Early stage of delayed coalescence of soluble paired droplets: A numerical study

Abstract

When two sessile droplets of miscible fluids come into contact, the coalescence process can be significantly delayed owing to the competition between the capillary and Marangoni effects. It is important to reveal the mechanism of the deformation and displacement of the sessile droplets at the early stage of the delayed coalescence, which determines the self-stabilized shape and joint motion of the two droplets later on. In this work, we numerically investigate the early-stage dynamics of the delayed coalescence between two sessile droplets of equal size and laden with aqueous mixtures of different solvent mass fractions. A three-dimensional numerical model is adopted based on lubrication theory and is validated by comparison against previous experimental results. Through simulation, we first showed how the concentration transport is coupled with droplet deformation. Then, we explained the underlying mechanism of delayed coalescence by analyzing the liquid bridge numerically and theoretically. A scaling law for the duration of liquid bridge growth is given and agrees well with the numerical results. Finally, the effects of the solubility on the dynamics are investigated. Our study reveals how the capillary and Marangoni effects dominate the flow during the early stage of the delayed coalesce and thus determine its following behavior.