The theoretical results of the present work reveal a significant interaction of the oncoming vortex ring of propellant muzzle gases with backward blood spatter. It is shown that there is even possibility that a blood droplet from the backspatter will fully turn around by a powerful vortex ring and land behind a victim. Such a predicted outcome is confirmed by experimental data of fully reversed drop trajectories observed in the experiments conducted in the second part of this work [N. Sliefert, G. Li, J. B. Michael, A. L. Yarin, “Experimental and numerical study of blood backspatter interaction with propellant gases,” Phys. Fluids 33, 043319 (2021)]. A parametric study is conducted here to investigate the totality of the outcomes of the vortex ring interaction with the backward blood spatter and the corresponding deflections and landing locations of blood drops. Furthermore, a secondary vortex ring is introduced here to reveal a continuous effect of the propellant gas.

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