This study presents a time-resolved three-dimensional investigation of the mixing of a Newtonian fluid in the laminar regime using 4D Lagrangian particle tracking (4D LPT) based on Shake-The-Box algorithm. To the authors’ knowledge, this is the first application of 4D LPT to characterize the periodic flow structures throughout the impeller area and in the volume of fluid below it, down to the wall. The experimental setup enabled high-resolution Lagrangian measurements of particle trajectories ( \(160\times 10^{3}\) particles tracked for 12,453 time steps), which were subsequently used to reconstruct Eulerian velocity fields. A detailed comparison with direct numerical simulations shows excellent agreement across all velocity components, confirming the accuracy of the method. This technique makes it possible to detect fluid velocities greater than the tip velocity of the blades, which had been identified in turbulent flow, but is shown to occur in laminar flow. In addition, modal analyses on the three-velocity components in the investigated volume (Proper Orthogonal Decomposition and Direct Fourier Transform) reveal that the flow is governed by the periodic passage of the impeller blades, and coherent structures, namely trailing vortices, are detected via the λ₂-criterion. The Lagrangian data further allow for the identification of laminar mixing characteristics, highlighted through Poincaré sections and lineal stretch. These results demonstrate the unique capabilities of 4D LPT to investigate both coherent structures and mixing dynamics at a low Reynolds number in a stirred tank reactor.
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