Effect of secondary flows on dispersion in finite-length channels at high Peclet numbers

Abstract

We investigate the effects of secondary (transverse) flows on convection-dominated dispersion of pressure driven, open column laminar flow in a conduit with rectangular cross-section. We show that secondary flows significantly reduce dispersion (enhancing transverse diffusion) in Taylor-Aris regime [H. Zhao and H. H. Bau, “Effect of secondary flows on Taylor-Aris dispersion,” Anal. Chem. 79, 7792–7798 (2007)], as well as in convection-controlled regime. In the convection-controlled dispersion regime (i.e., laminar dispersion in finite-length channel with axial flow at high Peclet numbers) the properties of the dispersion boundary layer and the values of the scaling exponents controlling the dependence of the moment hierarchy on the Peclet number \documentclass[12pt]{minimal}\begin{document}$m^{(n)}_{\rm out} \sim Pe_{\rm eff}^{\theta _n}$\end{document}m out (n)∼Pe eff θn are determined by the local near-wall behaviour of the axial velocity. The presence of transverse flows strongly modify the localization properties of the dispersion boundary layer and consequently the moment scaling exponents. Different secondary flows, electrokinetically induced and independent of the primary axial flow are considered. A complete scaling theory is presented for the nth order moment of the outlet chromatogram as a function of the axial Peclet number, the secondary flow's pattern and intensity. We show that some secondary flows (the corotating and the counter-rotating cavity flows) significantly reduce dispersion and \documentclass[12pt]{minimal}\begin{document}$m^{(n)}_{\rm out} \sim Pe_{\rm eff}^{(n-1)/3}$\end{document}m out (n)∼Pe eff (n−1)/3. No significant dispersion reduction is obtained with the cavity cross-flow \documentclass[12pt]{minimal}\begin{document}$m^{(n)}_{\rm out} \sim Pe_{\rm eff}^{(n-1)/2}$\end{document}m out (n)∼Pe eff (n−1)/2. The best result is obtained with the two full-motion counter-rotating cross-flows because \documentclass[12pt]{minimal}\begin{document}$m^{(n)}_{\rm out}$\end{document}m out (n) saturates towards a constant value. Theoretical results from scaling theory are strongly supported by numerical results obtained by Finite Element Method.