A New Analytical Formulation for the Electrophoretic Mobility of a Colloidal Sphere

Area of Science:

• Colloid and Surface Science
• Physical Chemistry
• Electrokinetics

Background:

• Electrophoretic mobility is crucial for understanding colloidal particle behavior.
• Existing models like Henry's equation have limitations at higher surface potentials.
• Accurate analytical solutions are needed for broader applications.

Purpose of the Study:

• Derive a new analytical equation for electrophoretic mobility of charged colloidal spheres.
• Validate the equation against numerical solutions across various surface potentials and electrokinetic diameters (κa).
• Investigate the specific case of constant surface charge.

Main Methods:

• Development of a novel analytical equation for electrophoretic mobility.
• Comparison of the new equation with established Henry's formulation.
• Validation against full numerical solutions for electrophoretic mobility.
• Analysis of the impact of surface potential and the κa parameter.

Main Results:

• The new equation accurately represents electrophoretic mobility for low surface potentials, reducing to Henry's formulation.
• The equation shows good agreement with numerical results up to 50 mV surface potential.
• For higher potentials, the equation is accurate for κa > 10.
• A simplified equation relating surface charge and mobility is derived for κa > 10.

Conclusions:

• The new analytical equation offers an improved and broader applicability for predicting electrophoretic mobility.
• It provides a valuable tool for researchers working with charged colloidal systems.
• The findings facilitate more accurate characterization of colloidal dispersions.