Mixing without turbulence
Two streams meeting in a microchannel do not mix. They run side by side down the channel as distinct laminae with a sharp interface between them, and cross only by molecular diffusion.
There is no turbulence to help, because Re is well under 1. Making the channel wider does not help. A bigger chamber does not help. Mixing has to be designed in.
The baseline: diffusion
Section titled “The baseline: diffusion”Left alone, molecules cross the interface by random thermal motion. The
characteristic time to diffuse a distance w:
t ≈ w² / (2D)where D is the diffusion coefficient — around 10⁻⁹ m²/s for a small molecule in
water, and one to two orders of magnitude smaller for a protein.
The squaring is what matters:
| Channel width | Approx. diffusion time (small molecule) |
|---|---|
| 1.0 mm | ~500 s |
| 0.5 mm | ~125 s |
| 0.25 mm | ~31 s |
| 0.1 mm | ~5 s |
Halving the width cuts the mixing time by four. Narrowing the channel is almost always a better move than making it four times longer — though it costs you sixteen times the pressure.
For a protein, multiply every figure by 10–100. A device that mixes dye in seconds may take minutes on an antibody.
Mechanism 1 — more length
Section titled “Mechanism 1 — more length”The obvious one. Give diffusion enough time by making the path long enough.
Residence time is internal volume over flow rate, so you need
length × area / Q > t.
This is what the serpentine mixer does: about 200 mm of contact length folded into a 40 × 60 mm chip.
Simple, predictable, and easy to print. Its cost is footprint and pressure drop, both linear in length. Start here.
Mechanism 2 — chaotic advection
Section titled “Mechanism 2 — chaotic advection”Stretch and fold the interface so the distance diffusion has to cross shrinks geometrically rather than staying constant.
Each fold roughly halves the striation thickness. After n folds the diffusion
distance is w/2ⁿ, and since time goes as distance squared, the mixing time
falls as 4⁻ⁿ. Ten folds is a factor of a million.
This is the same reason folding dough is faster than stirring it. It is not turbulence — the flow stays perfectly laminar and perfectly reversible. It is laminar flow arranged so that fluid elements are repeatedly reoriented.
The herringbone mixer is OpenChip’s implementation.
Mechanism 3 — secondary flow from curvature
Section titled “Mechanism 3 — secondary flow from curvature”In a curved channel, fluid at the centre is moving faster than fluid near the walls, so it experiences more centrifugal force. It is thrown outward, displaces fluid at the outer wall, and that fluid returns along the top and bottom.
The result is a pair of counter-rotating vortices in the cross-section: Dean flow. It stirs the fluid transversely while the flow stays laminar longitudinally.
Dean flow strengthens with flow rate, which makes it unusual — this is the one mixing geometry that gets better as you push it harder, where a serpentine gets worse (less residence time).
The spiral mixer is the implementation: two and a half turns of continuous curvature, and no corners at all.
What does not work
Section titled “What does not work”A bigger chamber. It increases residence time, which helps a little, but it does not stir. At Re ≪ 1 a large volume is a delay line. See Mixing chambers.
A sharp corner on its own. It stretches the interface slightly at the corner and adds pressure drop. One corner is not a mixer; nine staggered ones are.
Higher flow rate, in a straight channel. It raises Re, but nowhere near 2000, and it reduces residence time. Net effect: worse mixing.
Choosing
Section titled “Choosing”| Situation | Reach for |
|---|---|
| Plenty of chip area, simple is good | Serpentine |
| Short path needed, corners acceptable | Herringbone |
| High flow rates, no corners wanted | Spiral |
| Shear-sensitive contents | Y-junction plus length |