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How to use
Pick a preset, then move the sliders. Magma: silica, temperature and water set viscosity and gas. Plumbing: depth, volume, conduit radius and the rupture pressure set how violent and how long. The chamber fills (days), ruptures, then erupts (hours to years); the time-lapse is automatic, scale it with the factor. Trigger eruption now skips the wait. Drag to orbit, wheel to zoom, camera buttons for presets. Space pauses, R resets.
What to try. (1) Preset Pinatubo, then drop water to 1 wt %: the plume weakens to a Vulcanian burst, because there is much less gas to fragment the magma. (2) From Kilauea raise silica from 49 to 70: the same chamber now creeps. (3) Double the conduit radius: flux grows with R4, the plume rises about 60 % higher (MER1/4). (4) Raise wind to 30 m/s and watch the ash graph shift downwind. (5) Make the chamber small: the eruption is short.
The island, cut-away block, houses, trees and textures were modelled and baked in Blender; Three.js r160 animates the plume, bombs and lava from the same maths module as the 2D page. Plume height is drawn compressed (5 H0.55 scene units); the readouts give the real value.
The science
The page links six pieces of physics in a chain; every number you see comes from the shared module physics.js, so the 2D and 3D pages agree to the digit.
1. Magma viscosity. An empirical fit (order of magnitude only):
log10 eta = a(SiO2) + B(SiO2) (1/T - 1/1423 K) - k(SiO2) ln(1 + w)
Silica polymerises the melt (a, B and k grow with SiO2), heat thins it, dissolved water thins it strongly. It gives ~102 Pa s for hot basalt, ~105 for wet rhyolite and ~1010 for dry rhyolite.
2. Gas and fragmentation. Henry's law s = kH √P (kH = 3.4 to 4.1e-6 Pa-1/2) says how much water stays dissolved; the rest exsolves as vapour with volume fraction φ = nRT/P / (nRT/P + (1-n)/ρm). Where φ reaches 0.75 (Sparks 1978) the foam can fragment into a gas-pyroclast mixture; the pressure there sets the fragmentation depth zf = Pf/(ρg). Wilson (1980) gives the gas-thrust speed above it: Ug = √(2 n Rg T ln(Pf/Patm)), and a fountain height Ug2/2g.
3. Ascent. Viscous Hagen-Poiseuille flow in a cylindrical conduit driven by the chamber overpressure:
U = dP R² / (8 η L), Q = π R² U = π R⁴ dP / (8 η L), MER = ρ Q
U is softly capped at 150 m/s (choked flow).
4. Chamber. The chamber is a compliant reservoir: dP/dt = recharge - (K/Vc) Q with K = 1 GPa. Pressure builds until the rupture overpressure, the conduit opens, the chamber drains and the eruption stops at 30% of the rupture value; with repeat on this is a relaxation oscillator. The erupted volume is therefore Vc(dPrupture - dPend)/K.
5. Eruption style. The Deborah number De = (4 ηvent/Pf) / (zf / (½Ug)) compares how long viscous melt needs to let a bubble grow with how fast the mixture is decompressed. De < 0.01: gas escapes, the magma flows or fountains (Effusive, Strombolian, Hawaiian); 0.01 to 0.5: partial fragmentation (Vulcanian); above that fragmentation is complete (Sub-Plinian, Plinian). The fragmented share is De/(1+De). Mixtures that are gas-poor and fast collapse instead of rising (n < 3 wt %), which feeds a pyroclastic density current with runout H/0.2 (energy-line coefficient 0.2). These thresholds are calibrated heuristics, not first-principles.
6. Plume. Buoyant plume theory in a stratified atmosphere (Morton, Taylor and Turner 1956): H = 3.8 F1/4 N-3/4, buoyancy flux F = g QH / (π ρa cp Ta), N = 0.01 s-1, QH = MER cp (T - Ta). Independently, the Mastin et al. (2009) fit H[km] = 2.00 V0.241 with V the dense-rock flux in m³/s; both are plotted. Wind bending is not applied to the height.
7. VEI. The Volcanic Explosivity Index is a log scale of erupted bulk volume (VEI 2 starts at 106 m³, each step is 10x). Fragmented material is converted from dense rock to bulk tephra with a factor 2.4.
8. Lava. A Newtonian sheet on the mean flank slope (Jeffreys): flux per width q = ρ g sinθ h³ / (3 η), mean speed u = ρ g sinθ h² / (3 η) for a channel of width W. The front stops where the heat budget is spent (Pieri and Baloga style): L = Q ρ cp ΔT / (q W) with ΔT = 100 K and q = 20 kW/m². Real lava has a yield strength, crusts and tubes; this is a bound.
9. Ash. Five grain classes (16 µm to 4 mm) fall at the terminal speed from the Schiller-Naumann drag law while a constant wind carries them; the graph is the resulting mass per kilometre downwind, with Gaussian turbulent spread. Finer ash (higher De) travels further.
Honest simplifications. One conduit, steady Poiseuille flow with a cap, no bubble-dependent viscosity or crystals, no gas escape through permeable walls, constant wind, no conduit erosion, no caldera collapse, a rigid cone. Predictions are good to about a factor of two to ten, which is also the real uncertainty of the inputs. The checks at the bottom compare the code with independent integrals and ODEs.