Laminar dispersion at low and high Peclet numbers in finite-length patterned microtubes

Abstract

Laminar dispersion of solutes in finite-length patterned microtubes is investigated at values of the Reynolds number below unity. Dispersion is strongly influenced by axial flow variations caused by patterns of periodic pillars and gaps in the flow direction. We focus on the Cassie-Baxter state, where the gaps are filled with air pockets, therefore enforcing free-slip boundary conditions at the flat liquid-air interface. The analysis of dispersion is approached by considering the temporal moments of solute concentration. Based on this approach, we investigate the dispersion properties in a wide range of values of the Peclet number, thus gaining insight into how the patterned structure of the microtube influences both the Taylor-Aris and the convection-dominated dispersion regimes. Numerical results for the velocity field and for the moment hierarchy are obtained by means of finite element method solution of the corresponding transport equations. We show that for different patterned geometries, in a range of Peclet values spanning up to six decades, the dispersion features in a patterned microtube are equivalent to those of a microtube characterized by a uniform slip velocity equal to the wall-average velocity of the patterned case. This suggests that two patterned micropipes with different geometry yet characterized by the same flow rate and average wall velocity will exhibit the same dispersion features as well as the same macroscopic pressure drop.