Pattern Formation of Three-Dimensional Electroconvection on a Charge Selective Surface

Area of Science:

• Fluid Dynamics
• Electrochemistry
• Surface Science

Background:

• Charge selective surfaces induce hydrodynamic instability and electroconvection.
• Electroconvection involves vortical fluid motions driven by biased ion transport.
• Understanding electroconvection is crucial for applications involving ion transport and fluid control.

Purpose of the Study:

• To report the first laboratory observation of three-dimensional electroconvection.
• To categorize the distinct patterns of 3D electroconvection.
• To establish scaling laws governing pattern selection and ion flux.

Main Methods:

• Experimental observation of 3D electroconvection on a charge selective surface.
• Combining experimental data with theoretical scaling analysis.
• Analyzing the influence of electric Rayleigh number (Ra_{E}), Reynolds number (Re), and Schmidt number (Sc) on electroconvection patterns.

Main Results:

• Three distinct patterns of 3D electroconvection were identified: polygonal, transverse, and longitudinal rolls.
• Pattern selection depends on the ratio of Ra_{E} to Re^{2}Sc.
• The critical electric Rayleigh number (Ra_{E}^{*}) for pattern onset is determined by Sc, following Ra_{E}^{*}∼Re^{2}Sc.
• Convective ion flux, quantified by the electric Nusselt number (Nu_{E}), follows a power-law relationship with dimensionless parameters.

Conclusions:

• The study provides the first experimental evidence of 3D electroconvection patterns.
• A comprehensive categorization of electroconvection patterns based on key dimensionless numbers was achieved.
• The established scaling laws offer predictive capabilities for electroconvection behavior and ion transport in relevant systems.