Why industrial DAF targets a 20–80 µm Sauter-mean bubble: Stokes rise velocity, interfacial area, number density and the design trade-offs that set capture, hydraulic loading and float stability.
The single most important physical property of a dissolved-air-flotation (DAF) system is the size of the bubbles it produces. Bubble diameter sets the rise velocity, the available surface area for particle capture, the number density of bubbles in the contact zone and, ultimately, the solids-loading and hydraulic-loading rates the plant can sustain. Industrial DAF aims for a Sauter-mean bubble diameter of roughly 20–80 µm — an order of magnitude smaller than the coarse bubbles of dispersed-air flotation, and the reason DAF can clarify fragile, low-density flocs that would never settle.
A single bubble in quiescent water rises in the laminar (creeping-flow) regime, so its terminal velocity follows Stokes’ law:
vb = g(ρw − ρa)db2 ⁄ 18μ
where vb is rise velocity (m/s), g gravity (9.81 m/s²), ρw and ρa the densities of water and air, db the bubble diameter (m) and μ the dynamic viscosity of water. Rise velocity scales with the square of diameter — halve the bubble and it rises four times more slowly, quadrupling its residence (contact) time in the cell.
The specific interfacial area available for bubble–particle attachment is inversely proportional to diameter:
a = 6 ⁄ db (m² of interface per m³ of air)
Halving the bubble doubles the surface area per unit of injected air — the same air-to-solids (A/S) ratio captures far more particles when delivered as smaller bubbles.
Bubble number density scales with the inverse cube of diameter, n ∝ 1⁄db3, so for a fixed volume of released air a 40 µm population contains eight times as many bubbles as an 80 µm one. More bubbles means a higher statistical collision frequency with incoming flocs — the collision term in white-water flotation models that governs capture.
Smaller is better for capture — up to a point. Below about 20 µm a bubble’s buoyancy becomes so weak that a floc–bubble aggregate barely rises, and the bubble is carried out under the baffle with the clarified water (“wash-out”). Above about 100 µm the bubble rises so quickly it has little contact time, scours formed float and induces turbulence that shears delicate flocs. The 20–80 µm window balances buoyancy, contact time, surface area and gentleness.
| Bubble diameter (µm) | Stokes rise velocity (mm/s) | Surface area (m²/m³ air) | Behaviour in cell |
|---|---|---|---|
| 10 | ~0.05 | 600,000 | Effectively neutrally buoyant — washes out |
| 20 | ~0.22 | 300,000 | Lower bound — long contact, weak lift |
| 40 | ~0.87 | 150,000 | Ideal core of the distribution |
| 60 | ~2.0 | 100,000 | Strong lift, good contact |
| 80 | ~3.5 | 75,000 | Upper bound — fast, robust |
| 100 | ~5.4 | 60,000 | Too fast — scours float, shears flocs |
| 500 | ~135 (turbulent) | 12,000 | Dispersed-air regime — not DAF |
Stokes values are indicative for clean water at 15°C; real bubbles deviate as they approach the turbulent regime above ~120 µm where drag no longer follows Stokes’ law.
Slower-rising small bubbles spend longer in the contact zone, raising the probability of collision and attachment before they reach the surface.
The clarified-water downflow velocity must stay below the bubble–floc rise velocity. Smaller bubbles cap the achievable surface-loading rate; matched, well-conditioned flocs allow 5–15 m/h.
Fine bubbles build a stable, concentrated float blanket; coarse bubbles burst and release captured solids back into the cell.
Gentle, low-turbulence bubble release preserves the polymer-bridged flocs that coarse, high-energy bubbles would tear apart.
Bubble-size distribution is not assumed — it is measured. Reynolds & Bauhm characterises the released dispersion using high-speed bubble-viewer imaging with image analysis, laser-diffraction particle sizing adapted for bubbles, and particle-image velocimetry (PIV) to confirm rise velocity in the contact zone. The distribution is reported as a Sauter mean diameter (d32) — the surface-area-weighted mean — because it is d32, not the arithmetic mean, that governs interfacial area and capture. A tight distribution centred in the 30–60 µm band, with a small coarse tail, is the signature of a correctly designed saturator and release device.
Coarsening: worn or fouled nozzles, insufficient saturator pressure, or air binding shift the distribution coarse, dropping capture. Premature release: dissolved gas nucleating in the recycle pipework before the cell wastes air and erodes valves. Wash-out: an excess of sub-20 µm bubbles raises turbidity in the clarified water. Each has a distinct fingerprint in the bubble-size and effluent data.
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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