Spatiotemporal evolution of liquid-lens coalescence

What is it about?

Coalescence -- of droplets, in general, and liquid lenses, in particular -- is a fundamental problem in the fluid dynamics and statistical physics of multi-phase flows. Spatiotemporal dynamics of liquid-lens coalescence were investigated through direct numerical simulations of the three-phase Cahn-Hilliard-Navier-Stokes equations. The study reveals that, consistent with experimental findings, the neck height evolution follows h(t) ∼ t^1 in the viscous regime and h(t) ~ t^{2/3} in the inertial regime, where turbulence signatures were identified through quantification of kinetic-energy spectra. Additionally, an examination of the merger of asymmetric lenses indicates power-law forms for h(t) in the inertial regime with exponents intermediate between droplet-coalescence and lens-merger scenarios.

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Photo by Jennifer Aldoretta on Unsplash

Photo by Jennifer Aldoretta on Unsplash

Why is it important?

Through our direct numerical simulations, we successfully captured comprehensive spatiotemporal details regarding the coalescence of two lenses. For the first time, we provide a physical explanation for the distinct scaling exponents observed in the viscous and inertial regimes during coalescence. Furthermore, we report, for the first time, the emergence of turbulence in these seemingly simple systems.