Interface Fragmentation via Horizontal Vibration: A Pathway to Scalable Monodisperse Emulsification

Abstract

We present a scalable method for producing monodisperse micro-scale emulsions in a rectangular container holding two stably stratified layers of immiscible liquids by applying horizontal vibration. This setup enables the excitation of a single line of ordered Faraday waves along each end wall when viscous forces dominate interfacial dynamics. Our experiments and theoretical modelling show that the critical non-dimensional acceleration for the breakup of the wave tips in a regular array of droplets scales as $N^{-1/2} ω^{*3/2}$, where $N$ is the kinematic viscosity ratio and $ω^{*}$ is the frequency of forcing on the viscous-capillary scale. The droplet diameter can be easily tuned by varying the forcing parameters, and the number of droplets generated per cycle is proportional to the width of the container.

Figures (7)

• Figure 1: (a) Schematic diagram of the working part of the experiment, with angled side-view images showing interfacial dynamics near the container’s end walls as a function of increasing forcing acceleration. In the angled top-view (orange box), the pink arrow indicates subharmonic wave tips and the orange arrow points to the edge of the subharmonic Faraday waves right below the onset of droplet formation. (b) Top-view image of the formation of regular droplet trains at the end wall, which are separated by half-wavelengths of the Faraday wave, typically of a few millimeters (see Movie 1 in Supplemental Materials SM). (c) Different vibrational parameters generate droplets of different size, visualized in angled top-view (end wall indicated by yellow line). Several visible satellite droplets were generated before the system reached a stable oscillatory state (see Section S1 in Supplemental Materials SM) for details.
• Figure 2: Distinct regimes of wave and droplet behavior: (a) irregular droplets detaching from disordered waves, (b) regular droplet trains emerging from ordered near-wall waves. Dashed blue and red boxes highlight droplet detachment process. (c) Schematics showing the different types of interfacial breakup observed in (a) and (b). Red arrows indicate the dominant flow direction in the upper layer in the vicinity of the breakup location.
• Figure 3: (a) Variation of the critical acceleration with forcing frequency, $F$, with different symbols distinguishing different viscosity ratios $N$. Red (blue) symbols denotes regular (irregular) droplet formation. (b) Log-Log plot of non-dimensional acceleration vs non-dimensional frequency, where $\omega_r^*$ marks the transition point between disordered and ordered wave regimes. The linear regressions are shown as a dashed line for the blue data with $\omega^* < \omega_r^*$, and as a solid line for the red data with $\omega^* \geq \omega_r^*$.
• Figure 4: Droplet diameter normalised by $\lambda_\mathrm{c}$ as a function of non-dimensional forcing acceleration $a/a_\mathrm{c}$ for regular droplet formation at $N$=48.9 across different forcing frequencies $F$. The solid line is a linear fit to the data. Inset: dimensional droplet diameter vs forcing acceleration. Error bars denote the standard deviations of multiple measurements.
• Figure A1: Schematic diagram of the horizontal vibration system.