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
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