Quantum Hydrodynamics & Low-Temperature Physics
Superfluid Fountain
Simulate Tisza and Landau's two-fluid model of Superfluid Helium-4 ($^4\text{He}$) below the lambda point $T_\lambda = 2.17 \text{ K}$. Heating the capillary plug creates a thermomechanical pressure $\Delta P = \rho S \Delta T$, producing a liquid helium fountain jet.
Temperature T
1.50 K (Superfluid He II)
Superfluid Fraction ρ_s/ρ
88.5 %
Fountain Height h
120.0 mm
Cryogenic Setup
Visual Overlay
Controls
Thermomechanical Fountain Pressure Equations
Two-Fluid Density: ρ = ρ_normal + ρ_superfluid
Superfluid Fraction: ρ_s / ρ = 1 - (T / T_λ)^5.6 (for T < T_λ)
London Fountain Pressure: ΔP = ρ · S · ΔT = ρ · g · h_fountain
Superfluid Fraction: ρ_s / ρ = 1 - (T / T_λ)^5.6 (for T < T_λ)
London Fountain Pressure: ΔP = ρ · S · ΔT = ρ · g · h_fountain
Developer Reference
Core Algorithm & Standalone Script
// Superfluid helium thermomechanical fountain solver
const canvas = document.getElementById('canvas');
const ctx = canvas.getContext('2d');
// delta_P = rho * S * delta_T