The 3D companion sim renders bacteria in three dimensions but computes antibiotic transport with the textbook 1D closed-form solution C(x) = C₀·exp(−x/λ), λ = √(D/k) — every point at the same depth gets the identical concentration, because a plain slab has no lateral structure. Real biofilms do: confocal microscopy consistently shows biofilms threaded with water channels — low-resistance conduits through the EPS matrix where diffusivity approaches free water, dramatically higher than through the dense polysaccharide/eDNA matrix around them.
This 2D version drops the closed-form shortcut and numerically solves the actual steady-state reaction–diffusion PDE on a depth-resolved cross-section grid, with a spatially varying diffusivity field D(x,y):
∇·(D(x,y)·∇C) − k·C = 0
D(x,y) = D_matrix outside channels
D(x,y) = D_matrix · 6 inside a meandering water channel
Solved by successive over-relaxation (SOR) on a finite-volume grid:
C₀ fixed at the surface (Dirichlet), zero-flux substratum (Neumann),
periodic left/right — the same equation, but honestly in 2D.
The payoff is visible directly in the concentration field: away from channels the profile decays almost exactly like the 3D sim's exponential, but bright streaks trailing down from the surface show antibiotic reaching several times deeper than the smooth-slab prediction — sometimes reaching bacteria that the 1D model would have declared permanently protected. Toggle the channels off to confirm the two models converge to the same physics in the idealized case.
- C₀ slider — antibiotic concentration bathing the outer surface, in multiples of the planktonic MIC.
- D slider — baseline diffusivity through the dense EPS matrix (channels multiply this locally).
- k slider — degradation + binding rate; higher k shrinks the baseline λ sharply (λ ∝ 1/√k), but channels partly bypass it.
- L slider — biofilm thickness; the deeper the slab, the more channel structure matters to whether the core is reached at all.
- Water channels toggle — switch between a realistic heterogeneous biofilm and the idealized homogeneous slab the 3D sim assumes.
Real-world relevance: water-channel-mediated transport is one reason antibiotic tolerance in real biofilms is patchy rather than uniform — clinical biofilms on catheters and prosthetic joints often show surviving pockets right next to fully cleared regions at the same nominal depth, which a 1D exponential model cannot produce but a 2D heterogeneous-diffusivity model reproduces directly.