Radial basis function interpolation supplemented lattice Boltzmann method for electroosmotic flows in microchannel.

Area of Science:

• Fluid dynamics
• Computational physics
• Electrochemistry

Background:

• Electroosmotic flow (EOF) is characterized by steep gradients near channel walls.
• Conventional lattice Boltzmann method (LBM) simulations of EOF use uniform meshes, limiting efficiency for thin electric double layers (EDLs).
• Efficient EOF simulation requires nonuniform meshes, denser in EDLs and sparser in bulk regions.

Purpose of the Study:

• To develop an efficient LBM simulation for EOF in microchannels using nonuniform meshes.
• To introduce a radial basis function (RBF)-based interpolation supplemented LBM (ISLBM) for solving EOF governing equations.
• To enhance computational efficiency and accuracy for EOF simulations, particularly with small EDLs.

Main Methods:

• Formulation of a radial basis function (RBF)-based interpolation supplemented LBM (RBF-ISLBM).
• Solving the Poisson, Nernst-Planck, and Navier-Stokes equations within a nonuniform mesh system.
• Utilizing local RBF-based interpolation over circular supporting regions for prestreaming distribution functions.

Main Results:

• The RBF-ISLBM demonstrates robustness and accuracy in simulating EOF.
• Validation performed for EOFs in infinitely long and finitely long microchannels.
• Successful simulation of EOFs with the highest electrokinetic parameter (κa) in LBM.

Conclusions:

• The RBF-ISLBM is highly suitable for nonuniform meshes in EOF simulations.
• This method significantly enhances the efficiency of LBM for EOF, especially for small EDLs.
• The RBF-ISLBM provides accurate and robust simulations for complex EOF scenarios.