(141a) 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.