Marangoni-driven spreading of miscible liquids in the binary drop geometry

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 as a function of the surface tension difference between the liquids and the viscosity, revealing power-law behavior $L(t)\sim t^{\alpha}$ with a spreading exponent $\alpha \approx 0.75$. This value is consistent with viscosity-limited spreading over a deep bath.

A single power law of rescaled distance as a function of rescaled time reasonably captures our results as well as different geometries, miscibility, and surface tension modifiers (solvents and surfactants). This result enables engineering the spreading dynamics of various liquid-liquid systems. However, we also observe deviations between this scaling law and literature experiments, which give rise to open questions that deserve attention in future work.