Air Solubility and Henry's Law: The Physics Behind DAF

How does Henry's law govern air dissolution in DAF?

Gas solubility in water is described by Henry's law: at equilibrium the dissolved concentration of a gas is proportional to its partial pressure in the contacting gas phase. This is the single most important thermodynamic relationship in DAF air saturation design, because it sets exactly how much air a saturator can force into the recycle stream at pressure.

Air is roughly 78% N₂ and 21% O₂, and Henry's law applies to each component through its own partial pressure (Dalton's law). Nitrogen is less soluble than oxygen, so the dissolved air in the saturator is enriched in oxygen relative to atmospheric air, but for engineering purposes we work with an effective air solubility that lumps both gases together. At 1 atm and 20°C that effective air solubility is about 22–24 mg/L.

Why does warm water hold so much less air?

Dissolving a gas into water is exothermic — gas molecules give up kinetic energy as they enter the liquid — so by Le Chatelier's principle raising the temperature drives dissolved gas back out. The temperature dependence of the Henry constant follows a van 't Hoff relationship:

The effect is large and non-negotiable for DAF design. At atmospheric pressure the effective solubility of air in water is roughly:

Between 0°C and 30°C the solubility roughly halves. That is the physical reason a saturator sized for winter can be air-starved in summer, and it is why temperature is a first-order design input, not a footnote.

How does saturator pressure increase dissolved air?

Because C scales linearly with partial pressure, running the saturator at elevated pressure is the practical lever for dissolving more air per litre of recycle. At absolute pressure P the saturation concentration is simply the atmospheric value scaled by P:

The table below shows theoretical saturation air concentration at 15°C (S_a ≈ 20.6 mg/L) for a range of gauge pressures, before any efficiency factor:

(1 bar ≈ 0.987 atm; add atmospheric to convert gauge to absolute.) This precipitated air is what feeds the micro-bubble curtain in the flotation cell and, together with the recycle ratio, sets the air-to-solids ratio.

Worked example 1: mass of air dissolved at 5 bar and 15°C

Take a saturator at 5 bar gauge (P ≈ 5.93 atm absolute) and 15°C, with a saturator efficiency f = 0.9, treating a recycle flow Q_r = 20 m³/h.

• Atmospheric solubility: S_a(15°C) ≈ 20.6 mg/L.
• Saturation concentration: C_sat = f · S_a · P = 0.9 × 20.6 × 5.93 ≈ 110.0 mg/L.
• Dissolved air mass rate: 110.0 mg/L × 20,000 L/h = 2.20 × 10⁶ mg/h = 2.20 kg air/h carried in the pressurised recycle.

That 2.20 kg/h is the total dissolved air leaving the saturator. Not all of it is useful — only the fraction that comes out of solution when the pressure collapses does the flotation work, which is the subject of the next example.

Worked example 2: air released when the recycle drops to 1 atm

Using the same stream, the precipitated air is the difference between what the water holds at 5.93 atm and what it can hold at 1 atm once it enters the flotation tank. Only the excess above atmospheric saturation comes out as bubbles:

• Held at saturator: C_sat = 0.9 × 20.6 × 5.93 ≈ 110.0 mg/L.
• Retained at 1 atm: C_atm = 0.9 × 20.6 × 1.0 ≈ 18.5 mg/L (still in solution, not released).
• Released (precipitated) air: C_rel = f · S_a · (P − 1) = 0.9 × 20.6 × (5.93 − 1) = 0.9 × 20.6 × 4.93 ≈ 91.4 mg/L.
• Released air mass rate: 91.4 mg/L × 20,000 L/h ≈ 1.83 × 10⁶ mg/h = 1.83 kg air/h of bubbles.

So of the 2.20 kg/h dissolved, about 1.83 kg/h is available as micro-bubbles and ~0.37 kg/h stays dissolved and is wasted. If the design solids load were, say, 60 kg TSS/h, the resulting air-to-solids ratio would be 1.83 / 60 ≈ 0.031 kg air/kg solids — comfortably inside the usual 0.01–0.06 window. Work the mass balance through in the DAF air-to-solids ratio guide.

Worked example 3: the summer-vs-winter derating (30°C vs 10°C)

Now hold pressure, efficiency and recycle constant and change only temperature, to quantify the seasonal penalty. Winter is 10°C (S_a ≈ 22.8 mg/L); summer is 30°C (S_a ≈ 16.5 mg/L). Saturator at 5 bar (P = 5.93 atm), f = 0.9, Q_r = 20 m³/h.

• Winter released air: C_rel = 0.9 × 22.8 × (5.93 − 1) = 0.9 × 22.8 × 4.93 ≈ 101.2 mg/L → 2.02 kg air/h.
• Summer released air: C_rel = 0.9 × 16.5 × 4.93 ≈ 73.2 mg/L → 1.46 kg air/h.
• Seasonal derating: (2.02 − 1.46) / 2.02 ≈ 28% less air in summer for identical pressure and recycle.

That ~28% loss is the difference between a stable float and a collapsing blanket in July. The engineering conclusion is unambiguous: size the saturator and recycle for the warmest expected water temperature. To recover the lost air in summer you must either raise the recycle ratio (more litres of saturated water) or raise saturator pressure — both of which the Henry's law relations above let you size directly.

How do salinity and ionic strength change air solubility?

Dissolved salts reduce gas solubility — the classic salting-out effect — because ions structure the surrounding water and leave less room for non-polar gas molecules. It is captured empirically by the Setschenow (Sechenov) relation:

For seawater (ionic strength ~0.7 mol/L) air solubility is roughly 15–20% lower than in fresh water. In practice this matters for marine, brine and high-TDS industrial effluents: a DAF handling saline reject or produced water flotation will precipitate measurably less air than the fresh-water tables suggest, so apply a salting-out correction on top of the temperature and pressure terms. For brackish and reuse duties, cross-check against the industrial water reuse constraints on the recycle source.