Electrophoresis simulations using Chebyshev pseudo-spectral method on a moving mesh.

Area of Science:

• Computational chemistry
• Analytical chemistry
• Biophysics

Background:

• Electrophoresis simulations require high accuracy and computational efficiency.
• Existing methods face limitations in handling complex boundary conditions and high current densities.
• Adaptive mesh techniques can improve resolution in critical simulation regions.

Purpose of the Study:

• To implement and demonstrate a Chebyshev pseudo-spectral method combined with an adaptive mesh for electrophoresis simulations.
• To enhance computational efficiency and numerical accuracy in simulating various electrophoresis techniques.
• To validate the method's performance for nonlinear electrophoretic processes.

Main Methods:

• Utilized the Chebyshev pseudo-spectral method for higher numerical accuracy compared to finite difference methods.
• Implemented a novel moving mesh scheme to cluster grid points in regions of poor numerical resolution, improving efficiency.
• Applied the coupled method to simulate isotachophoresis (ITP), isoelectric focusing (IEF), and capillary zone electrophoresis (CZE).

Main Results:

• Demonstrated fast and highly accurate simulations of electrophoresis techniques, including ITP, IEF, and CZE.
• Successfully simulated nonlinear electrophoretic processes at high current densities (up to 1000 A/m).
• Showcased the superior efficacy of the adaptive moving mesh over methods focusing solely on concentration gradients.

Conclusions:

• The adaptive Chebyshev pseudo-spectral method provides a significant advancement for fast and accurate electrophoresis simulations.
• The developed method is versatile, applicable to various electrophoresis techniques and boundary conditions.
• Integration into the open-source SPYCE simulator and verification confirm its robust implementation.