Flow-enhanced mixing in nanoscale channels: Linking changes in shape to flow kinematics

We first experimentally study mixing of miscible liquids during pressure-driven flow in nanoscale channels that are created by patterned buckling in compressed films on silicone substrates. The buckled films display the telephone cord morphology with a characteristic configuration of a zig-zag shape along the length direction, where the cross-sectional shape, which is almost semi-circular, has a periodic asymmetry. The experiments demonstrate flow enhancement of the mixing. Second, we present a model for the low Reynolds number mixing based on an asymptotic (lubrication) analysis of the flow accounting for the periodic axial changes in cross-sectional shape. The variations in shape produce secondary flows that give rise to exponential stretching of material lines. The theory that thus describes the nanoscale mixer provides a complete kinematical characterization of the flow, which mixes using transverse shears that are out-of-phase. We compare the theoretical predictions to the experimental measurements.