Earthworm Burrows and Soil Oxygen Diffusion (2D)

Burrow Network

Burrow diameter 1.4 cm

Random burrows 6

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×

Burrow area fraction

How it works

Soil oxygen obeys Fick's second law with a microbial-consumption sink — a reaction–diffusion equation, solved here on a live 2D cross-section grid:

∂C/∂t = ∇·(D(x,y)∇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). Every cell you paint gets D_burrow instead of D_soil, so the finite-difference solver literally computes a spatially-varying D(x,y) each step. Averaged over the burrow area 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 area fraction meaningfully extends how far oxygen penetrates before microbial respiration consumes it — draw more burrows and watch the mean O₂ readout and the aerobic zone depth both climb.

Paint / Erase — click or drag on the soil cross-section to add or remove burrow cells by hand.
Random burrows — generates that many random-walk burrow tunnels on top of anything hand-drawn.
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 grid is solved live by explicit finite differences of the equation above every frame; color encodes local O₂ saturation.

Anoxic (low O₂) Partially aerated Well aerated

Drag on the soil to draw burrows