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

TL;DR

This study investigates the dynamics of Marangoni-driven spreading in binary drop geometries using laser-induced fluorescence, revealing a universal power-law behavior that aids in engineering liquid-liquid systems.

Contribution

It provides the first quantitative analysis of Marangoni spreading in drop-drop geometry, identifying a universal power-law exponent across various conditions.

Findings

Spreading follows a power-law with exponent ~0.75.

Universal behavior across different geometries and liquids.

Rescaled variables collapse data onto a single curve.

Abstract

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.