatography (GC) analysis of complex petroleum products. At the same time, the well-known fundamental equation of band broadening in OTCs under laminar flow regime was derived : the Golay equation 1 . Aris later confirmed the exactness of this equation by applying his general dispersion theory of solute dispersion through tubes by diffusion, convection, and exchange between phases 2 In contrast to laminar flow regime, turbulent flow along tubes occurs when the inertial stress, τinertial = ρU2 56 (ρ is the fluid density and U is the linear velocity), becomes much stronger than the viscous stress, τviscous = η U D 57 (η is the fluid viscosity and D is the inner diameter of the tube), 58 experienced by the fluid. However, the critical point for the onset of turbulence in pipe flow has always been a source of controversy: the critical ratio of the inertial to the viscous stress, e.g., the critical Reynolds number, typically varies over a wide range from 1500 to 3000 3–۶  More quantitatively, the onset of turbulence has been unambigously defined and observed by experimental physicists 7  . The principle of such method consists in taking a straight pipe, applying a series of flow velocity, and in creating turbulent puffs by disturbing the inlet flow by placing a fixed obstacle at the pipe inlet. It was shown that the temporal evolution of the generated turbulent puffs determined whether the flow regime was pre-turbulent or turbulent. There are only two possible  histories for the generated turbulent puffs: either they vanish or they split into two new turbulent puffs. In the first case scenario, the mean lifetime of the created turbulent puffs increases super68 exponentially with increasing Reynolds number and the flow regime is laminar or pre-turbulent. In the second case scenario, their mean lifetime is decreasing super-exponentially with increasing Reynolds number and a sustained turbulent flow regime is fully developed in the pipe. Accordingly, the onset of turbulence was observed for a very accurate and precise Reynolds number of 2030 ± ۱۰٫