Notes

Does a hydrogen blend stratify?

3 October 2026 /4 min read

A colleague and I were discussing a simple question: if hydrogen and nitrogen are mixed and stored in a tank, will they gradually separate? Heavier molecules seem likely to settle, but gases also mix readily. A hydrogen-rich release into air can also rise buoyantly, too. A little physics helps put these observations together.

Three practical questions follow:

Will a hydrogen-containing blend stratify if left in a tank? Essentially no.
Can a local hydrogen release still form a strongly stratified layer? Yes.
Does that layer survive indefinitely? No.

A premixed blend has almost no gravitational composition gradient over tank heights, while a fresh release can form a strongly stratified layer.

1. Will a gas blend eventually stratify?

Mixing increases the entropy of an ideal gas mixture:

\Delta S_{\mathrm{mix}} = -R\sum_i n_i\ln x_i >0.

At fixed temperature, ideal-gas mixing leaves internal energy unchanged, so the entropy increase lowers the Helmholtz free energy, $F=U-TS$ . The chemical potential measures how that free energy changes when the amount of species $i$ changes, with the other amounts held fixed:

\mu_i = \left(\frac{\partial F}{\partial n_i}\right)_{T,V,n_{k\ne i}}.

Gravity adds another energy term. Moving one mole of species $i$ from the bottom, $z=0$ , to height $z$ adds $M_i g z$ of gravitational potential energy. Local pressure and composition may vary with height, so write the chemical potential as $\mu_i(z)$ . At equilibrium, moving a mole between heights cannot lower the total free energy. Thus

\mu_i(z) + M_i g z = \text{constant}.

At height $z$ , the chemical potential of ideal-gas species $i$ is

\mu_i(z)=\mu_i^\circ+RT\ln\frac{p_i(z)}{p^\circ}.

Comparing this with the same species at $z=0$ cancels the reference pressure:

RT\ln\frac{p_i(z)}{p_i(0)}=-M_i g z \quad\Longrightarrow\quad p_i(z)=p_i(0)\exp[-\frac{M_i g z}{RT}].

Do this for both gases and divide the two expressions. Since $p_i(z)=x_i(z)P(z)$ at each height,

\frac{x_2(z)}{x_1(z)} = \frac{x_2(0)}{x_1(0)} \exp\left[-\frac{(M_2-M_1)gz}{RT}\right].

For a tank of height $H$ , the strength of gravitational separation can be characterized by

S_g=\frac{|\Delta M|gH}{RT}.

It compares the gravitational energy difference across the tank with the thermal energy scale. Consider a relatively tall tank: hydrogen and nitrogen in a 10 m high tank at 300 K. Their molar-mass difference is about $0.026\ \mathrm{kg/mol}$ , so $S_g\approx0.001$ . The H $_2$ /N $_2$ ratio therefore changes by only about 0.1% from bottom to top at equilibrium.

This is better described as a small equilibrium composition gradient than as a separated or layered gas. Over ordinary tank and room heights, gravity has very little ability to sort individual gas molecules by molar mass.

2. Why buoyancy remains strong after a hydrogen release

A premixed blend is already close to equilibrium; a local release begins with a hydrogen-rich region that is less dense than the surrounding gas. Buoyancy lifts the region toward the ceiling, where light gas above heavier gas is gravitationally stable. A pronounced upper layer can therefore form even though the final equilibrium composition gradient is tiny.

Gravitational stability is not thermodynamic equilibrium: diffusion and air motion still reduce the concentration difference. How long the layer lasts depends on how quickly they act.

3. How long can the buoyant layer last?

After the release stops, suppose molecular diffusion is the main mechanism dispersing the upper layer. Over a vertical distance $L$ , the characteristic mixing time is

t_D\sim\frac{L^2}{D}.

Here $D$ is the binary diffusion coefficient. For hydrogen in air near room temperature, $D$ is of order $10^{-4}\ \mathrm{m^2/s}$ . Over a few metres, molecular diffusion alone gives a characteristic time of several hours to roughly a day.

In the 80 m³ quiescent chamber studied by Lacome et al., the hydrogen-rich upper layer gradually dispersed, and the gas became nearly uniform about four hours after the release ended.

The $L^2/D$ estimate applies when molecular diffusion dominates. Ventilation, residual turbulence, jet momentum, thermal convection, room geometry, or continued release can change the actual mixing time.

Whether a hydrogen blend stratifies depends on its starting state and the time allowed for mixing: a premixed blend stays nearly uniform, while a fresh release can form a pronounced upper layer that gradually disperses once the release stops.