Surface jets and internal mixing during the coalescence of impacting and sessile droplets

The internal dynamics during the coalescence of a sessile droplet and a subsequently deposited impacting droplet, with either identical or distinct surface tension, is studied experimentally in the regime where surface tension is dominant. Two color high-speed cameras are used to capture the rapid internal flows and associated mixing from both side and bottom views simultaneously by adding an inert dye to the impacting droplet. Given sufficient lateral separation between droplets of identical surface tension, a robust surface jet is identified on top of the coalesced droplet. Image processing shows this jet is the result of a surface flow caused by the impact inertia and an immobile contact line. By introducing surface tension differences between the coalescing droplets, the surface jet can be either enhanced or suppressed via a Marangoni flow. The influence of the initial droplet configuration and relative surface tension on the long-term dynamics and mixing efficiency, plus the implications for emerging applications such as reactive inkjet printing, are also considered.

Figure 1

Schematic diagram of the experimental setup. The undyed, sessile droplet is deposited from blunt tip 1; the dyed, impacting droplet is deposited from blunt tip 2. The droplets were front-lit by a constant light source.

Figure 2

Side and bottom views of a dyed droplet impacting an undyed sessile droplet of the same fluid (fluid 2, 4% ethanol), for three lateral separations. In panels (a) and (b), the impacting droplet collides with the sessile droplet before the substrate. In panel (c), coalescence occurs as the impacting droplet spreads across the substrate. All scale bars are 1 mm.

Figure 3

Sketch depicting the coalescence of two droplets of the same fluid at the instance the maximum spread length is reached (typically 3 ms after coalescence), represented as a cut-plane through the precursor droplet centers. The impacting droplet lands on the substrate before spreading into the sessile droplet to induce coalescence.

Figure 4

Free surface edges at five early times during the coalescence of two droplets of the same fluid (fluid 2, 4% ethanol) overlaid onto the 5.8-ms side view (faded by 25%). The gray arrow indicates increasing time. The data correspond to Fig. 2.

Figure 5

Normalized free surface height for the leading edge positions of the bulk and jet, as indicated on the inset frames. The free surface height is extracted by image processing from each side view frame, matched to the horizontal position determined from the corresponding bottom view frame. Both droplets consist of fluid 2 (4% ethanol). The data correspond to Fig. 2.

Figure 6

Horizontal position of the bulk and (if applicable) jet leading edges, as indicated on the inset frame from case (c), determined from the bottom view frames. Each color (labelled) corresponds to a different experimental case: (a) Fluid 2 impacts fluid 2—Fig. 2. (b) Fluid 2 impacts fluid 2—Fig. 7. (c) Fluid 3 impacts fluid 2—Fig. 7. (d) Fluid 2 impacts fluid 3—Fig. 7.

Figure 7

Side and bottom views of a dyed droplet impacting an undyed sessile droplet, with the precursor droplet fluid properties varied between the panels. (a) A droplet of fluid 2 (4% ethanol) impacts a sessile droplet of the same fluid. (b) A droplet of fluid 3 (8% ethanol) impacts a sessile droplet of fluid 2 (4% ethanol). (c) A droplet of fluid 2 (4% ethanol) impacts a sessile droplet of fluid 3 (8% ethanol). The impacting droplet is always dyed (blue). All scale bars are 1 mm.

Figure 8

Regime map for the early time flow structures at various lateral separations and different relative droplet fluid properties, characterized by a dimensionless group involving the Ohnesorge number (of the impacting droplet) and the surface tension ratio.

Figure 9

Bottom views of a dyed droplet impacting an undyed sessile droplet, with the fluid properties varied between the panels. The side view is also shown in panel (b). (a) A droplet of fluid 3 (8% ethanol) impacts a sessile droplet of fluid 1 (water). (b) A droplet of fluid 1 (water) impacts a sessile droplet of fluid 3 (8% ethanol). (c) A droplet of fluid 2 (4% ethanol) impacts a sessile droplet of fluid 3 (8% ethanol). (d) A droplet of fluid 3 (8% ethanol) impacts a sessile droplet of the same fluid. (e) A droplet of fluid 4 (18% ethanol) impacts a sessile droplet of fluid 3 (8% ethanol). All scale bars are 1 mm.