= Solution
<Colloidal> particles experience attractive <Van der Waals forces>, arising from correlated molecular charge fluctuations and other dipolar interactions. Integrating many weak molecular attractions over two particles can give a deep near-contact well. For identical spheres of radius $a$ and surface gap $h\ll a$, a positive <Hamaker constant> gives approximately
$$
U_{\mathrm{vdW}}(h)\simeq-\frac{A_Ha}{12h}.
$$
<Brownian motion> brings particles into encounters. Without a repulsive barrier, they can reach the attractive primary minimum; if the binding <energy> is much larger than $k_BT$, thermal motion rarely separates them again. Repeated sticking produces aggregates. This is a kinetic stability statement: thermal agitation causes encounters but does not itself supply a stabilizing interparticle repulsion. The molecular cutoff and <hard sphere> exclusion prevent the unphysical $h\to0$ divergence of the continuum attraction.
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