Discovery of a dispersion model at high Peclet numbers
Peclet number characterises the transition from classical Taylor-Aris dispersion to convection-dominated longitudinal solute transport, with the classical model becoming inadequate at extremely high radial Peclet number $Pe_r$. We develop a novel explicit-closure one-dimensional (1-D) effective dispersion model for this high-$Pe_r$ regime by introducing two closure coefficients, $θ_u$ and $θ_d$, whose functional structures are identified using low-frequency transfer-function matching and a modified Kolmogorov-Arnold network (KAN). The resulting model captures the transition from classical Taylor-Aris dispersion at low $Pe_r$ to convection-dominated dispersion at high $Pe_r$. Analysis reveals that, in the high-$Pe_r$ regime, axial transport is redistributed between the effective convection flux and the dispersive flux, resulting in a reduced macroscopic convection velocity. Numerical validation demonstrates close agreement with the convection-diffusion model over the investigated high-$Pe_r$ conditions, while the classical Taylor-Aris model exhibits substantial deviations. Application of the proposed model to averaged flow velocity inversion further demonstrates improved velocity estimation, particularly in the high-$Pe_r$ regime. These results highlight the importance of accounting for non-classical dispersion for reliable contrast-agent-based arterial blood flow velocimetry and provide new insight into high-$Pe_r$ mass transport.