  When two liquids with different surface tensions come into contact, the
liquid with lower surface tension spreads over the other. This Marangoni-driven
spreading has been studied for various geometries and surfactants, but the
dynamics of the binary geometry (drop-drop) has hardly been quantitatively
investigated, despite its relevance for drop encapsulation applications. Here
we use laser-induced fluorescence (LIF) to temporally resolve the distance
$L(t)$ over which a low-surface-tension drop spreads over a miscible
high-surface-tension drop. $L(t)$ is measured for various surface tension
differences between the liquids and for various viscosities, revealing a
power-law $L(t)\sim t^{\alpha}$ with a spreading exponent $\alpha \approx
0.75$. This value is consistent with previous results for viscosity-limited
spreading over a deep bath. A single power law of rescaled distance as a
function of rescaled time reasonably captures our experiments, as well as
different geometries, miscibilities, and surface tension modifiers (solvents
and surfactants). This result enables engineering the spreading dynamics of a
wide range of liquid-liquid systems.
