Assessment of similarity scaling for droplet collection efficiency beyond stokes drag

This work investigates the similarity of particle-laden flows and the associated collection efficiency, which quantifies the impinging mass on a surface. A generalized similarity framework is proposed to relate particle trajectories across different geometric and dynamic scales. The formulation extends the classical inertia parameter originally derived under Stokes drag; by keeping both the flow Reynolds number and Mach number constant, it enables consistent scaling of impingement processes in gaseous flows also beyond Stokes drag assumption through Reynolds-dependent drag formulations and secondary impact models, such as splashing and rebound. Under Stokes drag assumptions, the proposed similarity is theoretically exact, and any deviation can be attributed solely to numerical discretization. In realistic conditions, however, the Stokes drag law rarely holds, as particle Reynolds numbers at impact typically exceed the Stokes regime. The analysis, therefore, quantifies the error introduced when more general drag formulations are adopted, including those accounting for Reynolds variation and deformable droplet behavior, as well as secondary impact effects, such as splashing and rebound. The numerical assessment, performed with the in-house Lagrangian particle-tracking solver PoliDrop, demonstrates that maintaining constant values of the modified inertia parameter, flow Reynolds number, and Mach number ensures dynamically similar collection efficiency distributions, with deviations remaining small even outside the Stokes regime. Finally, the Mach similarity is relaxed to illustrate the practical applicability of the scaling in scenarios where complete Mach number matching is not feasible, such as wind tunnel experiments and other scaled particle-impingement applications, including filtration, erosion, and deposition processes. These results provide a comprehensive quantification of the limits and robustness of similarity scaling in particle-laden impingement flows, identifying its primary applicability conditions, notably K 0.125 and matched Reynolds and Mach numbers, and showing that acceptable accuracy can still be achieved when Mach similarity is relaxed, as commonly occurs in wind tunnel applications.