Karst Conduit Breakthrough (2D Cross-Section)

A narrow limestone fracture widens as CO₂-charged groundwater dissolves its walls — but not uniformly. This 2D cross-section resolves the fracture into 40 cells along its length and solves for the single discharge that satisfies series mass-conservation through all of them at once, so whichever cell is narrowest controls the whole conduit's flow, exactly as in a chain of resistors. Coupled to real Plummer–Wigley–Parkhurst dissolution kinetics — including the kinetic trigger that sharply slows reaction rates near chemical saturation — the model reveals a genuinely two-dimensional effect a single-aperture model cannot: because the least-saturated water is always nearest the inlet, that end dissolves and widens dramatically faster than the outlet, opening a funnel shape and then sweeping a widening front downstream until the whole conduit breaks through into a fast, turbulent cave passage. Watch the inlet-to-outlet aperture ratio and the live saturation gradient to see exactly where the fracture is transport-limited and where it has already run away.