Applications of fluid dynamics and mechanics of continua in forensics

The present collection of six works is related to applications of fluid dynamics and, in a more general sense, mechanics of continua, to forensic science. Usually, far-fetched scientific fields dramatically benefit from cross-pollination, and the present example of Flow and Forensics collection is not an exception from this rule. Forensic science poses a number of intriguing novel questions, which can be resolved using the methods of mechanics of continua and, in particular, fluid mechanics. A successful search for novel important fields of applications was a key feature of mechanics of continua from the times it was established as a modern science in seminal works of Newton, Daniel Bernoulli, Euler, and Cauchy. This is the reason that such a 300-year old field stays relevant for many modern fields. To mention a few, one might list subjects, such as (traditionally) mechanical, aeronautical, chemical engineering, and gas dynamics, as well as electro- and magnetohydrodynamics, biomechanics, physics of polymers and rheology, physics of soft matter, plasma physics, microelectronics, meteorology, astrophysics, etc. Not only these fields benefit directly from the results born in the framework of the mechanics of continua, but they also stimulate development of such physico-mathematical bi-products as the asymptotic theory, novel applications of the group theory, the chaos theory, the fractal theory, etc. On the other hand, applications of the mechanics of continua, and fluid mechanics as its part, dramatically enriched their framework and repertoire, which makes them evergreen contemporary sciences.

One of the seemingly far-fetched fields in relation to the mechanics of continua is forensic science. People unrelated to the field of forensics still comprehend it in terms of Sherlock Holmes, Hercule Poirot, or the ever-present Inspector Lestrade, i.e., as a kind of a deductive–inductive reasoning, which is based on subtle observations, understanding of psychology, general intelligence, etc. Even the fact that modern forensic science uses genetics, DNA analysis, and many achievements of materials science do not sway the impression that forensic science is a predominantly empirical field, which does not recourse to rigorous models, differential equations, their analytical and numerical solutions, comparison with experimental data, and rectification of the models, which are characteristic of the mechanics of continua and fluid mechanics.

The current cycle of works aims to build a bridge between the mechanics of continua and fluid mechanics, on the one hand, and forensic science, on the other hand. One of the important, hot and contested subjects in the framework of forensic science is the so-called blood pattern analysis (BPA). Specifically, one is interested to predict the origin of blood spatter given a pattern of blood stains on a crime scene—a typical inverse problem of multi-phase fluid mechanics. As shown by the experimental data acquired and analyzed by Lee (2023), the very shape of such blood stains already contains significant information regarding an oblique impact of blood drops onto a surface. This information not only reveals the impact angle required as an initial condition for finding the drop trajectory by backward time-stepping (solving the kinematic and dynamic equations for a drop subjected to the air drag and gravity) but also immediately discriminates the high and low impact-angle events by means of a characteristic tail present in a stain. Some plausible conclusions can also be reached regarding the impact velocity and the drop size, i.e., all the main ingredients required for the solution of the inverse problem. The latter allows prediction of multiple trajectories starting from multiple stains. Their intersection in space, essentially, means prediction of the origin of blood spatter, say, in the case of a gunshot.

Another important and non-trivial question arose in relation to BPA in a real case where a woman, who was seated at a distance of several feet from a presumed shooter, was killed by a gunshot to her face, whereas a white outfit of a presumable murderer stayed snow white, even though a forensic experiment with shooting a mannequin filled with swine blood revealed a spectacular backspatter of blood toward the shooter, with his outfit becoming red. An impressive artistic reproduction of this bloodspatter in slow motion can be found in the famous movie “Phil Spector” based on this case (starring Al Pacino as Phil Spector and Hellen Mirren as his defense attorney; in reality, the above-mentioned forensic experiment ordered by the defense led to a hung jury during the first trial). Chen (2023) showed that a self-similar turbulent vortex ring of muzzle gases rapidly moving toward a nearby victim can fully deflect blood drops in the backward blood spatter moving toward the shooter. They predicted that in such cases blood drops can be completely turned around, surpass the victim, and land behind her, whereas shooter's white outfit would still stay clean and white.

An additional glimpse into the effect of muzzle gases on blood spatter (this time, the forward one) is provided by Huh (2023) who used supersonic gas jet issued from a small de Laval nozzle to disperse sheep blood from a cylindrical confinement. They studied experimentally the resulting blood-stain pattern on the floor and walls. The results clearly delineated the effect of muzzle gases on forward blood spatter resulting from a close-range shooting from that of a bullet itself (present in the case of gun shooting but absent in the case of de Laval nozzle). The results revealed that muzzle-gas caused blood drops settle on the floor closer than bullet-caused blood drops. Moreover, a combination of the bullet and muzzle gas effects causes a bimodal distribution of drops on the floor, which by itself would be a strong crime-scene evidence of a short-range shot.

Dynamics of waves might be also relevant in forensic science. Han (2023) argued that oxygen bubbles in blood make it an interesting research subject in conjunction to shock waves and soliton-like compression waves propagation (presumably caused by a bullet or nearby blast). Accordingly, these authors recourse to a modified Kadomtsev–Petviashvili equation and predict “elastic” interactions between shocks and elevation or depression solitons, or between the solitons alone. One can hope that these results would find some applications in forensic context in future.

Wave dynamics is also in focus in the two inter-related works of Yarin and Kosmerl (2023) and Kosmerl and Yarin (2023). These works are motivated by a short-range gunshot wound to the head, where a bullet penetrates brain tissue and can cause backspatter of brain tissue fragments. Understanding of related soft-matter mechanics could shed light on such forensic questions as whether a crime scene constitutes a genuine or a staged suicide (with the latter being a homicide). Such material as brain tissue is, essentially, a hydrogel, in which compressibility in the case of interest is provided mostly by the compressibility of an organic soft matter, whereas an encased water is essentially incompressible. Accordingly, a rheological constitutive equation based on elastic energy depending on the invariants of the Cauchy tensor is rigorously introduced. Based on it, it is possible to predict a significant asymmetry in the dynamic behavior of brain tissue: a much stronger resistance to compression, than to stretching. The constitutive equation also predicts a strongly nonlinear response to shear, which is also accompanied by the appearance of normal stresses. Such a hyperelastic model of brain tissue is also used as a kernel of the corresponding viscoelastic model based on an exponentially fading memory. It should be emphasized that in the case of brain shooting relevant in forensic context, the characteristic times are too short (∼10 ms) for viscoelasticity being relevant, with the hyperelastic modeling being fully sufficient. On the other hand, for blast-induced traumatic brain injuries (bTBI) and other types of traumatic brain injuries, a much longer post-traumatic viscoelastic relaxation could be relevant.

Using the above-mentioned hyperelastic model, Kosmerl and Yarin (2023) proposed a model of bullet penetration into brain after a gunshot wound to the head. Muzzle gases fill an almost empty bullet channel left by a fast-moving bullet. Then, an interplay begins between the muzzle gases in the bullet channel, the compression wave propagating from it through the brain tissue toward the skull and reflecting from the skull as a still stronger compression wave, which propagates through the brain tissue backward, then is reflected from the channel surface as a rarefaction wave in the brain tissue, etc. Accordingly, the bullet channel widens and then collapses causing an outflow of the muzzle gases. Simultaneously, the brain tissue undergoes fragmentation caused by stretching [a fragmentation model is also given in Kosmerl and Yarin (2023)], while fragments could move toward the bullet channel and be entrained there by the outflowing muzzle gases. This is how backspatter of brain tissue is formed. Such a backspatter was previously encountered in the experiments with shooting of live pigs and calves.

One might hope that the present collection of works related to the topic of Flow and Forensic would attract attention of the readership of Physics of Fluids and popularize this subject, which is still too distant from a regular menu provided by fluid mechanical journals. If that would happen, fluid mechanics could be enriched by a plethora of novel forensic situations, in which its approaches and tools might be effective and valuable. In its turn, many sections of forensic science would be put on a more rigorous foundation characteristic of fluid mechanics. One can strongly wish to see justice being served based on irrefutable arguments, which stem from the fundamental laws of nature given to this world even prior to the Code of Hammurabi.