# Blood drop analysis

### Abstract:

Blood drop analysis gives a better idea of the crime for the investigators in finding out the impact velocity which helps the investigators for a better understanding of the crime. Recent studies have developed drop impact dynamics which can be used in a variety of fields like firefighting, spray cooling, ink-jet printing, pesticide spraying (1). Different parameters of the blood stain like stain diameter, convergence point for multiple drops, relation between stain diameter and number of spines are calculated in this study. In this study we are trying to validate the smith et al methodology by dropping the pig blood on to flat paper surface. Different mathematical equations as used in smith et al are used to fit in model and correction factors were calculated to find the drop height and velocity of a blood drop and the results are compared.

### Introduction:

Blood drop analysis gives the investigators a better interpretation of the crime scene by calculating the impact velocity and drop height. The blood stains are classified based on the uncertainties as mist (<0.1mm), fine (0.1-2mm), medium (2-6mm) or large (>6mm) without reference to velocity (4). When a blood drop is observed carefully we can say that it will provide more details which can be compared other than size (1). Spines are defined as the rays, scallops, fingers or radial arms which come out from the periphery of the blood stain (2). According to the studies by Balthazard et al fluid mechanics of the impact should also be taken into consideration during the evaluation using the information of spines (5). Assuming the physical properties of the drop to be constant and blood viscosity changes with shear rate several studies have been done which doesn't give any conclusive results (7). Blood is a non Newtonian fluid which is composed of RBC and many other components whose properties changes with time. In this method we have calculated the drop heights of two unknown drops from the data we have recorded by dropping the blood from different known heights and compared the correlation factor introduce by smith et al paper. The number of spines and the velocities calculated are used in the mathematical equations smith et al to calculate the height and impact velocity of the blood drop dropped on to a paper surface which further used to deduce the correction factor.

### Methods:

Pig blood was used to carry out the study. 0.25 ml of pig blood was taken in a 1ml syringe and the syringe is clamped to a laboratory stand which has a variable length fixture such that the syringe length can be varied as shown in figure .1. Blood drops were released from the syringe manually by pressing the plunge of the syringe. A 21 gauge hypodermic needle of inner diameter 0.514mm and outer diameter 0.813mm was used in this study. Data from 5 blood drops were used recorded for performing the calculations.

As the blood drop has fallen down under its own gravitational pull we used the value of earth gravitational pull to calculate the velocity of the impact. The volume of blood in the syringe is recorded, because the difference in the volume of the blood in the syringe at each recording is the actual volume of the blood drop. So, from the volume the blood drop we calculated the drop diameter (Do). The volume of the blood drop which can be calculated using the formula

V=4/3 *pi*r3

Stain diameter is calculated by using a scale as shown in the figure 2. Numbers of spines are calculated manually. Spines were initially defined as the rise and fall above the smooth outer rim which includes waves, triangles, lines, or other protrusions (1).

Blood is a non Newtonian fluid, whose viscosity depends on the flow rate. Viscosity of the blood increases at a low flow rate as the blood aggregate and vice versa. According to rein et al, when a drop hits a surface the inertia causes the liquid to move outwards, whose magnitude is a function of drop diameter (Do), impact velocity (Vo) and liquid density (ρ). Drop spread depends on viscosity (μ) and surface tension (1). From smith et al. Reynolds number (Re) defined as the ratio of fluid inertia to viscous forces is given by dimensionless ratio:

Re = ρ Do Vo /μ.

Similarly the ratio of inertia to surface tension forces is given by the Webber number (We):

We = ρ Do Vo2 /. σ

### Calculations:

The values of the drop height are obtained by performing the blood drop experiment as smith et al which is shown in Plot 1 and 2. The drop height of Drop A and Drop B are taken as unknown 1 and unknown 2. The drop heights were obtained by drawing a plot between the Blood stain diameter and the drop height of the values which are obtained from the experiment performed in the lab. The unknown value is found out by intersecting the blood drop diameter value on to the curve and the corresponding values gives the values of the drop height.

From smith et al paper we know that

Vo =0.81 (σ5N10 / μ(ρ Ds)4 )1/9

Where N is Number of spines, Ds is Drop stain diameter, ρ (density) = 1062 kg/m3, μ (viscosity) =0.0048 Kg/ms, σ (surface tension) = 0.056 N/m

1) For Blood drop A: N= 19, Ds = 7.04 * 10^-3 m.

By substituting all the value in the above equation

Vo = 3.18 m/sec

2) For Blood drop B : N= 21 , Ds = 8.36*10^-3m

By substituting all the values in the above equation we get

Vo = 3.293 m/sec

From smith et paper we know that:

Do = 0.324 * (Ds/N) 2/9

By substituting the values of Drop A Ds= 7.03*10^-3 and N=19 we get

Do = 2.066*10^-3m

Similarly Drop B Ds= 8.36*10^-3 and N = 21 are substituted in the above formula to get

Do= 2.3546 *10^-3 m

Smith et al has a introduced a correction factor called Cd and Cn which has given a better fit for the equations below.

Ds / Do = Cd * Re 1/4 / 2

N = 1.14 Cn (We) ½

For Drop A :

Cd = 7.04*2 / 2.066 * (1453.58)^0.25

=1.104

Cn = N/ 1.14 * We ½

= 19/1.14*(396.206) ½

= 0.8373

Similarly For Drop B:

Cd = 8.36*2 / 2.3546 * (1715.06)^0.25

=1.105

Cn = N/ 1.14 * We ½

= 21/1.14*(451.5) ½

= 0.898

Results:

### Table 1: Drop Stain Diameter Vs Drop Height

Stain Diameter(mm)

Drop height (cm)

5.74

28

6.01

32.3

6.46

55

6.68

69

7.04

Drop A

7.56

73

8.36

Drop B

8.5

100

Plot 1:

Plot: 2

From plot 1 and 2 we can find the values of the drop heights of the Blood drop A and B by intersecting the stain diameter values of drop A and drop B on to the curve and the corresponding value on the x axis which gives the drop height of the blood drop.

### Table: 2 Number of spines versus the drop height

height (cm)

Spines

Blood drop A

70.5

19

Blood drop B

96

21

### Table: 3

Number of Finger as A function of Reynolds number and Webber number

Spines

Reynolds Number

Webber number

Blood Drop A

19

1453.5

396.206

Blood Drop B

21

1715.06

451.5

Plot: 4

Table: 4

Cd

Cn

Drop A

1.104

0.8373

Drop B

1.105

0.898

### Discussion:

From plot 1 and 2 we derived at the value of an unknown drop height and velocity by comparing the plot drawn between the drop stain diameter and the impact velocity. Plot 3 gives a conclusion that as the velocity of impact increases number of spines also increases. The velocity of impact which is calculated by using the formula in smith et al is then used to find out the Reynolds number and the Webber number which is almost similar to the values (Cd= 1.11 Cn=0.838) as mentioned in smith et al. The blood which we used in performing the experiment is left at room temperature until it was actually used. But, leaving the blood at room temperature makes the blood cells to clot due to clotting factors present in the blood which will increase the viscosity is not being considered in this study. Instead, the viscosity value is taken from the smith et al paper and the calculations are done which arrived at a similar value might be a limitation to this study. Blood drop diameter was calculated using the mathematical equations mentioned in the smith et al paper where as smith et al have used a high speed camera for capturing the images of the blood drop impact to measure the drop volume. Smaller sample size is a limitation to this study. Smith et al had also considered drag factor in their consideration which is not being considered in this study also.

### Conclusion:

The Drop Stain Diameter and number is dependent on the impact velocity and the drop size diameter. In study we have used the mathematical equations from smith et al and blood drop height is found out by performing the experiment in the lab. We can conclude that as the drop diameter and velocity of impact increases number spines and the stain diameter also increases. This study can be used in any future crime investigation in order for a better understanding of the crime incident with adding more criteria like impact angle which gives better assumptions.

### References:

1. Lee Hulse-Smith,1 M.S.; Navid Z. Mehdizadeh,2 Ph.D.; and Sanjeev Chandra,2 Ph.D. Deducing Drop Size and Impact Velocity from Circular Bloodstains

2. MacDonell HL, Bialousz LF. Flight characteristics and stain patterns of human blood. Washington, DC: National Institute of Law Enforcement and Criminal Justice, US Dept of Justice, Law Enforcement AssistanceAdministration, 1971.

3. Pizzola PA, Roth S, De Forest PR. Blood droplet dynamics—I. J Forensic Sci 1986;31(1):36–49. [PubMed]

4. Laber TL. Blood classification. IABPA News 1985;2(4).

5. Balthazard V, Piedelievre R, Desoille H, DeRobert L. Study of projected drops of blood. Ann Med Leg Criminol Police Sci Toxicol 1939;19: 265–323.

6. Rein M. Phenomena of liquid drop impact on solid and liquid surfaces. Fluid Dyn Res 1993;12:61–93.

7. Mehdizadeh NZ, Chandra S, Mostaghimi J. Formation of fingers around the edges of a drop hitting a metal plate with high velocity. J Fluid Mechanics 2004;510:353–73.