Mixing with viscoelastic waves at low Reynolds numbers

Abstract

Mixing at the microfluidic scale is challenging due to the low Reynolds numbers and often high Péclet numbers. Without turbulence, mixing relies solely on diffusion, resulting in slow and inefficient mixing. We demonstrate enhanced mixing in a simple Y-shaped microfluidic channel using viscoelastic turbulence in fluids containing macromolecules, suchas DNA and polyethyleneoxide. We investigated mixing at two distinct scales: the mixing of small molecules and the mixing of polymers. We show how the viscoelastic fluctuations fold the solvent, resulting in enhanced reaction rate between two reagents. We also show how the viscoelastic turbulence enhances the mixing of the macromolecules. We discuss optimization strategies taking into account mixing efficiency, mixing time, mixing length and energy efficiency. Viscoelastic turbulence unlocks rapid mixing in microfluidic channels where conventional turbulence cannot operate, offering a versatile platform for applications ranging from chemical synthesis to biomedical assays.

Figures (5)

• Figure 1: Mixing of two fluids, one containing Fluorescein. Both fluids are 0.2% w/v PEO in water, one has added Fluorescein for visualization. (A) Measured flow rate as a function of applied pressure, showing two linear regimes, with a transition at P $\approx$ 185 mbar. (B,C) Fluorescence microscopy images of the microchannel for an applied pressure P = 100 mbar (B), resulting in a laminar flow with purely diffusive mixing, and P = 600 mbar (C), clearly showing the presence of waves with a viscoelasticity-enhanced mixing.
• Figure 2: Quantifying mixing via fluorescence generation from reactant solutions in the device. Fluo-3 was added to the 0.2% w/v PEO aqueous solution and loaded in one inlet. $\text{Ca}^{2+}$ was added to the 0.2% w/v PEO aqueous solution and loaded in the other inlet. The gray area shows the wave onset, see Fig. \ref{['fig:fluorescein']}. (A) Fluorescence microscopy image of the Fluo-3 fluorescence at an applied pressure P = 150mbar, when the flow is laminar. (B) Fluorescence microscopy image of the Fluo-3 fluorescence at an applied pressure P = 600 mbar, when waves are present and the flow is turbulent. (C) Mixed fraction of the Fluo-3 and $\text{Ca}^{2+}$ solutions as a function of flow rate (mean value $\pm$SD). The dashed line is a reciprocal fit corresponding to a purely diffusional mixing (D) Mixing rate of the two solutions as a function of flow rate (mean value $\pm$SD). The dashed lines are linear fits of the rates with and without waves.
• Figure 3: Energy cost per mixed volume of mixing a Fluo-3 solution and a $\text{Ca}^{2+}$ solution in the device. The energy efficiency is compared for two fluids: Newtonian fluid, water (blue symbols) and a viscoelastic fluid, 0.2% w/v PEO aqueous solution (yellow symbols). The gray region indicates the estimated onset of elastic viscoelastic instabilities (waves).
• Figure 4: Mixing performance of DNA macromolecule solutions in the device. (A) Fluorescence microscopy image of the green DNA, showing viscoelastic waves. (B) Fluorescence micropscopy image of the red DNA. (C) Overlap of the two colors, representing the mixing of the 2 DNA, with color scale from 0 to 1.(D) mixed fraction, (mean value $\pm$SD) and Mixing rate (mean value $\pm$SD). Spline curves are included to guide the eye.
• Figure 5: Schematics of the device (not to scale). The inlets contain channels and support pillars. The main channel is 800$\times$8000$\times$11 and contains a square array of pillars (14 in diameter, with a pitch of 18.5). The $x$ and $y$ directions are shown in the figure. The $z$ direction points out of the device plane.