Sharp transition between coalescence and non-coalescence of sessile drops

Abstract

AbstractUnexpectedly, 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 non-coalescence, connected through a thin liquid bridge. Here we investigate the transition between the states of instantaneous coalescence and temporary non-coalescence. 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 the two liquids. These relevant parameters can be combined into a single system parameter, a specific Marangoni number $\widetilde{M}=3\Delta \gamma /(2\overline{\gamma }\overline{\Theta }_{a}^2)$. This $\widetilde{M}$ universally characterizes the coalescence transition behaviour 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 realistic material parameters. The simulations indicate that the absolute value of $\widetilde{M}_t$ very weakly depends on the molecular diffusivity.