Hydrodynamics of Droplet Coalescence

We study droplet coalescence in a molecular system with a variable viscosity and a colloid-polymer mixture with an ultralow surface tension. When either the viscosity is large or the surface tension is small enough, we observe that the opening of the liquid bridge initially proceeds at a constant speed set by the capillary velocity. In the first system we show that inertial effects become dominant at a Reynolds number of about $1.5\pm 0.5$ and the neck then grows as the square root of time. In the second system we show that decreasing the surface tension by a factor of ${10}^5$ opens the way to a more complete understanding of the hydrodynamics involved.

Figure 1

Coalescence of two water drops; eight consecutive images taken at $11.200\mathrm{\text{frames}}/\mathrm{s}$ at a resolution of $256\times 256$ pixels. The image size is 5.12 mm by 5.12 mm and $R_0=2\mathrm{mm}$.

Figure 2

The time evolution of the radius of the neck for high viscosity fluids. Squares: 100 mPa s; circles: 300 mPa s; triangles: 500 mPa s; plusses: 1 Pa s. The inset in (a) zooms in on the data for the highest viscosity close to $t=0$ compared to the prediction by Eggers et al. [5] (full curve). (b) The data collapse after scaling with $R/R_0$ and $t/{\tau }_v$. The full line is for $0.55\gamma /\eta$.

Figure 3

The time evolution of the radius of the neck for low viscosity fluids. Open squares: water; circles: 5 mPa s; triangles: 20 mPa s; filled squares: 50 mPa s. In (b) the data collapse after scaling with $R/R_0$ and $t/{\tau }_i$. The full line has a slope of 1.2. For the system of 50 mPa s the crossover between the viscous and inertial regimes can be observed; the curve has been shifted upwards artificially for the late-time behavior to coincide.

Figure 4

LSCM images of droplet coalescence in a phase-separated colloid-polymer mixture. Shown are a polymer-rich droplet ($R_0=30\mu \mathrm{m}$, top row) and a colloid-rich droplet ($R_0=15\mu \mathrm{m}$, bottom row) coalescing with their bulk phases. In the bottom row we have partially bleached the dye of the colloids in the droplet, which allows following the extrusion of droplet material into the bulk phase; see also the accompanying movie [17]. Note the typical shape of the retracting interfaces, which is similar to predictions in 5.

Figure 5

The time evolution of the radius of the neck in a colloid-polymer mixture for polymer-rich gas droplets (open symbols: three different events with $R_0=16$, 17, and $18\mu \mathrm{m}$) and colloid-rich liquid droplets (closed symbols: two different events with $R_0=15$ and $17\mu \mathrm{m}$). Full curves are linear fits to the data.