Why does stock go cloudy?
Because agitation and high heat emulsify fat and suspend fine protein particles in the liquid, rather than letting them separate out — and once they are dispersed, they generally stay dispersed.
What causes it, in order of importance:
Boiling. This is the main cause. A rolling boil churns the liquid, breaking fat into tiny droplets that emulsify into the stock and breaking up coagulated proteins into particles too fine to settle. A stock should never boil — it should sit at a bare simmer, with occasional bubbles rather than continuous ones.
Not skimming. Proteins and blood coagulate and rise as scum in the first stage of heating. Removing them as they appear is the single most effective thing you can do; leaving them means they eventually break up and disperse.
Starting with hot water. Beginning cold allows proteins to leach out slowly and coagulate gradually into a removable raft; starting hot sets them abruptly throughout the liquid.
Stirring or disturbing the pot.
Bones not blanched or rinsed first, leaving blood and residue.
Starchy vegetables such as potato, which release starch.
Squeezing the solids when straining, which pushes fine particles through. Let it drain under its own weight.
Does it matter? For flavour, barely — a cloudy stock tastes much the same. It matters for clear soups and consommé, where appearance is the point, and for aspic and sauces where clarity is expected. For a stew or a risotto, nobody will know.
How to make a genuinely clear stock: start cold, bring slowly to a bare simmer, skim persistently in the first twenty minutes, never let it boil, keep the surface barely moving, and strain gently through muslin without pressing.
How to rescue a cloudy one. A raft — egg whites, sometimes with minced meat and mirepoix, whisked into the cold stock and heated gently. The proteins coagulate and rise, trapping suspended particles as they go, forming a crust. Ladle the liquid out from beneath it. This is how classical consommé is made, and it works remarkably well.
Chill and lift the fat separately, which is easier than skimming warm.