Raw water carries colloidal turbidity — clay and organic fines a few micrometres across that repel each other (negative surface charge) and never settle on their own. Adding a coagulant like alum neutralises that charge; how well depends strongly on dose:
sticking efficiency α(dose) ≈ triangular peak near 20 mg/L
underdose → charge not neutralised, particles still repel
overdose → charge reversal (restabilization), particles repel again
Particles that do collide while charge-neutralised stick and grow (Smoluchowski flocculation). Mixing intensity G raises the collision frequency between particles:
orthokinetic collision rate ∝ G · (r₁+r₂)³ · n₁ · n₂
merged floc radius: r = (r₁³ + r₂³)^(1/3) (volume conserved)
Once a floc is large enough, gravity settles it out following Stokes' law, with viscosity from the empirical Vogel equation for water:
μ(T) = 2.414×10⁻⁵ · 10^(247.8 / (T + 133.15)) Pa·s
v = 2·g·r² · (ρ_floc − ρ_water) / (9·μ)
- Dose slider — sets the charge-neutralisation efficiency α; try sweeping it to find the optimal dose window.
- G slider — rapid-mix (high G) disperses coagulant and drives early collisions; too high keeps shearing flocs apart before they can grow.
- Temperature — warmer water is less viscous, so flocs of the same size settle faster.
- Turbidity (NTU) — approximated from the total light-scattering cross-section of particles still in suspension, relative to the raw-water baseline.
Real-world relevance: this is the exact jar-test procedure water utilities run daily to pick a coagulant dose before scaling it up to a full clarifier basin.