Colloid Science & DLVO Theory: Why Milk Doesn't Separate

Too big to dissolve, too small to settle

Pour a glass of milk and leave it on the counter. Hours, even days later, it remains a uniform white liquid — the fat droplets suspended throughout, not pooled at the surface. A colloid is a system in which particles of one material, roughly 1 nanometre to 1 micrometre in diameter, are dispersed through a continuous medium. That size window is the "colloidal regime": large enough that gravity eventually matters, but small enough that Brownian motion, the thermal jostling of surrounding solvent molecules, keeps particles suspended for timescales from hours to years. Milk is an emulsion — liquid droplets dispersed in another liquid — and the reason it stays stable, and the reason it curdles when acid or salt is added, is elegantly explained by DLVO theory, named after Derjaguin, Landau, Verwey and Overbeek.

Van der Waals attraction: the force pulling particles together

Between any two electrically neutral bodies, quantum-mechanical fluctuations of electron clouds create transient dipoles that induce correlated dipoles in neighbouring atoms. Hamaker showed that between two flat surfaces separated by a gap H, this always-attractive interaction scales as 1/H², and between two spheres of radius R (with H much smaller than R) as 1/H — decaying slowly enough that it can dominate at separations of a few nanometres. The Hamaker constant A depends on the dielectric properties of both particle and medium: for polystyrene in water A ≈ 1.3×10⁻²¹ J, while for gold in water A ≈ 4×10⁻¹⁹ J, which is why gold particles aggregate far more readily at a given separation.

Electrostatic repulsion: the electric double layer

Most colloidal particles acquire a surface charge in water and attract a diffuse cloud of counterions around them, forming the electric double layer. The potential decays roughly exponentially with distance, falling to 1/e of its surface value over the Debye screening length κ⁻¹. When two similarly-charged particles approach, their double layers overlap and the resulting osmotic pressure generates a repulsive force that decays exponentially with κ⁻¹ — so adding salt shrinks κ⁻¹ and shortens the range of repulsion.

V_DLVO(H) = V_EDL(H) + V_vdW(H)
          = 64π R n0 kB T κ⁻² γ² exp(-κH)  -  A R / (12 H)

pure water   (I = 1e-7 M):  κ⁻¹ ≈ 960 nm   → weak screening, strong repulsion
100 mM NaCl  (I = 0.1 M):   κ⁻¹ ≈ 0.96 nm  → strong screening, barrier collapses

The barrier that decides stable versus curdled

Summing the two interaction energies typically produces a deep primary minimum at H ≈ 0.1–0.5 nm (irreversible aggregation), a potential-energy maximum — the DLVO barrier — at H ≈ 1–10 nm, and a shallow secondary minimum at H ≈ 5–20 nm (reversible flocculation). If the barrier is much greater than the thermal energy k_BT (say, >10-15 k_BT), particles cannot cross it on any reasonable timescale and the colloid stays stable. Reduce the barrier — by adding salt, which compresses the double layer, or by shifting pH toward a protein's isoelectric point — and particles aggregate. This is exactly why vinegar or rennet curdles milk: acid lowers the pH toward casein's isoelectric point of about 4.6, collapsing the barrier and causing the micelles to clump into curds. The Schulze-Hardy rule captures how strongly this depends on counterion valence: critical coagulation concentration scales as z⁻⁶, so trivalent Al³⁺ is roughly 700 times more effective at destabilising a colloid than monovalent Na⁺.

Beyond DLVO, and where it matters

Simple DLVO theory assumes smooth, rigid, uniformly charged spheres, and real colloids often add other effects: steric stabilisation from adsorbed polymer chains that resist compression entropically even at high salt; depletion forces from non-adsorbing polymers that push particles together; and hydrophobic attraction between non-polar surfaces in water. These principles underpin industries far beyond the kitchen: pharmaceutical formulators use zeta potential (>|30| mV as a stability benchmark) as a routine quality-control tool; water-treatment plants dose aluminium sulphate to collapse the double layer on suspended clay and settle it out; and paint formulators tune pH and polymer additives so pigment stays dispersed in the can but aggregates the instant it's applied.

Frequently asked questions

Try it live

Everything above runs in your browser — open Colloids, dial up the salt concentration, and watch a stable sol flocculate into fractal aggregates as the DLVO barrier collapses. Nothing is installed, nothing is uploaded.