Working principle of a microfluidic channel

A microfluidic channel is a tiny conduit, typically 10 to 500 µm wide, etched or moulded in silicon, glass or a polymer and sealed with a cover. It carries nanolitre to microlitre volumes of liquid from an inlet to an outlet.

Working principle

1. Driving force: a syringe pump, pressure source, electric field (electroosmosis) or capillary action pushes the liquid through the channel.
2. Laminar flow: the Reynolds number Re = ρvD_h/μ is small (usually well below 100 and often below 1), so streams move in parallel layers without turbulence. Mixing happens only by diffusion.
3. Velocity profile: pressure-driven flow is parabolic: zero at the walls (no-slip) and maximum at the centre.
4. Hydraulic resistance: flow rate Q = ΔP/R_h. For a circular channel R_h = 8μL/(πr⁴); for a rectangular channel it rises sharply as the height shrinks, so very small channels need high pressure.
5. Surface effects: surface tension, capillarity and wall charge dominate at this scale.

Key relations

Quantity	Expression
Reynolds number	Re = ρvD_h/μ
Hydraulic diameter	D_h = 4A/P (A = area, P = wetted perimeter)
Flow rate	Q = ΔP/R_h
Diffusive mixing time	t ≈ w²/D

Exam tip

Draw the labelled side view, show the parabolic profile, and state that the flow is laminar because Re is small.