[Paper Review] Effect of Ionic Advection on Electroosmosis over Charge Modulated Surfaces: Beyond the Weak Field Limit

Uddipta Ghosh, Suman Chakraborty|arXiv (Cornell University)|Sep 21, 2015

Microfluidic and Capillary Electrophoresis Applications35 references3 citations

TL;DR

This study investigates electroosmotic flow over charge-modulated surfaces beyond the weak field limit by solving the coupled Poisson-Nernst-Planck and Navier-Stokes equations numerically and analytically. It reveals that ionic advection significantly alters flow velocity and potential distribution, invalidating the standard Smoluchowski slip boundary condition when advection effects are non-negligible, especially at higher ionic Peclet numbers and finite double layer thicknesses.

ABSTRACT

The present study deals with the effect of ionic advection on electroosmotic flow over charge modulated surfaces in a generalized paradigm when the classically restrictive "weak field" limit may be relaxed. Going beyond the commonly portrayed weak field limit (i.e, the externally applied electric field is over-weighed by the surface-induced electrical potential, towards charge distribution in an electrified wall-adhering layer) for electroosmotic transport, we numerically solve the coupled full set of Poisson-Nernst-Planck (PNP) and Navier-Stokes equations, in a semi-infinite domain, bounded at the bottom by a charged wall. Further, in an effort to obtain deeper physical insight, we solve the simplified forms of the relevant governing equations for low surface potential in two separate asymptotic limits: (i) a regular perturbation solution for Low Ionic Peclet number (Pe), where Pe is employed as the gauge function and (ii) a matched asymptotic solution for O(1) Pe in the Thin Electric Double Layer (EDL) limit. We demonstrate that reasonably good agreement is observed between the analytical and numerical solutions. Our analysis reveals that the primary effect of Pe on the flow is to slow down the "free stream velocity", adding to the periodicity of the flow, while it also induces significant changes in the overall potential. We further show that the electrical double layer thickness strongly dictates the "free stream velocity", and a simple Smoluchowski type of slip boundary condition cannot be used, if the effect of advection is taken into account. These results can be of significant importance in designing microfluidic and nanofluidic systems with surface charge modulation.

Motivation & Objective

• To analyze electroosmotic flow over charge-modulated surfaces when the weak field approximation no longer holds.
• To investigate the influence of ionic advection on flow dynamics and electric potential distribution in electrified systems.
• To determine the validity of classical slip boundary conditions (e.g., Smoluchowski) under non-weak field conditions.
• To compare analytical asymptotic solutions with full numerical simulations for accuracy and consistency.
• To provide design insights for microfluidic and nanofluidic systems with spatially modulated surface charge.

Proposed method

• Numerical solution of the coupled Poisson-Nernst-Planck and Navier-Stokes equations in a semi-infinite domain bounded by a charged wall.
• Use of the ionic Peclet number (Pe) as a gauge function for regular perturbation analysis in the low-Pe regime.
• Application of matched asymptotic analysis for O(1) Pe in the thin electric double layer (EDL) limit.
• Solution of simplified governing equations under low-surface-potential assumptions to enable analytical tractability.
• Comparison of analytical results with full numerical simulations to validate findings.
• Explicit modeling of charge modulation on the wall to capture periodic flow and potential structures.

Experimental results

Research questions

• RQ1 How does ionic advection alter electroosmotic flow when the weak field approximation is relaxed?
• RQ2 What is the impact of the ionic Peclet number on the free stream velocity and flow periodicity?
• RQ3 To what extent does the electric double layer thickness invalidate the Smoluchowski slip condition under advection effects?
• RQ4 How well do analytical asymptotic solutions match numerical solutions across varying Pe and EDL thicknesses?
• RQ5 What are the implications of these findings for the design of microfluidic devices with patterned surface charge?

Key findings

• Ionic advection significantly slows down the free stream velocity, introducing pronounced periodicity in the flow profile.
• The ionic Peclet number induces substantial changes in the overall electric potential distribution, especially near the charged surface.
• The thickness of the electric double layer strongly governs the free stream velocity, making it a critical design parameter.
• A standard Smoluchowski-type slip boundary condition fails to accurately represent the system when ionic advection is non-negligible.
• Good agreement is observed between analytical solutions (perturbation and matched asymptotic) and full numerical simulations.
• The results demonstrate that classical electroosmotic models break down under moderate to high ionic advection, necessitating more advanced modeling in nanofluidic systems.