Solute transport in complex channels is widely involved in environmental flows, microfluidic systems, porous media transport, and biochemical mixing processes. Compared with straight channels, curved or periodically varying channels can significantly modify the migration, spreading, and effective dispersion of solute clouds through the coupling between flow structures and wall geometries. To quantitatively investigate these effects, a high-accuracy multiple-relaxation-time lattice Boltzmann method (MRT-LBM) is developed based on the source-term reconstruction of the convection term. In this model, the convection term in the convection-diffusion equation is reformulated as a source term, so that the solute transport equation can be solved in the form of a diffusion equation with a reconstructed source. This treatment avoids the additional deviation that may be introduced by the conventional velocity-dependent equilibrium distribution and is suitable for high-accuracy simulations of solute transport in complex geometries.
Three typical two-dimensional channels are considered, namely a straight channel, a parallel sinusoidal channel with a constant local height, and a symmetric sinusoidal channel with a periodically varying local height. The Reynolds number is fixed at Re=10, and the Peclet number Pe is adjusted by changing the molecular diffusion coefficient D, while the background flow field remains nearly unchanged under different Pe conditions. The effects of Pe and the geometric amplitude \varepsilon on the cross-sectionally averaged concentration distribution, the mass-weighted average velocity, and the effective dispersion coefficient are systematically analyzed. The accuracy of the present model is first verified by the classical Taylor-Aris dispersion problem in a plane Poiseuille flow. The effective dispersion coefficients calculated by the present model agree well with the theoretical solution, with relative errors less than 0.1\%, demonstrating the high accuracy of the present model in capturing the long-time axial dispersion behavior of solute clouds.
The numerical results show that the transport mechanisms are strongly dependent on the channel geometry. In the straight channel, the solute cloud maintains a regular axial distribution without obvious geometric distortion. The variation of Pe mainly changes the effective dispersion coefficient D_\mathrmeff, thereby affecting the axial spreading range and the peak concentration of the solute cloud, whereas its influence on the mass-weighted average velocity is weak. In the parallel sinusoidal channel, the upper and lower walls shift synchronously along the streamwise direction, and the local channel height remains constant. As a result, increasing \varepsilon mainly enhances the lateral deflection of the solute cloud along the curved centerline, but has only a weak effect on the axial concentration distribution. The mass-weighted average velocity decreases slightly with increasing \varepsilon, while the velocity curves obtained at different Pe nearly overlap, indicating that Pe mainly affects the dispersion process rather than the overall migration speed.
In contrast, the symmetric sinusoidal channel exhibits a much stronger geometric modulation effect. Since the local channel height varies periodically along the streamwise direction, alternating contraction and expansion regions are formed. With increasing \varepsilon, the concentration peak shows an obvious axial lag, and the mass-weighted average velocity decreases significantly. This indicates that the periodic contraction-expansion structure can suppress the overall axial migration of the solute cloud and enhance the coupling between geometric modulation and dispersion. At relatively small amplitudes, the concentration distribution still exhibits characteristics similar to Taylor-Aris dispersion. However, when \varepsilon becomes large, the influence of the varying cross-section becomes dominant, and the concentration profiles under different Pe show more complicated differences.
Furthermore, based on numerical results in the ranges of 10\le Pe\le120 and 0.05\le\varepsilon\le0.3, an empirical correlation for D_\mathrmeff/D in the parallel sinusoidal channel is established. The correlation retains the Taylor-Aris-type Pe^2-dominated structure and introduces a geometric correction factor related to \varepsilon, thereby providing a quantitative description of the effective dispersion coefficient in a channel with a constant cross-section and a periodically curved centerline. These results demonstrate that the present high-accuracy MRT-LBM can effectively describe solute transport in complex channels and provide a useful numerical framework for analyzing geometry-regulated dispersion processes.