Sedimentation: Gravity Settling in Water Treatment

simulator beginner ~8 min
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v_s = 1.36 m/h — 50 μm particles, ρ=1200 kg/m³

A 50 μm particle with density 1200 kg/m³ settles at 1.36 m/h in water at 15°C. With overflow rate 1.75 m/h, removal efficiency is about 78%.

Formula

Stokes settling: v_s = g·d²·(ρ_p − ρ_w) / (18·μ)
Overflow rate: v_o = Q/A = H/t_d
Removal: η = v_s / v_o (for v_s < v_o)

Gravity: The Simplest Separation

Sedimentation exploits the density difference between suspended particles and water. Under gravity, denser particles sink at a rate governed by their size, shape, and density contrast with the surrounding fluid. For the small, roughly spherical particles in water treatment, Stokes' law provides an accurate prediction of settling velocity. The simulation shows how dramatically particle size affects this velocity — a 100 μm particle settles 100× faster than a 10 μm particle.

Clarifier Design

A sedimentation basin (clarifier) is sized so that its overflow rate — the upward velocity of water through the basin — is less than the settling velocity of the target particles. Any particle settling faster than the overflow rate will reach the bottom before being carried out. The detention time, depth, and surface area are interconnected design parameters that the simulation lets you explore.

The Colloidal Challenge

Particles smaller than about 10 μm settle so slowly that practical sedimentation is impossible. Colloidal particles (0.001-1 μm) also carry electrical surface charges that prevent aggregation. This is why coagulation — adding aluminum or iron salts to neutralize charges and bind particles into larger floc — always precedes sedimentation in conventional treatment plants.

Advanced Settling Systems

Lamella (inclined plate) settlers dramatically increase effective settling area by providing angled surfaces every few centimeters. Particles need only settle a few centimeters onto the nearest plate rather than meters to the basin floor. This allows 3-5× the flow rate in the same footprint. Dissolved air flotation reverses the process entirely, using microbubbles to float floc to the surface for skimming.

FAQ

What is Stokes' law for particle settling?

Stokes' law gives the terminal settling velocity of a spherical particle in a viscous fluid: v_s = g·d²·(ρ_p−ρ_w)/(18μ). It applies when Reynolds number is below 1, which covers most particles in water treatment (below ~100 μm). Settling velocity is proportional to the square of particle diameter — doubling size quadruples settling speed.

What is the overflow rate in a settling basin?

The overflow rate (or surface loading rate) equals the flow rate divided by the basin surface area, equivalent to depth/detention time. It has units of velocity (m/h). Any particle with settling velocity greater than the overflow rate will be completely removed. Typical values for conventional clarifiers are 1-2 m/h.

Why do small particles not settle?

Stokes' law shows settling velocity is proportional to d². A 1 μm particle settles roughly 10,000× slower than a 100 μm particle. Colloidal particles (< 1 μm) also carry surface charges that create electrostatic repulsion, keeping them suspended indefinitely. This is why coagulation chemicals (alum, ferric chloride) are essential.

What types of sedimentation basins are used?

Rectangular horizontal-flow basins are most common. Circular radial-flow clarifiers are used in larger plants. Lamella (inclined plate) settlers increase effective settling area by stacking angled plates, allowing 3-5× higher flow rates in the same footprint. Dissolved air flotation is an alternative for low-density floc.

Sources

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