Controlling the breakup of toroidal liquid films on solid surfaces

Andrew M J Edwards,Carl V Brown,Glen Mchale,Élfego Ruiz-Gutiérrez,Gary G Wells,Michael I Newton,Rodrigo Ledesma-Aguilar

doi:10.1038/s41598-021-87549-5

Andrew M J Edwards, Carl V Brown + Show 5 more

Open Access

https://doi.org/10.1038/s41598-021-87549-5

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Abstract

The breakup of a slender filament of liquid driven by surface tension is a classical fluid dynamics stability problem that is important in many situations where fine droplets are required. When the filament is resting on a flat solid surface which imposes wetting conditions the subtle interplay with the fluid dynamics makes the instability pathways and mode selection difficult to predict. Here, we show how controlling the static and dynamic wetting of a surface can lead to repeatable switching between a toroidal film of an electrically insulating liquid and patterns of droplets of well-defined dimensions confined to a ring geometry. Mode selection between instability pathways to these different final states is achieved by dielectrophoresis forces selectively polarising the dipoles at the solid-liquid interface and so changing both the mobility of the contact line and the partial wetting of the topologically distinct liquid domains. Our results provide insights into the wetting and stability of shaped liquid filaments in simple and complex geometries relevant to applications ranging from printing to digital microfluidic devices.

Highlights

The breakup of a slender filament of liquid driven by surface tension is a classical fluid dynamics stability problem that is important in many situations where fine droplets are required
It is important to note that the ability to form such a reversible, spread, ring-shaped liquid film on a solid flat surface is unique to our dielectrowetting approach. This would not be possible using an alternative Electrowetting on Dielectric (EWOD)[25,26] approach which suffers from contact angle s aturation[27,28], since in EWOD the limited extent to which the contact angle can be reduced would prevent the liquid from spreading down to the initial spread film state that we can achieve using dielectrowetting
We have studied the time evolution of the minimisation in detail, using Fourier analysis to elucidate how the complex interplay between geometry, and static and dynamic wettability results in the selection of pathway to the final state

Summary

Introduction

The breakup of a slender filament of liquid driven by surface tension is a classical fluid dynamics stability problem that is important in many situations where fine droplets are required. Free floating toroidal shaped droplets and bubbles can breakup through the capillary driven P–R instability, with the most unstable breakup mode being related to the geometry of the torus[11–13] Their unique topology allows an additional shrinking instability which is not possible in a cylinder. During the energy minimisation of a toroidal shaped droplet there exists a competition between the P–R instability and the shrinking instability, and so the shape and the topology add complexity to understanding the mode of breakup[14] Such complexity is further increased when a small droplet of a partially-wetting liquid is placed on a solid surface, where the balance of the solid–vapour, γsv solid–liquid, γsl and liquid vapour, γ surface tensions determines the static wettability of the surface and forces the liquid to take the shape of a spherical cap shaped droplet intersecting the solid with Young’s equilibrium angle, cos θe = (γsv − γsl)/γ15. By control over the degree of surface wettability through our dielectrowetting method, we elucidate selection of the pathway and mode during the evolution of a toroidal liquid filament

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Results

Conclusion