How dissolved air precipitates into a microbubble cloud on pressure release: Henry's-law supersaturation, classical nucleation theory (ΔG* ∝ σ³/ΔP²), and heterogeneous nucleation on nozzle roughness and micro-particles.
DAF microbubbles are not injected — they are precipitated out of solution. Pressurised recycle water leaves the saturator holding far more dissolved air than it can retain at atmospheric pressure. When that water is throttled into the flotation cell, the sudden pressure drop makes it supersaturated, and the excess gas comes out of solution as a dense cloud of microbubbles. The quality of that cloud — how many bubbles, how small, how uniform — is decided in the few milliseconds of nucleation at the release device.
The mass of air a given volume of water can dissolve is set by Henry’s law — solubility is directly proportional to the partial pressure of the gas:
C = kH · p
where C is the dissolved-gas concentration, kH Henry’s constant for air in water, and p the partial pressure. At a saturator pressure of ~5 bar absolute, water holds roughly 150–200 mg/L of air; at atmospheric pressure it holds only ~20–24 mg/L. The difference — the supersaturation — is the air that must nucleate into bubbles:
ΔC = kH(psat − patm)
It is this ΔC, multiplied by the recycle flow, that delivers the air-to-solids ratio the process needs.
Whether that excess gas forms many small bubbles or a few large ones is governed by classical nucleation theory. Creating a new gas–liquid interface costs energy; the free-energy barrier to forming a critical nucleus is:
ΔG* = 16πσ3 ⁄ 3(ΔP)2
where σ is surface tension and ΔP the effective pressure driving release. The barrier falls steeply with the square of ΔP — a sharper, larger pressure drop produces vastly more nucleation sites and therefore many more, smaller bubbles. It also rises with the cube of surface tension, which is why surfactants and conditioning chemistry matter.
Bubbles forming spontaneously in the bulk liquid. The energy barrier is enormous, requiring extreme supersaturation, so it contributes almost nothing in a real DAF saturator.
Gas nucleates preferentially on surface roughness inside the release nozzle and on existing micro-particles and pre-existing gas nuclei in the water. Wetting lowers the barrier dramatically, so this is the route that produces the working bubble cloud.
After nucleation each bubble grows by diffusion of dissolved gas across its surface. Excessive distance, low turbulence-control or high gas load lets bubbles coalesce into coarse bubbles — the cloud must reach the contact zone before that happens.
| Saturator pressure (bar g) | Absolute pressure (bar) | Dissolved air at 15°C (mg/L) | Air released to atmosphere (mg/L) |
|---|---|---|---|
| 0 (atmospheric) | 1.0 | ~23 | 0 |
| 3 | 4.0 | ~92 | ~69 |
| 4 | 5.0 | ~115 | ~92 |
| 5 | 6.0 | ~138 | ~115 |
| 6 | 7.0 | ~161 | ~138 |
Values assume full saturation efficiency; real packed saturators reach 90–100 % and unpacked vessels 50–80 %, scaling the released air accordingly.
We size the saturator and select the release device against the measured A/S demand, then verify the resulting bubble cloud by imaging before fabrication — so nucleation is engineered, not left to chance.
Reynolds & Bauhm can review your saturator, release and contact-zone design, run the CFD and propose a sized, validated solution. Send us your flow, stream analysis and target effluent.
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