THE FORCE

Blood drags on the vessel wall

Flowing fluid drags along the wall it moves past. Endothelial cells sense this wall shear stress and respond by lining up with the flow, tightening their junctions, and changing which genes they use. Cells in a static dish never feel it.

Shear stress is a signal, not just a push.

THE PICTURE

Fast in the middle, still at the wall

Fluid right at the wall is held still, and speed rises toward the middle. The steeper that change at the wall, the larger the shear stress.

Shear stress comes from how steeply the flow speed changes near the wall.

THE FORMULA

Shear in a wide, shallow channel

τ = 6 μ Q ÷ (w h²)

τ is wall shear stress in pascals, μ is the fluid's viscosity, Q is the flow rate, w is the channel width, and h is the channel height. Brain capillaries are often modeled at about 1 to 2 pascals, or 10 to 20 dyn/cm².

Set Q, w, and h, and you set the force on the cells.

A WORKED EXAMPLE

How fast should the pump run?

Given μ = 0.7 mPa·s, w = 1 mm, h = 0.1 mm, target τ = 1 Pa

Rearrange Q = τ w h² ÷ (6 μ)

Result Q ≈ 2.4 µL/s, or about 140 µL/min

A small syringe pump can deliver brain-like shear.

A SENSITIVE KNOB

The height is squared

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Height h

Halve the channel height and the same flow gives four times the shear

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Flow Q

Double the flow rate and the shear doubles

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Why it matters

Many studies report tighter barriers and higher TEER when brain endothelial cells see shear

Small channel tolerances become big force differences, so precision in fabrication matters.

UNIT 11 STUDY COMPLETE

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Ready for the Fab Challenge?

You've calculated how much flow a channel needs to give cells the shear stress of a real vessel.