The interactions between two drops floating on a partially miscible liquid pool

TL;DR

This study examines how two identical oil drops float on a partially miscible ethanol–water pool, where dissolution-induced Marangoni flows create repulsion that competes with attraction from surface deformations (the Cheerios effect). By systematically varying drop volume $V$ and ethanol fraction $w_e$, the authors identify Repel, Coalesce, and Rebound as distinct behaviors and develop a scaling theory that separates repulsive from attractive regimes, aided by a lubrication-film mechanism that explains why coalescing drops rebound at high $w_e$. The work provides a predictive framework for two-drop interactions on multicomponent interfaces and highlights the role of a short-range lubrication layer in dictating contact outcomes, with potential implications for emulsions, coatings, and microfluidic applications.

Abstract

The interaction of drops floating on liquid surfaces is important for many natural processes and industrial applications. In many of the cases, the system is multicomponent, leading to Marangoni flows on the surface. Here we investigate the competing effect of the attractive ``Cheerios effect'' and the repulsive solutal Marangoni flow by observing the behaviors of two identical oil drops floating on partially miscible pool made of ethanol-water mixtures. Three typical behaviors are found: Repel, Coalesce and Rebound, in which the drops repel each other, attract each other and then coalesce, and attract and rebound upon contact. A scaling theory based on the two competing forces is developed to distinguish the repulsive and attractive behaviors of the drops. For the transition from Coalesce to Rebound, a lubrication layer is found to form when the immersed lower halves of the drops are more than half a sphere, which prevents the drops from coalescing.

Figures (7)

• Figure 1: Sketch of the experimental setup. A glass container is filled with ethanol-water mixture and two dodecane drops of the same volume are deposited onto the surface of the mixture via two needles. The container is put in a lager container made of acrylic glass to prevent the preferential evaporation of ethanol and subsequent interfacial flows. The behaviors of the drops are monitored from above, from which the drop radius $R$ and the central distance $L$ between the drops are measured. The ethanol weight fraction of the liquid pool is $w_\mathrm{e}$.
• Figure 2: (a) A dodecane drop float on the air-liquid interface of an ethanol-water mixture with the ethanol weight fraction $w_\mathrm{e}$. The gradient of color from pink to blue on the surface of the mixture represents a decreasing concentration of dodecane in the mixture, which results from the dissolution of the drop. The dissolution of dodecane reduces the surface tension of the mixture, thus the surface tension near the drop is lower than in the far field. The consequent Marangoni flow on the pool surface induces a flow inside the container, indicated by the red arrows. (b) Surface tension of the dodecane saturated ethanol-water mixture $\gamma_\mathrm{saturate}$ and the ethanol-water mixture free of dodecane $\gamma$lide2004crc. For $\gamma_\mathrm{saturate}$, each point is an average of six measurements and the error bar is the standard deviation. The black and red solid lines are polynomial fittings. (c) The flow field for two 3dodecane drops floating on a mixture of $w_\mathrm{e}=90wt%$, obtained by PIV measurements. To better visualize the flow field, the two drops are fixed by attaching them to two needles.
• Figure 3: Three typical behaviors of the two identical drops. (a) Repel. $V=30µL$ and $w_\mathrm{e}=20wt%$. The drops repel each other. (b) Coalesce. $V=100µL$ and $w_\mathrm{e}=20wt%$. The drops attract each other and coalesce upon contact. (c) Rebound. $V=100µL$ and $w_\mathrm{e}=90wt%$. The drops attract each other and rebound upon contact.
• Figure 4: Phase diagram of the behaviors of the drops. Black circles represent Repel, red diamonds represent Coalesce and blue squares represent Rebound.
• Figure 5: Sketch of the distortion of the liquid surface induced by a solid sphere (a) and a liquid drop (b).