Charge-Induced Saffman-Taylor Instabilities in Toroidal Droplets

Area of Science:

• Fluid dynamics
• Instability phenomena
• Electrically stressed fluids

Background:

• Saffman-Taylor instabilities typically occur in quasi-2D fluid systems.
• Rayleigh-Plateau instabilities lead to the breakup of fluid threads.
• Charged toroidal droplets present a unique 3D geometry.

Purpose of the Study:

• To investigate the development of Saffman-Taylor instabilities in charged toroidal droplets.
• To determine the conditions under which fingerlike structures form in this 3D system.
• To relate the observed finger formation to fluid timescales and confinement effects.

Main Methods:

• Experimental observation of charged toroidal droplet expansion.
• Control of droplet expansion speed using imposed electric stress.
• Comparison of instability timescales (Saffman-Taylor vs. Rayleigh-Plateau).
• Analysis of finger number using linear stability theory for radial Hele-Shaw cells.

Main Results:

• Charged toroidal droplets develop fingerlike structures during expansion.
• Toroidal confinement effectively creates quasi-2D conditions for instability.
• Finger formation is observed when the Saffman-Taylor timescale is less than the Rayleigh-Plateau timescale.
• The number of observed fingers aligns with theoretical predictions for radial Hele-Shaw cells.

Conclusions:

• Saffman-Taylor instabilities can manifest in 3D toroidal geometries under specific conditions.
• Electric stress is a key parameter in controlling the expansion dynamics and instability.
• The study validates the application of 2D instability models to this 3D toroidal system through symmetry breaking.