OHM'S LAW FOR LIQUIDS

Pressure pushes, channels resist

Pressure (ΔP) Like voltage: the push

Flow rate (Q) Like current: how much liquid passes per second

Resistance (R) Set by the channel's length, shape and the liquid's viscosity

ΔP = Q × R The same equation as V = I × R

Because flow on a chip is laminar, you can calculate it with circuit rules.

SHAPE MATTERS

Height is everything

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Longer = more resistance

Double the length, double the resistance

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Shallower = much more

Wide, shallow channel: R grows as 1 ÷ h³. Halve the height, eight times the resistance

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Round tubes

R = 8 μ L ÷ (π r⁴): halve the radius, sixteen times the resistance

Small changes in channel height cause big changes in flow, so fabrication must be precise.

SERIES AND PARALLEL

Designing a fluid network

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In series Resistances add; the same flow passes through each

In parallel Flow splits, and the low-resistance branch takes the most

Serpentine resistor A long winding channel adds resistance in a small area

Even splitting Matching branch resistances sends equal flow to each chamber

Engineers draw a chip as a circuit before they draw it as channels.

COMPLIANCE

Soft walls act like capacitors

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Soft PDMS walls, flexible tubing and trapped bubbles all stretch under pressure and store a little liquid, just as a capacitor stores charge. The result is a delay: a syringe pump may take minutes to reach a steady flow. Rigid materials and short, stiff tubing respond faster.

Resistance times compliance sets how quickly a chip responds to a change.

SHEAR STRESS

The force flow puts on the walls

For a wide, shallow channel, wall shear stress τ = 6 μ Q ÷ (w h²). Blood vessel walls feel shear from flowing blood, so chips that grow vessel cells must set it on purpose.

Flow rate and channel height decide how hard the liquid drags on cells.

UNIT 5 STUDY COMPLETE

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Ready for the Fab Challenge?

You've seen how pressure, resistance and flow relate, why channel height matters so much, and how flow sets the shear on cells.