The efficiency of hydrometallurgical leaching of cathode materials, a critical step in lithium-ion battery recycling, is often limited by the complex and poorly studied interaction between turbulent transport and multi-step reaction kinetics. To study this problem, this work uses a computationally efficient hybrid Eulerian-Lagrangian model. In this model, individual particles are simulated. Each particle evolution is described by a detailed Shrinking Core Model (SCM). The particles move through a pre-computed, high-fidelity velocity field from a Direct Numerical Simulation (DNS). This method separates the calculation of the particle reaction from the fluid dynamics simulation, which, computationally is the most expensive part. This separation makes it possible to do many parametric studies that would otherwise be too slow, which makes the model a powerful tool for process analysis.

The simulations show a clear non-monotonic performance penalty caused by turbulence. The global reaction rate is lowest at a resonant Kolmogorov-based Stokes number of 0.23. At this condition, preferential concentration is the strongest. This causes strong local clustering and reactant starvation inside the dense particle filaments. This resonant condition is the basis for a predictive engineering model for mixer design. The model defines a "clustering risk" zone for critical particle sizes as a function of mixer power and geometry. The analysis also shows internal kinetic limits, like the formation of a product layer, that if not quickly dissolved, inhibits the overall performance.

The main conclusion is that making the process faster by increasing mixing is not always as productive as expected. It is limited by a resonant clustering penalty.
This challenges the common engineering idea that more mixing energy is always good for dissolution. Finally, this work gives a physics-based model to help with practical industrial problems. These problems include reactor design, process scale-up, and optimization of solids loading. This optimization must balance throughput with the performance reduction from particle clustering.