Photon Penetration Depth in Photoredox Flow Reactors

Reactor Geometry

Channel diameter 2.0 mm

Parallel channels (numbering-up) 3

Photochemistry

Catalyst absorptivity ε·c 2.0 mm⁻¹

Incident LED irradiance 60%

Live Readouts

Penetration depth (1/e)

0.50 mm

Illuminated fraction

100%

Throughput vs. 1 channel @ 2 mm baseline

1.50×

How it works

Light entering a photoredox flow reactor through the tube wall is absorbed by the photocatalyst as it travels inward, following the Beer–Lambert law:

I(x) = I₀ · exp(−ε·c·x)
x = depth from the illuminated wall
ε·c = molar absorptivity × catalyst concentration
1/e penetration depth δ = 1 / (ε·c)

Near the wall, catalyst molecules see full intensity and turn over quickly (bright particles below). Past a few penetration depths, intensity collapses exponentially and the reactor core sits in the dark — a "photon-starved" core radius r_c where I(r_c) has fallen to 10% of I₀:

r_c = R − ln(10)/(ε·c)
Illuminated area fraction = 1 − (r_c / R)²   (r_c clamped ≥ 0)

Channel diameter — a wider tube grows R faster than δ, so the dark core swallows a bigger share of the volume: this is why photoredox reactions don't scale by simply making the tube bigger.
Catalyst absorptivity — a more absorbing catalyst shortens δ, which speeds up near-wall turnover but shrinks the illuminated shell faster too.
Incident irradiance — sets the excitation (pulse) rate of catalyst molecules that do see light; it doesn't change the geometric penetration depth.
Parallel channels — "numbering-up": running several thin channels side by side multiplies throughput (∝ channels × D²) without touching D, so δ and the illuminated fraction stay exactly as good as a single thin channel.

This is the physical reason process chemists scale photoredox flow chemistry by adding identical thin channels rather than by widening one — exactly the trade-off the on-screen throughput readout tracks against illuminated fraction.

Excited catalyst (lit shell) Ground-state (dark core) LED wall illumination

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