Presets
Playback
Apparatus
Model checks
The science
What is modelled
The coffee puck is a packed bed of grains. Water driven by the pump pressure difference percolates through its pores at a speed proportional to that pressure, as Darcy's law says. The permeability follows the Kozeny-Carman relation and falls steeply with finer grains and tighter packing. A thermoblock heater has limited power, so a faster flow means cooler water.
Equations
- Bed height
h = m / (ρs (1 - ε) A), ρs = 1300 kg/m³, basket diameter 58 mm. - Kozeny-Carman
k = ψ ε³ d² / (180 (1 - ε)²)with an empirical fines-and-swelling factor ψ = 1.5e-5 that calibrates the textbook value to a realistic flow of about 1 mL/s. - Darcy
Q = k A ΔP / (μ h); water viscosity (Vogel)μ = 2.414e-5 · 10247.8 / (T - 140) Pa s, T in kelvin. - Shot time for a yield
t = mout / (ρ Q). - Heater:
Tout = min(Tset, 20 + P / (ρ Q c)), c = 4186 J/kg K.
Checks run in the page
- Layer-by-layer series resistance against the single-bed pressure drop.
- Vogel viscosity against reference values at 20 and 100 C.
- Bed height rebuilt from the porosity and the solid mass.
- Heater energy balance against the outlet temperature.
Honest simplifications
The 3D page is an assembly viewer with no flow solver, so this model is the 2D twin's own. The factor ψ is a single calibration constant, the bed is uniform and incompressible, there is no channelling, pre-infusion, swelling or extraction chemistry and no taste claim is made. A teaching model of the hydraulics, not a barista recipe.
What to try
- Press Choked puck: a finer grind and a tighter tamp slow the shot sharply, since flow scales with grain size squared.
- Press Fast gusher and see the flow rise while the heater can no longer keep the water hot.
- Lower the pump pressure to 6 bar and watch the flow fall in direct proportion.