Turbulent flow in capillary gas chromatography : evaluation of a theoretical concept by Golay

Early in 1989, the late Marcel Golay derived a theory for turbulent flow capillary gas chromatography. He assumed that the flow pattern under turbulent conditions consists of a turbulent core separated from the tube wall by a very thin laminar flow layer. Further, it was assumed that the viscosity and the diffusion constant are uniform within the turbulent core. The core radius is a fraction p of the tube radius; the core viscosity is m times the laminar flow viscosity and the core diffusivity is assumed to be d times the laminar flow diffusion constant. Values for p, m and d have to be calculated from experimental data; p, m and d are essentially functions of Reynolds number (Re). Using experimental data obtained in the laboratory, Golay's plate-height theory was evaluated for turbulent flow gas chromatography. In this verification an empirical relationship was used for the average turbulent diffusion constant as a function of Reynolds number and an empirical relationship for the thickness of the laminar sublayer. Further, it was assumed that m = d (Reynolds' analogy). The experiments and theory agree fairly well at Re = 6200; at lower and higher values of Re the agreement is much poorer. The disagreement may be due to the empirical relationships used or to the postulations in the theory: Golay assumed a discontinuous change from laminar to turbulent viscosity and diffusion constants. In engineering literature often a gradual change in properties from the laminar sublayer to the turbelent and in the turbulent core is assumed.