Microfluidic circuit analysis I: ion current relationships for thin slits and pipes

Area of Science:

• Physical Chemistry
• Fluid Dynamics
• Electrokinetics

Background:

• Microfluidic circuit theories traditionally apply conservation of volume and total charge.
• A stricter approach requires conservation of individual ion species number (charge).
• Accurate microfluidic modeling necessitates understanding electrokinetic ion currents within channels.

Purpose of the Study:

• To develop analytical and numerical methods for calculating ion currents and fluid flowrates.
• To investigate ion transport in Newtonian binary electrolyte solutions within confined geometries.
• To extend microfluidic circuit theory by accounting for individual ion species conservation.

Main Methods:

• Analytical derivations in low potential, high potential, and thin double layer limits.
• Numerical methods for calculating ion currents and fluid flowrates.
• Application to two-dimensional thin slits and pipes.

Main Results:

• Demonstrated validity of Boltzmann distribution with a local geometric mean for reference ion concentration, irrespective of double layer overlap.
• Quantified electrokinetic ion currents and fluid flowrates in confined geometries.
• Revealed complex ion current behavior even in single microfluidic channels.

Conclusions:

• The developed methods provide a more rigorous foundation for microfluidic circuit theory.
• Individual ion species conservation is crucial for accurate modeling of microfluidic systems.
• The findings highlight the intricate nature of ion transport in microscale fluid dynamics.