2D companion to the 3D scene: the same DLVO theory governing whether nanoparticles released into water stay dispersed and mobile, or clump together and drop out of the water column, drawn as a live cross-section instead of rendered spheres. The total interaction energy between two approaching particles is the sum of attractive van der Waals forces and repulsive electrostatic double-layer forces.
V(D) = V_vdW(D) + V_edl(D)
V_vdW = −A·a / (12D)
V_edl = 64π·ε₀ε_r·a·(k_BT/e)²·Γ²·exp(−κD), Γ = tanh(zeψ₀/4k_BT)
κ⁻¹ (Debye length) ∝ 1/√(ionic strength)
A = Hamaker constant, a = particle radius, D = surface separation, ψ₀ = zeta potential. If V(D) has a large positive barrier (≫ 10 kBT), Brownian collisions can't overcome it and the suspension is colloidally stable. Raise the ionic strength (more salt screens the double layer, shrinking κ⁻¹) or push the zeta potential toward zero, and the barrier collapses — every collision sticks and particles aggregate. Each aggregate's radius grows as (a₁³+a₂³)^⅓ (volume conserved), its diffusion coefficient falls as D∝1/a (Stokes–Einstein), and its Stokes settling velocity grows as v∝a² — so aggregates fall out of suspension and settle onto the sediment much faster than the primary nanoparticles ever would.
- Ionic strength — screens electrostatic repulsion; seawater (~500 mM) collapses the barrier almost completely, which is why estuaries are hot spots for engineered-nanoparticle deposition.
- Zeta potential — the particles' own surface charge (from coatings, pH, natural organic matter); near 0 mV there is no repulsion left at all.
- Particle radius — sets both the van der Waals and electrostatic prefactors and the resulting settling speed of any aggregate that forms.
The animation time-accelerates real diffusion and settling (both are normally far too slow to watch) but keeps the physical scaling relationships — and every number in the readouts above — exact.