Biofilm Antibiotic Penetration — 2D Water-Channel Diffusion Field

Real bacterial biofilms are not uniform slabs — they are threaded with water channels, low-resistance conduits through the extracellular polymeric substance where antibiotic molecules move far faster than through the dense surrounding matrix. This 2D companion to the 3D biofilm sim replaces the 1D closed-form exponential C(x) = C₀·exp(−x/λ) with a full numerical solution of the steady-state 2D reaction–diffusion equation ∇·(D(x,y)·∇C) − k·C = 0 on a depth-resolved cross-section, where D(x,y) is genuinely spatially varying: baseline EPS diffusivity everywhere except along a handful of meandering channels where it jumps sixfold. The result is a concentration field with real lateral structure — antibiotic visibly reaches deeper along channel streaks than a smooth 1D model would ever predict — so bacteria at the same nominal depth can have very different survival odds depending on whether they happen to sit near a channel, exactly the patchy tolerance pattern seen in real confocal-microscopy studies of clinical biofilms.