Gravity driven current during the coalescence of two sessile drops

Coalescence of liquid drops is critical in many phenomena such as emulsion stability, inkjet printing, and coating applications. For sessile drops on a solid surface, the coalescence process is more complicated than the coalescence of drops suspended in a fluid medium as a result of the coupling of the contact line motions to the fluid flow. In this paper, we use video microscopy to track the evolution of the interfaces and contact lines as well as the internal fluid motion within a merged sessile droplet. In this study, the fluids in the coalescing drops are miscible and have similar surface tensions and drop volumes but different viscosities and densities. Coalescence occurs in three stages. During the first stage, rapid healing of the bridge between the drops occurs just after they touch. In the second stage, slower rearrangement of the liquids occurs. We show that these intermediate rearrangements are driven by gravity even for density differences of the two fluids as small as 1%. For the systems examined, little to no mixing occurs during these first two stages. Finally, in the third stage, diffusion leads to mixing of the fluids. Dimensional analysis reveals the scaling of the intermediate flow behavior as a function of density difference and geometric dimensions of the merged drop; however, the scaling with viscosity is more complicated, motivating development of a lubrication analysis of the coalescence problem. Numerical calculations based on the lubrication analysis capture aspects of the experimental observations and reveal the governing forces and time scales of the coalescence process. The results reveal that internal fluid motions persist over much longer time scales than imaging of the external interface alone would reveal. Furthermore, nearly imperceptible motions of the external composite drop interface can lead to important deviations from the predominant gravity current scaling, where viscous resistance of the lighter fluid layer plays a significant role in the internal fluid motion. C 2015 AIP Publishing LLC. INTRODUCTION Coalescence of drops is critically important to numerous technological and natural processes. For example, coalescence of drops on surfaces leads to the formation of a uniform film in spray coating and influences heat transfer in spray cooling. 1–3 While the coalescence of drops suspended in a fluid medium has been examined extensively, 4,5 coalescence of two sessile drops on a solid surface adds the feature that the contact lines of the drops must move during the merging process. 6 …