Dispersion-induced mixing in simple flows: Evidence for new anomalous scaling laws in the mixing boundary layer beyond the Lèvêque theory

Dipartimento di Ingegneria Chimica Materiali Ambiente, Università di Roma “La Sapienza” Via Eudossiana 18, 00184 Roma, Italy, EU

^a fabio.garofalo@uniroma1.it

Received: 21 September 2010
Accepted: 11 February 2011

Abstract

We investigate the mixing layer thickness, δ(ξ), along the streamwise coordinate ξ of a straight channel fed with alternating streams of segregated solutes. We show the occurence of convection-enhanced mixing regimes downsteram the channel: i) an early-mixing regime, δ(ξ)∼ξ^1/3 resembling the classical Lèvêque scaling of the thermal boundary layer, ii) an intermediate anomalous regime δ(ξ)∼ξ^3/5, where most of mixing occurs, and iii) an asymptotic scaling where the dynamics of mixing depends on the spanwise velocity profile and can be predicted by localization theory (Giona M. et al., EPL, 83 (2008) 34001). We develop a complete theoretical derivation for each of these regimes and discuss the implications of the results presented for real-world microflow devices.