Colloidal Stability & DLVO Theory: Why Milk Doesn't Separate

A colloid is a size window, not a substance

A colloid is a system where particles roughly 1 nanometre to 1 micrometre across are dispersed in a continuous medium — large enough that gravity eventually matters, small enough that Brownian motion keeps them suspended for hours to years. Milk, paint, fog, whipped cream and blood plasma are all colloids of different types. A 1 µm sphere has a specific surface area of roughly 6 m²/g, so surface forces — negligible for bulk objects — completely dominate colloidal behaviour, making stability fundamentally a surface-chemistry problem.

Two forces in permanent competition

Quantum-mechanical fluctuations of electron clouds create a universal, always-attractive van der Waals force between particles, summed across their volume via the Hamaker approach. Working against it, most colloidal particles pick up a surface charge in water, attracting a diffuse cloud of counterions — the electric double layer — whose overlap between two approaching particles generates osmotic electrostatic repulsion. DLVO theory, named for Derjaguin, Landau, Verwey and Overbeek, simply adds the two energies together as a function of separation H.

V_vdW ≈ −A·R / (12H)                       (Hamaker constant A, two spheres)
V_EDL = 64π·R·n₀·k_BT·κ⁻²·γ² · exp(−κH)    (κ⁻¹ = Debye screening length)
V_DLVO(H) = V_EDL(H) + V_vdW(H)

κ⁻¹ ≈ 0.304/√I nm   pure water (I≈10⁻⁷ M): κ⁻¹≈960 nm   100 mM NaCl: κ⁻¹≈0.96 nm

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Salt collapses the barrier — and curdles milk

V_DLVO typically has a deep primary minimum at H ≈ 0.1-0.5 nm (irreversible aggregation), an energy barrier at H ≈ 1-10 nm, and a shallow secondary minimum at H ≈ 5-20 nm (reversible flocculation). If that barrier stays well above thermal energy k_BT — say 10-15 k_BT or more — particles can't cross it and the colloid is stable. Adding electrolyte compresses the double layer and shrinks the barrier; adjusting pH toward a protein's isoelectric point does the same by neutralising surface charge, which is exactly why vinegar or rennet curdles milk by collapsing the barrier around casein micelles. The Schulze-Hardy rule captures how strongly valence matters: critical coagulation concentration scales as z⁻⁶, so trivalent Al³⁺ is roughly 729 times more effective per ion than monovalent Na⁺ — the basis of alum dosing in water treatment.

Frequently asked questions

What does DLVO theory actually predict?

DLVO theory sums the electrostatic double-layer repulsion and the van der Waals attraction as a function of separation between two colloidal particles. If the resulting energy barrier is high enough — typically more than about 10-15 times the thermal energy k_BT — particles cannot cross it on any reasonable timescale and the colloid stays stable; if the barrier collapses, particles aggregate.

Why does adding salt make a colloid coagulate?

Added electrolyte ions compress the electric double layer around each particle, shrinking the Debye screening length and therefore the range of electrostatic repulsion. Once the repulsive barrier falls below the thermal energy, particles can approach closely enough for the always-attractive van der Waals force to pull them together irreversibly.

Why is trivalent aluminium so much more effective than sodium at destabilising a colloid?

The Schulze-Hardy rule states the critical coagulation concentration falls as the sixth power of counterion valence. That makes trivalent Al3+ roughly (3/1)^6, about 729 times more effective per ion than monovalent Na+, which is exactly why water treatment plants dose alum or ferric chloride at much lower concentrations than any monovalent salt would require.

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Everything above runs in your browser — open Colloidal Stability — DLVO Theory and adjust particle radius, surface potential, ionic strength and the Hamaker constant to watch the total interaction energy curve rise and collapse. Nothing is installed, nothing is uploaded.

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