Electrokinetic Power-Series Solution in Narrow Cylindrical Capillaries for All Zeta Potentials

Area of Science:

• Fluid dynamics
• Electrochemistry
• Physical chemistry

Background:

• Previous models for electrokinetic flow in capillaries were limited to low or high zeta potentials, using piecewise functions with discontinuities.
• Existing approximations introduce significant errors, particularly for parameters like volume transport and apparent viscosity.

Purpose of the Study:

• To derive a singular, continuous, and finite equation for the full Poisson-Boltzmann equation applicable to all zeta potentials in a cylindrical capillary.
• To provide an exact solution that overcomes the limitations and inaccuracies of prior approximate models.

Main Methods:

• Developed a novel analytical solution to the full Poisson-Boltzmann equation for electrokinetic flow.
• Compared the derived exact solution against established approximate solutions for high zeta potentials.

Main Results:

• The new singular equation provides exact results for all zeta potential ranges, unlike previous piecewise approximations.
• Approximate solutions showed significant errors, with volume transport (up to 9.76%) and apparent viscosity (up to 57.4%) being notably affected.
• The function $$ exhibited errors up to 10.5% when compared to the exact solution.

Conclusions:

• The presented singular equation offers a unified and accurate approach to modeling electrokinetic flow in capillaries across all zeta potential regimes.
• This exact solution highlights the inaccuracies inherent in previous approximate methods, necessitating a re-evaluation of their application in scientific research.