It's been a while but we're back with the field of blood spatter analysis. This is, in my opinion, one of the most interesting fields, and hopefully you think so too!
Blood typically behaves pretty strangely for a liquid. For a long time blood was considered as only a Newtonian fluid. A Newtonian fluid can be described as one where liquid drops form due to surface tension and can oscillate during flight away from their source. However Non-Newtonian fluids form by virtue of internal cohesion and are extremely stable in flight.
Blood's interesting because it can either act Newtonian or non-Newtonian depending on victim's condition and the type of injury.
Let's start with Newtonian fluids. The principles used to define Newtonian fluids are taken from his Principia, which say: "The resistance that arises from the lack of (viscosity) of the parts of the liquid, other things being equal, is proportional to the velocity with which the parts of the liquid are separated from one another". Newtonian flow is mainly dependant upon a viscosity constant and surface tension, where each is proportional to the rate of flow. As shown by the equation:
tau=mu*(dv/dy)
Tau = shearing or frictional stress per unit area against the walls of the containing vessel or the enveloping air around a drop, this is called a Reynolds number.
Mu = Coefficient of viscosity, it is a constant of proportionality
dv/dy = A linear change in velocity gradient of flow
So a higher Reynolds number means a fluid is more viscous fluid.
Non-Newtonian fluids, however, follow the formula:
tau=kappa*(dv/dy)^n
Where kappa is a constant but not of viscosity, as the viscosity is no longer a constant. While the shear rate (friction) is constant at any given velocity, it changes depending on the flow rate, which now equals a changing velocity gradient: (dv/dy)^n. The change is now exponential, rather than linear. Tau now refers to the Deborah number, rather than the Reynolds number. It is named after the biblical quote from Deborah: “Everything flows before the lord”. This is because non-Newtonian fluids follow the principle that everything flows given enough time. Non-Newtonian fluids generally flow much more slowly than Newtonian fluids as the shear (friction) against their path of flow is considerably greater (exponential not linear).
Blood normally behaves as a non-Newtonian fluid as its flow is not evenly distributed but is in fact formed of a core of red blood cells, surrounded by a layer of white blood cells, which in turn are surrounded by a platelets scattered through plasma (axial flow). This type of flow is stable when your bloods flowing normally. However when there are high rates of flow, or in stressful situations, the body shifts water into the veins, disrupting the axial flow and converting the blood to a Newtonian fluid. As we now know, Newtonian fluids are less viscous and less stable. Essentially the blood becomes turbulent.
So why are we interested in this in the first place? Well first of all some organs in the body (for example the brain and adrenal glands) receive Newtonian blood all of the time. This means by looking at blood spatter evidence, and the proportion to which it acts as Newtonian or non-Newtonian can locate where the blood spatter pattern comes from.
The most obvious difference in blood spatter patterning is that Newtonian fluid spatters causes small, dense central circle with a fine satellite spatter, whereas non-Newtonian is more likely to project streaks outwards from the central circle.
Anyway, this has all been very maths-y, but hopefully interesting! Over and out, and until next time!
No comments:
Post a Comment