Delayed coalescence of surfactant containing sessile droplets

When two sessile drops of the same liquid touch, they merge into one drop, driven by capillarity. However, the coalescence can be delayed, or even completely stalled for a substantial period of time, when the two drops have different surface tensions, despite being perfectly miscible. A temporary state of noncoalescence arises, during which the drops move on their substrate, only connected by a thin neck between them. Existing literature covers pure liquids and mixtures with low surface activities. In this paper, we focus on the case of large surface activities, using aqueous surfactant solutions with varying concentrations. It is shown that the coalescence behavior can be classified into three regimes that occur for different surface tensions and contact angles of the droplets at initial contact. However, not all phenomenology can be predicted from surface tension contrast or contact angles alone, but strongly depends on the surfactant concentrations as well. This reveals that the merging process is not solely governed by hydrodynamics and geometry, but also depends on the molecular physics of surface adsorption.

Figure 1

(a) Cross-sectional sketch of the experimental setup, defining the parameters ${\theta }_i$ and ${\gamma }_i$. Panels (b) and (c) show typical images obtained from side- and top-view cameras, respectively. In both images, the scale bar represents 3 mm. The left droplet is pure water; the right droplet contains SDS. Note that in the top view the needle visible in the image is no longer in contact with the droplets.

Figure 2

The spreading behavior for a single SDS droplet, depending on relative humidity and surfactant concentration (normalized with the critical micelle concentration $c^{*})$. Blue circles represent the stable circular spreading; see upper image (relative humidity [RH] = $55\%$ and $0.3c^{*})$. Red diamonds depict the fingering case, shown in the bottom image (RH = $55\%$ and $1c^{*})$. Both images are taken 1.5 s after droplet deposition. The scale bar represents 5 mm. The dashed line between the regimes is intended as a guide to the eye.

Figure 3

Coalescence behavior for a surfactant drop (droplet 1) and a pure water drop (droplet 2), ${\gamma }_2>{\gamma }_1$. Three regimes are observed for different contact angles: (a) precursor-mediated interactions, (b) fingering regime, and (c) stable delayed coalescence. $t=0$ refers to the moment the droplets touch. In each series, the upper drop consists of pure water and the bottom drop is the surfactant solution; in all cases $\mathrm{\Delta }\gamma =13$ mN/m. In all series, the scale bar represents 3 mm.

Figure 4

Phase diagram of the coalescence behavior of a water drop and an SDS drop. Both the surface tension difference $\mathrm{\Delta }\gamma$ and contact angle are varied. Red squares, vapor- and/or precursor-mediated interaction; green diamonds, fingering instability; yellow triangles, stable delayed coalescence. The color regions are intended as a guide to the eye. The insets show enlargements of the top view of the contact region between the two drops (scale bars: 3 mm).

Figure 5

Phase diagram of two coalescing droplets of different SDS concentrations; the same legend as in Fig. 4 applies for the regimes. Several concentration couples are used to obtain series at $\mathrm{\Delta }\gamma =10$ mN/m and 20 mN/m. From left to right, we move to higher concentrations. The table specifies the concentrations, in terms of the critcal micelle concentration $c^{*}$. The open symbols at 20 mN/m represent the water-SDS case from Fig. 4, included for comparison.

Figure 6

The capillary number of the front of the moving drop (droplet 2) vs reduced surface tension difference $\mathrm{\Delta }\gamma /{\gamma }_1\left({\gamma }_1<{\gamma }_2\right)$ and contact angle, for the delayed coalescence regime. In panel (a), the open symbols represent the coalescence of water and SDS droplets, and closed symbols represent two SDS droplets. The color bar shows the contact angle in degrees and the dotted lines serve as a guide for the eye to see the trend for Ca for $\theta =6$, 10, and ${14}^{\circ }$. In panel (b), the black series are the water-SDS case and the red series are the SDS-SDS case, including the best fit as a blue line. The second column of the legend shows the results for delayed coalescence of different alkane pairs from Ref. [9], inserted for comparison.

Figure 7

Image sequences for two experiments with approximately the same surface tension difference: panel (a) shows the coalescence of a pure water droplet with an SDS solution droplet (0.$3c^{*})$, with $\mathrm{\Delta }\gamma =13$ mN/m, whereas panel (b) shows the coalescence between two SDS solutions droplets (droplet 1, 0.$6c^{*}$, and droplet 2, 0.$3c^{*})$, with $\mathrm{\Delta }\gamma =10$ mN/m. In both cases (a) and (b), $\overline{\theta }=8^{\circ }$. The time at which the images are taken are labeled below [the same for both panels (a) and (b)]. The black dashed line indicates the position of the front separating the two droplets, at $t=0.25$ s. In case (b), the front does not move any more after $t\sim 0.1–0.3$ s. The scale bars represent 5 mm.

Figure 8

Mechanism of lifetime difference between cases (a) and (b) explained. Panels (a) and (b) show the difference in surfactant coverage. Panel (b) shows the accumulation of surfactants at the surface of droplet 2 in a schematic way. In all images, the size of the surfactant molecules is exaggerated as well as the number of surfactants at the interface as compared to the bulk.