Sprial Vortex Instability in Microfluidic Cross-Slot Flow

Improved understanding and characterization of stability conditions for flows through intersecting geometries is vital for the optimization of many laboratory microfluidic experiments and also practical lab-on-a-chip designs, including for the specific goal of enhancing the mixing of fluids in channels with small dimensions operating at low Re.

In this work, we report the results of detailed experimental studies of the spiral vortex flow instability of Newtonian fluids and dilute polymer solutions in cross-slots with a range of aspect ratios and over a wide range of Re. In contrast to previous studies, we identify appropriate order parameters that characterize the instability as a function of Re in each case. At small Reynolds numbers, Re, the flow is two-dimensional and a sharp symmetric boundary exists between fluid streams entering the cross-slot from opposite directions. Above an ÒaÓ (aspect ratio) dependent critical value Re_c ~ 20-100, the flow bifurcates to an asymmetric state (though remains steady and laminar), and a single three-dimensional spiral vortex structure develops around the central axis of the outflow channel. Image analysis allows an assessment of the mixing quality between the two incoming fluid streams (one stream fluorescently-dyed with rhodamine b), which undergoes a significant increase following the onset of the instability. For Re > Re_c, the mixing parameter grows according to a sixth-order Landau potential. Fitting parameters indicate the transition is second order at aspect ratio a = 0.5, and passes through a tricritical point, becoming first order for a > 1. A simple scaling of the fitting parameters with allows full collapse of the experimental data. This instability can be used to drive enhanced mixing at the moderate Re that can be achieved in microfluidic devices and we show that further mixing enhancement can be achieved by patterning the surfaces of the channel walls. The effect of adding a small concentration (~0.01 wt%) of high molecular weight polymer is to reduce the value of Re_c in comparison to the Newtonian solvent. 

Fig.1 (a) Schematic drawing of the experimental set-up showing the cross-slot device vertically mounted on an inverted microscope. (b) Detail of the coordinate system showing the fluid flow direction and the measurement plane (x = 0 plane, green). (c) Confocal microscope images obtained in the x = 0 plane for the flow of water at  (top) and at  (bottom). Water with fluorescent dye enters from the left, undyed water from right; outflow is normal to the page.