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The effects of stone size on the process and comminution efficiency in shock wave lithotripsy (SWL) are investigated by experiments, numerical simulations, and scale analysis. Cylindrical BegoStone phantoms with approximately equal height and diameter of either 4-, or 7- or 10-mm, in a total aggregated mass of about 1.5 g, were treated in an electromagnetic shock wave lithotripter field. The resultant stone comminution (SC) was found to correlate closely with the average peak pressure, P+(avg), incident on the stones. The P+(avg) threshold to initiate stone fragmentation in water increased from 7.9 to 8.8 to 12.7 MPa, respectively, when the stone size decreased from 10 to 7 to 4 mm. Similar changes in the P+(avg) threshold were observed for the 7- and 10-mm stones treated in 1,3-butanediol where cavitation is suppressed, suggesting that the observed size dependency is due to changes in stress distribution within different size stones. Moreover, the slope of the correlation curve between SC and ln(Pfalse‒+(avg)) in water increased with decreasing stone size, while the opposite trend was observed in 1,3-butanediol. The progression of stone comminution in SWL showed a size-dependency with the 7- and 10-mm stones fragmented into progressively smaller pieces while a significant portion (> 30%) of the 4-mm stones were stalemated within the size range of 2.8 ~ 4 mm even after 1,000 shocks. Analytical scaling considerations suggest size-dependent fragmentation behaviour, a hypothesis further supported by numerical model calculations that exhibit changing patterns of constructive and destructive wave interference, and thus variations in the maximum tensile stress or stress integral produced in cylindrical and spherical stone of different sizes.

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Most reports simulating in-flight particle temperatures in polymer cold spray ignore intra-particle thermal gradients that develop in-flight, and, to date, no research group has simulated the effects of thermal gradients on polymer particle impact dynamics. This report investigates the effects of intra-particle thermal gradients on the impact response of thermoplastics, using properties of polyether-ether-ketone (PEEK) in a simulated like-onlike cold spray deposition process. Particle velocities and internal temperatures are calculated from compressible flow models of the spray process under several heat transfer assumptions. The commonly used lumped thermal capacitance assumption differs in average particle impact temperature by over 70 °C from simulations involving a more physically representative thermal gradient model assuming finite-rate heat conduction. Additionally, the intra-particle temperature differences of over 100 °C in some particles imply significant variation in material properties within a particle. The predicted average temperatures and temperature gradients are used as initial conditions for a finite element-based impact model that shows distinct mechanical responses of isothermal and thermally graded particles. These results suggest that thermal gradients in polymer particles should be considered for further refinements of model-based predictions for the cold spray of polymers and optimized by process design.