Electrophoretic Mobility of a Sphere in a Spherical Cavity

Area of Science:

• Colloid and Surface Science
• Electrochemistry
• Fluid Dynamics

Background:

• Electrophoresis is crucial for understanding particle behavior in confined spaces.
• Double layer polarization is a key factor influencing electrokinetic phenomena.

Purpose of the Study:

• To theoretically analyze the electrophoretic mobility of a spherical particle within a spherical cavity.
• To investigate the influence of double layer polarization on particle mobility under various charge conditions.

Main Methods:

• Theoretical analysis of particle motion in an electric field within a spherical cavity.
• Incorporation of double layer polarization effects in the mathematical model.
• Parametric study varying surface potential, Debye length (kappa), particle radius (a), and cavity radius (lambda).

Main Results:

• A minimum in particle mobility versus kappa*a was observed for high surface potentials (positively charged particle, uncharged cavity), absent without polarization effects.
• Mobility dependence on kappa*a showed a minimum at intermediate lambda, diminishing at small or large lambda.
• For an uncharged particle and charged cavity, mobility exhibited a maximum at high surface potential and monotonic increase at low potential, driven by drag force.

Conclusions:

• Double layer polarization is essential for accurate prediction of particle electrophoretic mobility in confined geometries.
• The interplay between electric and drag forces dictates particle behavior, influenced by surface charge and cavity size.
• The findings provide a framework for understanding complex electrophoretic systems with charged particles and cavities.