Sharp Transition between Coalescence and Noncoalescence of Sessile Drops

TL;DR

This study investigates the transition between coalescence and noncoalescence of sessile drops of miscible liquids, identifying a universal Marangoni number that predicts the behavior regardless of viscosities or surface tensions.

Contribution

It introduces a specific Marangoni number that universally characterizes the coalescence transition in sessile drops based on shape and liquid properties.

Findings

Transition occurs at a threshold Marangoni number around 2.

Viscosities and absolute surface tensions have minimal influence on the transition.

Simulations confirm the experimental threshold and show weak dependence on molecular diffusivity.

Abstract

Unexpectedly, under certain conditions, sessile drops from different but completely miscible liquids do not always coalesce instantaneously upon contact: the drop bodies remain separated in a temporary state of noncoalescence, connected through a thin liquid bridge. Here we investigate the transition between the states of instantaneous coalescence and temporary noncoalescence. Experiments reveal that it is barely influenced by viscosities and absolute surface tensions. The main system control parameters for the transition are the arithmetic means of the three-phase angles, $\overline{\Theta}_a$ and the surface tension differences $\Delta\gamma$ between both liquids. These relevant parameters can be combined into a single system parameter, a speciffic Marangoni number $\widetilde{M} = 3\Delta\gamma / (2\overline{\gamma}\overline{\Theta}_a^2)$. This $\widetilde{M}$ universally characterizes the coalescence respectively transition behavior as a function of both, the physicochemical liquid properties and the shape of the liquid body in the contact region. The transition occurs at a certain threshold value $\widetilde{M}_t$ and is sharp within the experimental resolution. The experimentally observed threshold value of $\widetilde{M}_t \approx 2$ agrees quantitatively with values obtained by simulations assuming authentic real space data. The simulations indicate that the absolute value of $\widetilde{M}_t$ very weakly depends on the molecular diffusivity.