Particle-laden pipe flows are ubiquitous in food, chemical and pharmaceutical processes, where solid particles significantly alter fluid deformation and mixing. Understanding these transport mechanisms is critical for process optimisation. A Lagrangian analysis framework based on a SPH-DEM simulation is proposed to compute finite-time Lyapunov exponent (FTLE) fields and extract Lagrangian coherent structures (LCSs) for non-Newtonian particle-laden pipe flows. The method directly exploits the inherently Lagrangian particle trajectories and computes the FTLE fields using the SPH interpolation scheme, avoiding the costly numerical integration required by conventional Eulerian approaches. Subsequently, LCSs are extracted via a ridge detection algorithm and the combined FTLE is introduced to quantify mixing intensity. The framework is validated against the Kármán vortex street benchmark, showing good agreement with experiment and numerical results. Then the validated framework is applied to non-Newtonian particle-laden pipe flows for a wide range (0 vol.%~30 vol.%) of particle loading. Results reveal a critical concentration range of 20 vol.%~30 vol.%, where the cross-sectionally average combined FTLE increases with concentration up to 20 vol.%, indicating enhanced mixing, but decreases beyond 30 vol.% as particle–particle interactions suppress near-wall fluid deformation. These findings provide a robust Lagrangian tool and new quantitative insights for optimising mixing and transport in industrial particulate flows, such as in food processing pipelines and chemical reactors.
Li et al. (Sat,) studied this question.