= Solution
A <Pickering emulsion> is stabilized by particles adsorbed at the liquid–liquid interface. A partially wetting sphere removes a patch of that interface. The smaller detachment barrier into either bulk phase is approximately
$$
\Delta E=\pi r_p^2\gamma_{ow}(1-|\cos\theta|)^2,
$$
where $\theta$ is the three-phase <contact angle>. At approximately neutral wetting, $\theta=90^\circ$, the stated particle radius gives
$$
\Delta E=\pi(20\times10^{-9})^2(0.050)
=6.28\times10^{-17}\ \mathrm J
\simeq\boxed{1.53\times10^4\,k_BT}
$$
at $25^\circ\mathrm C$. Such a large attachment <energy> makes thermal detachment unlikely. A sufficiently covered interface resists drop coalescence, and a water-wet particle preference supports an oil-in-water dispersion. However, \b[radius alone does not guarantee stabilization]: completely water-wet or oil-wet particles have a vanishing attachment barrier in this model, and sufficient particle coverage is necessary. Sedimentation and droplet ripening are separate failure modes. The classical particle-stabilized-emulsion experiments provide the historical basis of the terminology.<CXCVI.—Emulsions by Spencer Umfreville Pickering>[Journal of the Chemical Society, Transactions 91 (1907), pp. 2001–2021]{ref}
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