The model uses percolation theory to predict the fragmentation process of blood, resulting in forward spatter to determine the number of droplets, as well as their sizes and initial velocities resulting from the flow field generated by a 7.62 39 mm and a 0.45 auto bullet. Blood viscoelasticity, which slows down the initial velocities of the droplets, is accounted for. The main physical mechanisms responsible for the chaotic disintegration of blood in the case of forward spattering are (i) the Rayleigh-Taylor instability associated with denser blood accelerating toward lighter air and (ii) a cascade of instability phenomena triggered by the original Rayleigh-Taylor instability because the Reynolds number is of the order of 107. Blood is viscoelastic; therefore, its disintegration into individual droplets results in ligament formation with strong uniaxial elongation, which is characterized by the extremely high values of the Deborah number, leading to an almost purely elastic behavior and brittle-like fracture. The blood droplet spray then propagates in air, and deposition on the floor is calculated accounting for gravity and air drag forces, with the latter being diminished by the collective effect related to the droplet-droplet interaction. Also, the experimental data acquired in this work are presented and compared with the theoretical predictions. The agreement between the predictions and the data is satisfactory. The present fluid mechanical model holds great promise for forensic applications. (publisher abstract modified)
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