Dynamics of Droplet Pinch-Off at Emulsified Oil-Water Interfaces: Interplay between Interfacial Viscoelasticity and Capillary Forces

The presence of submicrometer structures at liquid-fluid interfaces modifies the properties of many science and technological systems by lowering the interfacial tension, creating tangential Marangoni stresses, and/or inducing surface viscoelasticity. Here we experimentally study the break-up of a liquid filament of a silica nanoparticle dispersion in a background oil phase that contains surfactant assemblies. Although self-similar power-law pinch-off is well documented for threads of Newtonian fluids, we report that when a viscoelastic layer is formed in situ at the interface, the pinch-off dynamics follows an exponential decay. Recently, such exponential neck thinning was found theoretically when surface viscous effects were taken into account. We introduce a simple approach to calculate the effective relaxation time of viscoelastic interfaces and estimate the thickness of the interfacial layer and the viscoelastic properties of liquid-fluid interfaces, where the direct measurement of interfacial rheology is not possible.

Figure 1

The dynamics of droplet pinch-off. (a) Schematic of droplet pinch-off. (b) Minimum neck radius versus time to pinch-off for DI water (black), 4.0 wt.% silica dispersion (red), glycerol (blue), and a water-glycerol mixture (5%, $\mathrm{v}/\mathrm{v}$) (green) in Span 1.0 wt.% micellar solution. Representative error bars are shown.

Figure 2

Images of droplet pinch-off that highlight the role of interfacial viscoelasticity on the neck thinning dynamics. (a) DI water, (b) glycerol mixture, (c) 4.0 wt.% silica dispersion, and (d) glycerol-water (5%, $\mathrm{v}/\mathrm{v}$). Although the silica dispersion droplet has a viscosity close to that of DI-water, its pinch-off occurs at a single point, which is not similar to the pinch-off of liquids with $\mathrm{Oh}<1$ or liquids with $\mathrm{Oh}>1$.

Figure 3

Rheological properties of the interfacial layer. (a) Formation of an interfacial layer at the silica dispersion droplet-Span micellar solution interface. (b) Shear viscosity of the emulsion phase at the oil-water interface. The inset shows a confocal image of the collected emulsion phase from the silica dispersion-micellar solution interface. The red color shows the oil phase and the black zone represents the submicrometer water droplets. (c) Frequency sweep test of the emulsion.

Figure 4

Effect of viscoelasticity on the pinch-off. (a) Minimum neck radius over time for the silica dispersion droplet that is formed with the injection flow rates of 0.1, 0.2, and $0.3\mathrm{\mu }\mathrm{l}/\mathrm{s}$ in blue, red, and green, respectively. The neck thinning of a bulk phase emulsion droplet formed with $0.1\mathrm{\mu }\mathrm{l}/\mathrm{s}$ flow rate is shown in black. (b) Images of the emulsion droplet during the neck thinning.