Physics-informed neural networks for two-dimensional wall-reactive solute dispersion in canonical shear flows

Abstract

The dispersion of reactive solutes in shear flows is governed by the interplay between advective stretching, transverse diffusion, and boundary exchange kinetics. While classical analytical methods and grid-based numerical solvers have extensively characterised these transport mechanisms, accurately resolving the spatiotemporal evolution of solute plumes in asymmetric reactive environments remains computationally demanding. In this study, we introduce a physics-informed neural network (PINN) framework to simulate two-dimensional wall-reactive solute dispersion in canonical shear flows (Couette, Poiseuille, and Couette-Poiseuille) bounded by absorbing walls. By embedding the governing convection-diffusion equation and Robin boundary conditions into a unified loss function, the mesh-free PINN reconstructs the spatiotemporal concentration field. The network predictions are validated against an alternating-direction implicit (ADI) finite-difference benchmark, showing close agreement across non-reactive, symmetric, and asymmetric reactive regimes. The computations are carried out at $\mathrm{Pe}=10$ for impermeable walls, symmetric absorption $(β_1,β_2)=(1,1)$, and tenfold asymmetric wall-reactivity contrasts $(β_1,β_2)=(0.2,2)$ and (2,0.2). Leveraging the differentiable nature of the trained PINN, we extract wall-resolved transport diagnostics, including the apparent axial dispersion coefficient, cumulative wall-removal dynamics, and localised uptake fluxes. The results show that the imposed shear profile governs the streamwise organisation of reactive uptake, while unequal wall reactivities induce transverse asymmetry that modifies the macroscopic spreading rate. Overall, this framework establishes PINNs as an interpretable mesh-free tool for analysing boundary-coupled reactive transport in shear flows.