Approximate Analytic Expression for the Time-Dependent Transient Electrophoretic Mobility of a Spherical Colloidal...

Area of Science:

• Colloid and Surface Science
• Electrochemistry
• Physical Chemistry

Background:

• Electrophoretic mobility describes particle movement in an electric field, crucial for understanding colloidal systems.
• Transient behavior, especially under a step electric field, is complex to model theoretically.
• Existing models often require numerical methods for accurate transient analysis.

Purpose of the Study:

• To derive a general expression for the Laplace transform of transient electrophoretic mobility for spherical colloidal particles.
• To develop an approximate analytical method to bypass numerical inverse Laplace transformations.
• To provide a simpler method for calculating transient electrophoretic mobility, particularly for weakly charged particles.

Main Methods:

• Derivation of a general expression for the Laplace transform of time-dependent electrophoretic mobility.
• Application of numerical inverse Laplace transformation for exact solutions.
• Development and validation of an approximate analytical method for simplified calculations.

Main Results:

• A general Laplace transform expression for transient electrophoretic mobility applicable to various zeta potentials and double-layer thicknesses.
• An approximate analytical mobility expression that accurately predicts transient behavior for weakly charged particles.
• Excellent agreement between the approximate analytical results and exact numerical solutions.

Conclusions:

• The derived general expression and approximate method simplify the analysis of transient electrophoretic mobility.
• The new analytical approach offers a computationally efficient alternative to numerical methods.
• This work enhances the understanding and prediction of colloidal particle dynamics in electric fields.