Presets
Playback
Conditions
Bath temperature, total pressure and ambient humidity (water only).
Tube and clock
Starting air gap and how many simulated seconds pass per real second (log scale).
Layers
Model checks
The science
What happens
A liquid sits at the bottom of a narrow vertical tube and a gentle draught sweeps across the open top. Vapour leaves the liquid surface, diffuses up through the stagnant air gap of length L and is carried away at the top. As the liquid level falls, the diffusion path gets longer and evaporation slows down.
Equations
Vapour pressure comes from the Antoine equation, log10 p[mmHg] = A - B / (C + T[C]), giving the surface mole fraction y_s = p_sat / P. Diffusion with a net upward (Stefan) flow of the evaporating species through stagnant air gives the molar flux N = (c D / L) ln[(1 - y_inf) / (1 - y_s)], with c = P / (R T) and D = D0 (T / 298.15)^1.75 (P_atm / P).
The level falls by dL/dt = N M / (rho L) per unit time, which integrates to the L-squared law L^2 = L0^2 + 2 K t, with K = (c D M / rho) ln[(1 - y_inf)/(1 - y_s)]. The slope of L squared against t therefore measures the diffusivity D. For small y_s the flux reduces to the plain Fick result (c D / L)(y_s - y_inf); at larger y_s the bulk flow raises it by about 1 + y_s / 2.
Honest simplifications
The air gap is treated as quasi-steady and isothermal: evaporative cooling of the liquid surface, convection in the gap and meniscus effects are ignored, and the diffusivities are single-point literature values scaled by T^1.75. Ambient vapour is only modelled for water. The 2D page uses the same physics module as the 3D page.
Checks in the page
Check 1 tests the Antoine anchors (water 3.17 kPa at 25 C, boiling points at 1 atm). Check 2 compares the closed-form flux with an independent RK4 shooting solution of the diffusion equation for all three liquids. Check 3 integrates the level ODE with RK4 and compares it with the L-squared law, then recovers D from a straight-line fit.
What to try
- Watch the three lines in graph 1: each is straight, which is the L-squared law, and the slope gives the vapour diffusivity.
- Choose Warm bath 40 C: acetone and ethanol speed up a lot because vapour pressure rises exponentially.
- Choose Humid air 90 %: the water line flattens because the ambient vapour cuts the driving mole-fraction difference.
- Compare the solid Stefan profile with the dashed Fick line in graph 3 for acetone: the bulk flow bends it.