RANDOM WALK

Molecules wander on their own

🎲

Random

Molecules jostle in every direction and slowly spread out

🐇

Small is fast

A salt ion diffuses about 30 times faster than an antibody

🚫

No turbulence

On a chip, diffusion is often the only thing mixing two streams

Without turbulence, mixing depends on molecules wandering across the channel.

THE SQUARE LAW

Twice the distance, four times the wait

⏱️

t ≈ x² ÷ (2D) x is the distance, D the diffusion coefficient

10 µm About 0.1 s for a small molecule (D ≈ 5 × 10⁻¹⁰ m²/s)

100 µm About 10 s

1 mm About 17 minutes

1 cm More than a day

Shrinking the distance is the most powerful way to speed mixing up.

RACE: FLOW VS. DIFFUSION

The Péclet number

🏁

Pe = v w ÷ D compares how fast liquid flows along the channel with how fast molecules diffuse across it. Water at 1 mm/s in a 100 µm channel carrying a small molecule gives Pe ≈ 200: the streams travel about 200 channel widths, roughly 2 cm, before they are mixed.

High Péclet number means the flow outruns diffusion, so you need a mixer or a long channel.

MICROMIXERS

Folding the flow

🐟

Herringbone grooves

Angled ridges on the floor twist the flow and fold the layers over and over

✂️

Split and recombine

Each stage doubles the number of thin layers

🫧

Droplets

Liquid inside a moving droplet circulates and mixes in milliseconds

Chips mix by making the diffusion distance short, not by stirring.

A FEATURE, NOT A BUG

Slow mixing builds gradients

🌈

Because streams mix slowly and predictably, a branching "Christmas tree" network can blend two inputs into a ladder of concentrations. Cells across the channel then see a smooth gradient, the way immune cells follow a chemical trail in the body.

Diffusion lets a chip build stable chemical gradients that a dish can't hold.

UNIT 3 STUDY COMPLETE

🌫️

Ready for the Fab Challenge?

You've seen why diffusion time grows with distance squared, how chips mix anyway, and how diffusion builds useful gradients.