Earthworm Burrows and Soil Oxygen Diffusion

Burrow Network

Worm burrows 6

Burrow diameter 1.4 cm

Soil Texture (bulk D₀)

Microbial respiration k 0.030 s⁻¹

Live Readouts

Mean O₂ saturation

Aerobic zone depth

0 cm

Effective D / bulk D₀

1.00×

How it works

Soil oxygen obeys Fick's second law with a microbial-consumption sink — a reaction–diffusion equation:

∂C/∂t = ∇·(D∇C) − kC

With a constant-oxygen surface (atmosphere, C = C₀) and no burrows, the 1-D steady state decays exponentially with depth y:

C(y) = C₀ · exp(−y √(k/D))
attenuation depth: δ = √(D/k)

Earthworm burrows are open macropore channels whose air-filled diffusivity (D_burrow ≈ free-air O₂ diffusivity) is far higher than the soil matrix (D_soil). Averaged over the burrow volume fraction f, the profile behaves as if it had an effective diffusivity:

D_eff = f · D_burrow + (1 − f) · D_soil

Because attenuation depth scales as √D, even a modest burrow volume fraction meaningfully extends how far oxygen penetrates before microbial respiration consumes it — the mechanism behind earthworms improving soil aeration.

Worm burrows / diameter — sets the macropore network: more and wider burrows raise the burrow volume fraction f.
Soil texture — sets the bulk matrix diffusivity D_soil (clay lowest, sand highest, reflecting air-filled porosity).
Respiration k — the rate microbes and roots consume O₂; higher k shortens the aerobic zone.
The voxel field is solved live on a 3D grid by explicit finite differences of the equation above; color encodes local O₂ saturation.

Anoxic (low O₂) Partially aerated Well aerated

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