OFFICE OF JUSTICE PROGRAMS 

~ BJS N/J OJJ[F OVC SMART 

The author(s) shown below used Federal funding provided by the U.S. 

Department of Justice to prepare the following resource: 

Document Title: The Fluid Dynamics of Droplet Impact on 

Inclined Surfaces with Application to 

Forensic Blood Spatter Analysis 

Author(s): G. Paul Neitzel, Marc Smith 

Document Number: 251439 

Date Received: December 2017 

Award Number: 2013-DN-BX-K003 

This resource has not been published by the U.S. Department of 

Justice. This resource is being made publically available through the 

Office of Justice Programs’ National Criminal Justice Reference 

Service. 

Opinions or points of view expressed are those of the author(s) and 

do not necessarily reflect the official position or policies of the U.S. 

Department of Justice. 
 

 

 

 

 

 

 

 

 

 

 

 

 

Abstract 

Bloodstain pattern analysis is a technique used in crime-scene reconstruction to determine the point 

of origin of a blood droplet as well as the method of its creation, e.g., dripping, wiping, or low-to-highspeed impact caused by anything from blunt trauma to cast-off to gunshot wounds. The primary 

problem of interest in this analysis is to determine of the initial size, speed, and impact angle of a blood 

droplet that has struck a solid surface through an examination of the bloodstain pattern left on the 

surface. This research project addressed this problem using a detailed fluid dynamical study of the 

impact and spreading of a liquid droplet on planar surfaces of variable roughness, wettability, and 

absorbency oriented at various angles with respect to the velocity vector of the approaching droplet. In 

particular, this research used a coordinated program of laboratory experiments and numerical 

simulations to examine the influence of the many parameters associated with such droplet impacts. 

Given its importance to crime-scene reconstruction, the focus of this work is on how to use the shape of 

the final stain to determine the initial conditions of droplet impact. 

The main goals of this research program are as follows: a) quantify the effects of the droplet impact 

angle, the initial droplet size and speed, and the solid surface roughness and wettability on the pattern 

of the final observed stain, and b) analyze this data to provide simplified, but relevant phenomenological 

models of droplet impact, spreading, and splashing that can be directly used by practitioners in the field 

of forensic science. 

The experimental portion of this research used a specially designed droplet generator to create 

individual liquid droplets of a specified diameter and velocity. The liquid was a specially prepared 

mixture of water, glycerin, and alcohol that has the same density, viscosity, and surface tension as 

human blood. These liquid droplets were propelled against three different solid surfaces, i.e., glass, 

bathroom tile, and paper, held at a specified angle with respect to the vertical. The droplet impact 

speed was measured by a pair of photodiodes and the impact of the droplet against the surface was 

recorded with a high-speed video camera held normal to the impact surface. The video images were 

analyzed to obtain the maximum spreading width and length of the droplet as well as the number of 

irregularities or projections in the shape of the droplet (spines) that may be present. These data were 

then analyzed to determine any specific relationships with the main fluid dynamical parameters that 

govern this impact process, i.e., the Reynolds and Weber numbers. 

The development of a numerical simulation of the droplet impact problem was partially completed 

during this project. When completed, this will be a time-dependent, 3-D, multiphase flow simulation 

based on a wavelet adaptive grid that was designed from scratch using modern computing techniques 

optimized for fast parallel processing on a single graphic processing unit (GPU). This simulation will be 

capable of accurately predicting the motion of a liquid droplet as it impacts and spreads along a solid 

surface, a typical droplet impact event. 

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Department of Justice. Opinions or points of view expressed are those of the author(s) and do not 

necessarily reflect the official position or policies of the U.S. Department of Justice 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table of Contents 

Abstract......................................................................................................................................................... 1 

Executive Summary....................................................................................................................................... 3 

I. Introduction .............................................................................................................................................10 

II. Project Design and Methods...................................................................................................................14 

1) Experimental methods .....................................................................................................................14 

2) Blood simulant .................................................................................................................................16 

3) Numerical methods..........................................................................................................................17 

4) Data analysis.....................................................................................................................................17 

III. Results....................................................................................................................................................19 

1) Experimental work ...........................................................................................................................19 

2) Numerical work ................................................................................................................................23 

IV. Conclusions............................................................................................................................................24 

1) Discussion of findings.......................................................................................................................24 

2) Implications for policy and practice .................................................................................................25 

3) Implications for further research .....................................................................................................26 

V. References ..............................................................................................................................................27 

VI. Dissemination of Research Findings......................................................................................................29 

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This resource was prepared by the author(s) using Federal funds provided by the U.S. 

Department of Justice. Opinions or points of view expressed are those of the author(s) and do not 

necessarily reflect the official position or policies of the U.S. Department of Justice 
 

 

 

 

 

 

 

 

 

 

 

Executive Summary 

I. Introduction 

Crime scene reconstruction is the process of determining the events involved with a crime using the 

physical evidence present at the scene along with scientific methodology and deductive reasoning. 

Various techniques are used as part of this reconstruction process; including DNA evaluation, fingerprint 

identification, and the focus of this work, blood spatter analysis. In blood spatter analysis, the residual 

bloodstains left at the scene of a crime are used to determine the point of origin of a particular 

bloodletting event and the type of trauma that led to the bloodstain (e.g., gunshot, blunt force, sharp 

object, etc.). The determination of these factors assists crime-scene analysts in their efforts to establish 

the sequence of events that occurred during the crime. 

The size and shape of a typical bloodstain on a solid surface is the result of the physical 

characteristics of the blood droplet and the solid surface just prior to impact. The relevant droplet 

characteristics are the impact angle with respect to the surface, impact speed, droplet size, and the 

blood material properties of viscosity, density, and surface tension. The relevant characteristics of the 

solid surface are its average roughness, hardness, wettability, and porosity. The size of a bloodstain is 

quantitatively described as the area of the stain’s circular or elliptical shape, whereas shape is quantified

by the bloodstain’s aspect ratio as well as the number of spines and satellite drops around the outer 

contour of the bloodstain. 

In a forensics analysis of blood spatter, the size and shape of the bloodstain is used to determine the 

blood droplet impact conditions, i.e., its impact angle, speed, and size. One long standing correlation in 

common use relates the impact angle  to the aspect ratio of the droplet Ar using the equation 

sin( ) /    W L Ar

, where W and L are the width and length (along the impact direction) of the 

bloodstain. A bloodstain on a solid surface occurs when the blood penetrates, chemically reacts, or just 

adheres and dries onto the solid surface. When a droplet impacts the surface, it spreads out to a 

maximum extent and then may or may not retract to some degree back toward the center of impact. 

The working definition in this project is that the bloodstain left by the spreading droplet corresponds 

closely to the region of maximum spreading. Note that this initial region of droplet spreading is exactly 

where the process is most affected by the impact properties of the droplet and the properties of the 

solid surface. 

If the blood droplet does not penetrate, chemically react, or adhere to the solid surface, its final 

static shape after the spreading and retraction process would be a spherical cap with a circular contact 

line on the solid surface. In this case, the initial impact information is lost except for the initial droplet 

size, which would correlate to the final diameter of the circular contact line. Part of any forensic analysis 

of blood spatter would be to recognize if the impact process in question behaved in accordance to this 

working definition. If not there would be little point in proceeding further because most of the initial 

conditions of the droplet impact would be obscured. 

The important physical parameters of the droplet associated with the spreading stage of droplet 

impact are the droplet impact velocity V, diameter D, and impact angle ; and the fluid properties of 

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Department of Justice. Opinions or points of view expressed are those of the author(s) and do not 

necessarily reflect the official position or policies of the U.S. Department of Justice 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

density , viscosity , and surface tension . The properties of the solid surface are its average 

roughness, hardness, wettability, and porosity. In this first project, the properties of the droplet are of 

primary concern, while the effects of the solid properties on the spreading process (particularly the 

surface roughness) were explored to a lesser extent. The impact and fluid properties can be combined 

using dimensional analysis to produce two main dimensionless parameters, the Reynolds number Re 

and the Weber number We, defined as follows: 

VD

Re





 , 

2

V D

We





 . 

The Reynolds number is the ratio of inertial to viscous forces and the Weber number is the ratio of 

inertial to surface tension forces. In a crime scene situation where blood spatter may result from 

dripping, blunt-force trauma, or gunshot wounds, these dimensionless parameters fall into the following 

ranges: 

240 < Re < 6,000, 20 < We < 2,100 dripping 

10 < Re < 4,800, 1 < We < 3,400 trauma 

1 < Re < 12,000, 1 < We < 85,000 gunshot 

Note that the domains for dripping and trauma are almost the same whereas the higher parameter 

ranges are typically accessed in a gunshot situation. 

Although previous work in the literature provides some valuable insight into various aspects of 

droplet spreading behavior, many questions still remain. Thus, the main goals of the present research 

program are as follows: 

a) quantify the effects of the droplet impact angle, the initial droplet size and speed, and the solid 

surface roughness and wettability on the pattern of the final observed stain defined by the point 

of maximum droplet spreading, and 

b) analyze this data to provide simplified, but relevant phenomenological models of droplet 

impact, spreading, and splashing that can be directly used by practitioners in the field of forensic 

science. 

II. Project Design and Methods 

The experimental facility designed for this work has four primary components: a droplet generator, 

a target assembly, a high-speed video camera, and a control computer. The droplet generator produces 

a single liquid droplet on demand with a specified size and speed directed vertically downward. It is 

mounted on a movable platform that can be positioned at a variable vertical distance to the target in 

order to increase the speed of the droplet using gravitational acceleration. The droplet impacts a solid 

surface held on the target assembly at a specified angle with respect to the vertical. The target 

assembly contains a pair of lasers and photodiodes used to measure the impact speed of the 

approaching droplet. The initial droplet diameter, assuming a spherical droplet, is obtained by 

measuring the mass of the target surface before and after each droplet impact. The droplet generation 

and the experimental measurements are controlled and recorded using a personal computer with a 

Labview interface to the experimental equipment. With this facility, single liquid droplets with 

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Department of Justice. Opinions or points of view expressed are those of the author(s) and do not 

necessarily reflect the official position or policies of the U.S. Department of Justice 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

diameters from 2–5 mm can be reliably and predictably produced. Droplet impact speeds can be as high 

as 5 m/s. In a forensics context, these droplets correspond to those created via dripping or some large 

droplet, low speed, blunt force trauma situations. Droplets resulting from gunshot wounds are typically 

much smaller and faster. However, the Reynolds and Weber number ranges covered in these 

experiments include both dripping and blunt force trauma situations. 

The primary data of interest in these experiments is the spreading behavior of the droplet as it 

spreads along the solid target surface. Images of this process are observed and recorded with a highspeed video camera mounted on the target assembly. The camera is held above the target surface and 

its view angle of the impact plane is always 90° (normal) even when the target surface is inclined. 

Blood is both a viscoelastic and shear thinning fluid. However, for shear rates larger than 100 s-1 , 

which are typical in the droplet impact problems seen in this experimental facility, it behaves as if it 

were a Newtonian fluid. Thus, to simplify the experimental procedures a blood simulant was developed 

based on a mixture of water, glycerin, and alcohol. The resulting mixture matched the kinematic 

viscosity of blood at 4.15 cSt and the surface tension of blood at 62 mN/m. Due to the temperaturedependent nature of the viscosity of water-glycerin mixtures, ambient conditions were carefully 

monitored to ensure that test conditions and liquid properties were maintained at constant values. The 

simulant liquid was prepared and tested before each experimental run to verify that the properties were 

correct. A Newtonian blood simulant also provides a baseline study from which the non-Newtonian 

effects of blood can be explored in a later project. 

A numerical simulation of this droplet impact problem was designed from scratch using modern 

computing techniques optimized for parallel processing on a graphic processing unit (GPU). The 3-D 

time dependent simulation uses the fluid-flow governing equations for mass, momentum, and energy 

written in compressible form since this formulation is ideally suited for GPU parallelization. Air was 

treated as an ideal gas and an appropriate equation of state for liquid compressibility was used. The 

equations are integrated in time using an implicit dual-time stepping scheme that accurately accounts 

for the stiffness of the liquid to compute the pressure field during the low-speed incompressible motion 

typical of a droplet impact event. The spatial discretization of the equations is based on a fourth-order 

finite difference scheme with a wavelet adaptive multi-resolution grid to automatically resolve and 

capture all of the length scales of the motion. The interface of the droplet was modeled using the levelset method. 

The high-speed performance of these parallel GPU computations is a direct result of using the 

compressible form of the underlying flow equations. With this form the computations can more 

effectively access the memory and computational threads of the GPU. In the droplet impact problem, 

the effect of compressibility is very small in the liquid, but is important in the gas layer underneath the 

droplet. This is accounted for in these simulations by an implicit dual-time stepping scheme that 

integrates the acoustic pressure field on an extremely fast time scale to compute the bulk pressure 

experienced by each fluid as it moves. In fact, the compressible form of the flow equations is a more 

accurate reflection of the underlying physics of the flow field and the wave propagation of the acoustic 

pressure is the physical process through which the bulk pressure field is established in an incompressible 

flow. The net effect of the fast acoustic field is to maintain an incompressible flow in the domain of the 

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This resource was prepared by the author(s) using Federal funds provided by the U.S. 

Department of Justice. Opinions or points of view expressed are those of the author(s) and do not 

necessarily reflect the official position or policies of the U.S. Department of Justice 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

liquid, i.e., no volume change in the liquid, while allowing for compressibility effects in the gas layer 

underneath the droplet. Thus, this GPU simulation with dual time stepping will compute an 

incompressible flow field in the liquid even though the equations are written in compressible form. 

III. Results 

The experimental facility was used to perform 182 experiments with five different impact angles and 

three different target surfaces: 78 on clean glass, 52 on bathroom tile, and 52 on paper. Over all of 

these experiments, the aspect ratio of the fully spread droplet is almost constant with Reynolds number, 

except for a small increase as the Reynolds number increases for an impact angle of 30°. The aspect 

ratio versus the angle of impact for all experiments follows the common practice relation 

sin( )   Ar

for near normal impact angles. However, this relation under-predicts the impact angle for a given 

bloodstain aspect ratio for impact angles less that about 40°. These data were fitted in a least-squares 

sense to a new curve based on the common practice relation with the form 

  1 2

90 , asin( )

898

      x x x Ar . 

While this relation is useful for all surfaces, the data suggest some effect due to surface roughness 

for the smaller impact angles. A rougher surface produces a stain with a smaller aspect ratio. 

The experimental data was analyzed using some of the phenomenological spreading models 

available in the literature. For normal droplet impact, the maximum spreading diameter is governed by 

the transfer of the kinetic energy of the droplet to capillary energy (surface energy of the fully spread 

droplet) with some energy dissipation through a viscous boundary layer on the solid surface. This 

suggests a relationship between the width of the spreading droplet in the lateral direction 

(perpendicular to the impact velocity) and the normal component of the impact velocity. In 

dimensionless form this relationship is 

max 1/5 2/5 ( ),

n n n

W

Re f P P We Re

D

 

  , 

where 

Wmax

is the maximum lateral spreading width of the droplet, and 

Ren

and 

Wen

are the Reynolds 

and Weber numbers based on the normal impact velocity. This relationship provides a decent fit to the 

data although there was not a very large range of the data in this parameter space. It is also clear that 

there is a dependence of the spreading width on the roughness of the surface. 

Other parameters computed for the bloodstain were the eccentricity ratio, defined as 

Ec L W D   ( ) /

; and the spreading factor, 

2

/

f S LW D 

. The eccentricity ratio results suggest that 

this scaling may capture some of the appropriate physics. However, there is significant scatter in the 

data, which may just be the inherent variability in the data from this experiment. The spreading factor 

data shows a weak influence of the impact angle, and this effect increases as the Reynolds number 

increases. The data fit for the spreading factor data seems to be slightly better than the data fit for the 

eccentricity ratio. There also appears to be a slight surface effect with the data for paper being smaller 

than those for glass. 

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Department of Justice. Opinions or points of view expressed are those of the author(s) and do not 

necessarily reflect the official position or policies of the U.S. Department of Justice 
 

 

 

 

 

 

 

 

 

 

 

 

When the impact velocity of the droplet is large enough, spines and/or satellite droplets appear in 

the bloodstain. This indicates either the start or the presence of splashing. The number of spines was 

plotted using the same scaling parameter P and the results show a clear effect of the surface roughness 

on the number of spines that appear during spreading. The glass surface is the smoothest and it has the 

fewest number of spines. The next smoothest surface is tile, but it seems to have more spines than the 

roughest surface, which is paper. The surface roughness affects the spreading of the droplet and the 

subsequent instability of the droplet rim. The mechanism of this interaction is not clear and needs to be 

studied in future work. 

Recent work by Eggers et al. [Phys. Fluids 22, 062101, 2010] presented a simple model for droplet 

spreading on a solid surface with a normal impact velocity. The model is based on the bulk acceleration 

of the droplet rim driven by a stagnation point flow in the thin film of liquid near the droplet center. In 

this thin film there is also a boundary layer flow that eventually arrests the stagnation point flow. This 

model was investigated and improved in several ways in the present work. The results seem to be quite 

successful for normal impact. It seems likely that this model can be extended to the situation of oblique 

droplet impact, which is a problem of direct relevance to blood spatter. 

The GPU-based, wavelet-adaptive, 3-D, multiphase flow simulation was partially completed during 

this project. Currently, it can solve for single-phase flow fields under compressible and/or 

incompressible flow conditions. The wavelet grid allows it to provide fully resolved flow fields and the 

GPU programming provides extremely fast execution speeds. These capabilities were validated in three 

example simulations. The level-set formulation to allow for the simulation of multiphase flows was not 

completed and is still under development. 

IV. Conclusions 

1) Discussion of Findings 

The experimental findings from this work demonstrate that the common practice relation between 

the droplet impact angle and the bloodstain aspect ratio, i.e., 

sin( )   Ar

, is in significant error for 

shallow impact angle less than about 40°. A new correlation to correct this error was found. While this 

correlation is based on all of the experiments on three different surfaces, the data indicate that the 

correction is greater for rougher surfaces, i.e., rougher surfaces produce smaller aspect ratios for the 

final bloodstain. This is a significant result and the effect is worthy of further investigation. 

Simple phenomenological or mechanistic ideas of droplet spreading indicate that the maximum 

droplet spreading normal to the impact vector is governed by the transfer of the kinetic energy of the 

droplet to capillary energy (surface energy of the fully spread droplet) with some energy dissipation 

through a viscous boundary layer on the solid surface. When the experimental data for the lateral width 

of the droplet are scaled using appropriate scaling parameters that reflect this balance they collapse 

near a representative curve and compare well with other data in the literature. Again, the roughness of 

the surface does appear to have some influence where a rougher surface decreases the lateral 

spreading of the droplet. 

Three other bloodstain parameters where examined using these same ideas; the eccentricity ratio, 

the spreading factor, and the number of spines on the periphery of the bloodstain. The results for the 

eccentricity ratio and the spreading factor seem to collapse into a single region, but there is still 

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Department of Justice. Opinions or points of view expressed are those of the author(s) and do not 

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significant variability in the data. The results for the spreading factor indicate that this variability is not 

due to variations in the impact angle. The results for the number of spines collapse into a single curve 

for small values of the parameter P, but there is a significant surface roughness effect as P increases. 

The variability seen in all of the data is a significant source of concern that needs to be understood. 

One possible cause may be the droplet generator, since any method of droplet generation will cause 

droplet oscillations. In addition, droplet deformation and oscillation may also occur due to aerodynamic 

forces on the droplet as it travels toward the surface. If these oscillations are not damped out before 

the droplet strikes the surface, the deformed shape of the droplet may affect the spreading process. 

Another possible cause of the data variability may be variable surface roughness. The roughness of the 

tile and paper surfaces used may not have had the same roughness from sample to sample, and the 

roughness of each surface may not have been uniform across the surface. Even for the smooth glass 

surface, it is known that contamination can affect the droplet spreading process. To verify the source of 

the data variability, the experiments need to be repeated with more careful control or at least better 

characterization of the droplet generation process. There should also be better control on the uniformity 

and magnitude of the roughness of the impact surfaces. It would also be useful to have a larger number 

of impact surfaces covering a wider range of roughness magnitude. 

A simple phenomenological or mechanistic model for the spreading of a droplet under normal 

impact on a surface seems to capture the essential physics of the droplet spreading process. The idea is 

that the droplet rim is accelerated outward by a stagnation point flow produced by the impacting 

droplet. The results for an improved version of this model compare well with numerical simulations of 

droplet spreading and seem to do a good job in predicting the maximum spreading diameter of the 

droplet. 

The GPU-based, wavelet-adaptive, 3-D, multiphase flow simulation was partially completed during 

this work. In its current form, the simulation is only capable of computing single phase flows. The 

simulation was verified against a number of well characterized benchmark flow problems, including both 

compressible and incompressible flows. The comparisons were excellent, with the resolution of the 

simulation self-adapting to the flow conditions to meet a user-specified error tolerance. The 

development of the level-set model to enable the wavelet multiphase flow simulation and its use on the 

droplet impact problem will be the subject of a future investigation. 

The first goal of the project was to quantify various parameter effects on the observed pattern of 

maximum droplet spreading (assumed to characterize a bloodstain). The second goal was to provide 

useful models of these effects for forensic practitioners. The effects of the droplet impact angle, size, 

and speed on the maximum spreading aspect ratio were measured and useful correlations were 

obtained from these data to meet these two goals. In addition, correlations for the number of spines in 

the final spreading pattern were also found. The measured data showed a clear effect of solid surface 

roughness and/or wettability on the final spreading pattern, but there was not enough data to fully 

quantify this effect. The usefulness of these results is limited by the observed variability and scatter in 

the data, especially for the rougher paper surface. Another limitation is that the results are limited to a 

forensic parameter range typical of either dripping or blunt force trauma situations. 

- 8 -

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2) Implications for policy and practice 

Bloodstain pattern analysis is an important tool in the criminal justice community. The bloodstain 

problem of interest to this research is the impact of a blood droplet on a solid surface. The final 

bloodstain on the surface is the result of very complex fluid dynamical processes involved in the 

spreading and splashing of the droplet. Thus, it is not surprising that the current simple relations used 

to predict the droplet impact velocity and angle from the appearance of the final bloodstain do not work 

well in all cases. 

The results of this research have produced a new set of simple correlations for use in bloodstain 

pattern analysis. From the normal measurements of the length and width of a bloodstain, this work has 

produced a correction to the standard practice relation used to compute the impact angle of the blood 

droplet; a correction that depends on the roughness of the surface (the correction is larger for rougher 

surfaces). This work also developed other correlations for the bloodstain based on the lateral spreading, 

the eccentricity, the spreading factor, and the number of spines versus an appropriate dimensionless 

parameter relevant to the impact and spreading process. These correlations can be used together to 

determine the impact speed and diameter of the blood droplet. However, these predictions have 

significant error because of the variability of the data seen in these experiments. If this variability can be 

quantified, it is expected that the use of these correlations would allow for a more accurate assessment 

of the initial conditions related to a given bloodstain in a crime scene. This would be a significant benefit 

to the criminal justice community. 

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, - Satellite 

• ' · / drop 

I. Introduction 

Crime scene reconstruction is the process of determining the events involved with a crime using the 

physical evidence present at the scene along with scientific methodology and deductive reasoning. 

Various techniques are used as part of this reconstruction process; including DNA evaluation, fingerprint 

identification, and the focus of this project, blood spatter analysis. In blood spatter analysis, the residual 

bloodstains left at the scene of a crime are used to determine the point of origin of a particular 

bloodletting event and the type of trauma that led to the bloodstain (e.g., gunshot, blunt force, sharp 

object, etc.) [1]. The determination of these factors assists crime-scene analysts in their efforts to 

establish the sequence of events that occurred during the crime. 

Two typical bloodstains are shown in Figure 1. It is known 

that the size and shape of a bloodstain are caused by some of 

the physical conditions of the blood droplet at the point and 

time of impact and the roughness of the impact surface [2]. 

Stain size is quantitatively described as the area of the stain’s

circular or elliptical shape, whereas shape is quantified by the 

stain’s aspect ratio as well as the number of spines and satellite 

drops around the stain contour [2] [3] [4] [5]. A spine is a 

disruption in the smooth periphery of a stain whereas a satellite 

drop is a small drop that has completely separated from the 

main droplet and has landed away from the main bloodstain, 

i.e., a small splash. 

Within this general framework of using the bloodstain size 

and shape to determine the blood droplet impact conditions, a 

number of different models and tools are used in the field [1] 

[6]. The use of specific correlations, strategies, software, etc. is 

dependent on the resources available to an examiner, which in 

turn are impacted by where and for whom the examiner works. 

As an example, the simplest technique is called stringing [2]. This method starts by using the aspect 

ratio of a bloodstain 

Ar

to determine the impact angle 



of the blood droplet using the relation 

sin( ) /    W L Ar

(1) 

where the impact angle 



is measured from the plane of the impact surface and the width W and the 

length L of the bloodstain are indicated in the bottom image in Figure 1. Balthazard, Piedelivre, Desoille 

and DeRobert [7] proposed this relationship in 1939 based on their experimental work, and it has 

become the predominant correlation in forensics analysis [2]. Using this relationship, a ray is typically 

drawn in a straight line from the stain in the direction of the angle 

 . Repeating this process for a large 

number of individual droplet stains in a blood spatter pattern, the individual rays may converge in a 

nexus, or region of convergence. The point of origin of the bloodletting event is presumed to be this 

nexus. Additionally, under this method the speed of the droplet is determined by the size of the stain 

and the assumption that the volume of the blood droplet was “normal” [2], where a “normal” droplet is 

Figure 1: Typical bloodstain patterns. 

(Top) Near normal impact showing spines 

and satellite drops. (Bottom) Oblique 

impact to the right showing length and 

width measurements of the elliptical 

portion of the bloodstain. 

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This resource was prepared by the author(s) using Federal funds provided by the U.S. 

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defined as one containing 0.05 mL of blood [2]. This technique assumes that all stains are created by 

droplets of equal volume. 

Recently, more refined methods have been developed in an effort to increase the accuracy of the 

results. Ballistics software has allowed for a more rigorous application of physics in determining droplet 

flight paths [1]. Using these tools, gravity, drag, and other forces acting on a droplet in flight may be 

taken into account. Correlations have also been developed that relate the number of spines to droplet 

impact speed [3] [4]. With these developments, the assumption of a droplet of “normal” volume is no

longer required. Although these methods represent significant improvements over previous methods, 

they are still limited. A correlation is only valid for impacts within a certain range of impact conditions 

and for impacts on certain materials. Surface properties such as roughness, stiffness, and porosity affect 

spreading behavior and can either inhibit or promote spine and satellite formation [8] [9]. Thus, a more 

complete examination of the physics of droplet impacts may improve current blood stain examination 

techniques and lead to less ambiguity in the events surrounding crime-scene blood spatter analysis. 

It is helpful in the discussion of droplet impact behavior to separate the droplet impact process into 

four stages: pre-impact, spreading, retraction, and final. Figure 2 illustrates the first three of these 

Figure 2: Illustration of droplet impact stages. This impact is for a 2.4 mm diameter water drop, 

traveling at 3.46 m/s, impacting glass at an angle of 70°. The Reynolds number is 7414. For each group 

of images, time increases from left to right. The surface slants downwards from left to right in every 

image. 

stages. Pre-impact is the time after droplet generation but preceding the collision of the droplet with 

the surface. Here, the droplet is in free fall, gravity accelerates the droplet downward, the surrounding 

air exerts a drag force, and the droplet may experience oscillation due to its method of origination 

and/or the aerodynamic forces from flight. Impact signals the end of this stage and the beginning of the 

spreading stage. In this stage, the droplet spreads out along the substrate until the wetted area of the 

droplet on the substrate reaches a maximum, as shown in the top right image of Figure 2. Here, the 

liquid from the droplet is concentrated in a thick rim around the circumference of the droplet and there 

is a thin film of liquid inside the rim known as the lamella. 

- 11 -

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r' F ... - . . ' ~ ·/ \ • £ 1 I' I , ,. , ,,\ , • I ,• 

·- . . 

At this point of maximum spread the retraction process begins because the surface tension in the 

liquid rim pulls the rim back toward the center of the drop. The surface tension forces on the interface 

of the droplet must overcome the adhesive forces between the droplet and the solid surface for the 

retraction process to occur. Blood has a smaller surface tension than water and so on the same surface, 

water tends to retract while blood tends to remain in a fully spread state. This is shown in Figure 3 

where there is noticeable retraction for an impact of a water droplet but almost no retraction during the 

impact of a liquid droplet with the fluid properties of blood. 

Figure 3: The spreading and retraction stages of droplet impact. (Top row) water at Re = 7400. 

(Bottom row) a blood simulant liquid at Re = 4000. 

After the initial retraction of the droplet, the final stage of the droplet impact process is where the 

motion of the droplet is arrested by viscous dissipation and a final steady state shape is attained. During 

this stage, ambient conditions and the particular properties of the solid surface play greater roles than in 

the previous stages. For example, liquid can be wicked into the substrate material, it may begin to flow 

due to its own weight, and drying may inhibit the flow. 

In the context of forensic science, a bloodstain is produced when blood from the impacting droplet 

penetrates, chemically reacts, or just adheres and dries onto the substrate material. The blood residue 

left behind on the substrate can be observed visually or with the help of chemicals such as luminol. 

Luminol mixed with an oxidizing agent such as hydrogen peroxide exhibits chemiluminescence when it 

reacts with the iron in hemoglobin, a protein in red blood cells, and it is the predominant chemical used 

in blood spatter analysis [10] [11]. The retraction stage is minimal for blood due to its lower surface 

tension and higher viscosity. The final stage as the droplet reaches steady state is affected by ambient 

conditions, such as temperature and humidity, and other factors such as wicking into the substrate 

material. However, these factors do not change the final shape of the bloodstain. Thus, the bloodstain 

is most affected by the spreading stage of droplet impact and this is exactly the process most affected 

by the impact properties of the droplet. 

If the blood droplet did not penetrate, chemically react, or adhere to the solid surface, it would then 

eventually retract back into a static shape called a spherical cap with a circular contact line along the 

solid surface. In this case, the initial impact information would be lost except for the initial droplet size, 

which would correlate to the final diameter of the circular contact line on the solid surface. Part of any 

forensic analysis of blood spatter would be to recognize if the impact surface in question behaved in this 

- 12 -

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way. If not, there would be little point in proceeding further because most of the initial conditions of 

the droplet impact would be obscured. 

In this project, the working definition for the shape of the bloodstain is that it corresponds to the 

region of maximum spreading of the droplet. Note that this initial region of droplet spreading is exactly 

where the process is most affected by the impact properties of the droplet and the properties of the 

solid surface. 

The important physical parameters associated with the spreading stage of droplet impact are the 

droplet impact velocity V, diameter D, and impact angle ; and the fluid properties of density , 

viscosity , and surface tension . The properties of the solid surface, such as its average roughness, 

stiffness, wettability, and porosity are important in the details of the spreading process, but were not 

explored in detail in this project. The impact and fluid properties can be combined using dimensional 

analysis to produce two main dimensionless parameters, the Reynolds number Re and the Weber 

number We, defined as follows: 

VD

Re





 , 

2

V D

We







(2) 

The Reynolds number is the ratio of inertial to viscous forces and the Weber number is the ratio of 

inertial to surface tension forces. In a crime scene situation where blood spatter may result from 

dripping, blunt-force trauma, or gunshot wounds, these dimensionless parameters fall into the following 

ranges [12]: 

240 < Re < 6,000, 20 < We < 2,100 dripping (3a) 

10 < Re < 4,800, 1 < We < 3,400 trauma (3b) 

1 < Re < 12,000, 1 < We < 85,000 gunshot (3c) 

Note that the domains for dripping and trauma are almost the same at the high end, whereas the upper 

limit is much larger in a gunshot situation. 

Some work on the role of fluid mechanics in the blood spatter problem has appeared in the 

literature. Adam [4] experimentally validated relationships between droplet size and velocity and the 

resulting stain size and the number of spines. He used stored human blood and focused specifically on 

droplet impacts on paper. For the range of droplet sizes and speeds tested, he concluded that there was 

a strong dependence of the number of spines and stain size on the impact speed. The majority of his 

work was focused on perpendicular impacts, but he performed a limited amount of work on inclined 

surfaces. He proposed the following relationship between the number of spines N, the impact angle , 

and the Weber number 

1/2 7/2 N We  sin( ) 

(4) 

Carroll [13] also conducted droplet-impact research and her method of droplet generation was the 

starting point for the generator design used in this work. Carroll used a glycerin-water mixture for the 

droplets and similarly concluded that number of spines was dependent on the impact velocity. She also 

- 13 -

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-

found that the aspect ratio of the fully spread droplet on a surface was wildly unpredictable when 

comparing results obtained for different impact angles and materials. These results run counter to 

many standard practices in the forensics community and provided some motivation for the present 

work. 

Finally, Hulse-Smith and Illes [3] used human blood to experiment with stain patterns on paper, 

wood, and drywall for perpendicular impacts. Based on their measurements, they developed two 

correlations relating the droplet impact diameter and velocity to the number of spines in the bloodstain 

and the diameter of the bloodstain Ds 

2 N DV    146 12.8, 3

13.8 D

s DV

D

  . (5) 

Using these two correlations, the impact diameter and velocity of a droplet of blood could be calculated 

from the observed number of spines and the bloodstain diameter. Hulse-Smith and Illes [3] neglected to 

include the physical properties of the blood in these correlations, arguing that since the properties of 

blood were the same for all impacts, the use of dimensional correlations was more practical. While true 

for their experiments, the physical properties of blood do influence the behavior of the droplet during 

spreading, and so this effect cannot be observed in the dimensional correlations of equation (5). 

Although this previous work provides valuable insight into various aspects of droplet spreading 

behavior, many questions remain. Thus, the main goals of the present research program are as follows: 

a) quantify the effects of the droplet impact angle, the initial droplet size and speed, and the solid 

surface roughness and wettability on the pattern of the final observed stain defined by the point 

of maximum droplet spreading, and 

b) analyze these data to provide simplified, but relevant phenomenological models of droplet 

impact, spreading, and splashing that can be directly used by practitioners in the field of forensic 

science. 

II. Project Design and Methods 

1) Experimental methods 

The experimental facility designed for this work is shown in Figure 4. The primary components are a 

droplet generator, a target assembly, and a high-speed video camera. The droplet generator produces a 

single liquid droplet on demand with a specified size and speed directed vertically downward. The 

generator is mounted on a movable platform that can be positioned at a variable vertical distance to the 

target in order to increase the speed of the droplet using gravitational acceleration. The droplet impacts 

a solid surface held on the target assembly at a specified angle with respect to the vertical. The target 

assembly contains a pair of lasers and photodiodes used to measure the speed of the approaching 

droplet and a high-speed video camera used to observe and record the spreading of the droplet on the 

solid target surface. 

- 14 -

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" 

Step 1: fill chamber 

Generator 

... __ Step 2: Sea l chamber 

..... 

Step 3: generate droplet 

Rotating shaft 

Target assembly frame 

The droplet generator can produce a single 

liquid droplet on-demand with various 

diameters and speeds. The generator has a 

liquid and an air chamber separated by a thin 

latex membrane as shown in Figure 5. To 

produce a droplet, the test liquid is allowed to 

flow into the liquid chamber until it is 

completely filled and all air bubbles are 

removed. The inlet and vent ports are then 

closed. A pressure pulse with a specified 

magnitude and duration is then used to inject 

air into the air chamber. The pulse is regulated 

by a pressure regulator and a solenoid valve 

and controlled by a LabView program. This 

pressure pulse determines the size and speed of 

the ejected droplet as it leaves the nozzle of the 

generator. The final impact speed of the 

droplet as it approaches the target surface is set 

by changing the height of the droplet generator 

above the target. The maximum height for this 

facility is 2.5 m, which is sufficient to reach 

terminal velocity of the droplet. 

With this facility, single liquid droplets with 

diameters from 2–5 mm can be reliably and 

predictably produced. Droplet impact speeds 

can be as high as 5 m/s. In a forensics context, 

these droplets correspond to those created via 

dripping or some large droplet, low speed, blunt 

force trauma situations. Droplets resulting from 

gunshot wounds are typically much smaller and 

faster. However, the Reynolds and Weber 

number ranges covered in these experiments 

include both dripping and blunt force trauma 

situations. 

A droplet produced by the droplet 

generator travels vertically downward until it 

strikes the target surface mounted on the target 

assembly shown in Figure 6. The target surface 

is mounted on a movable arm that can be 

positioned to orient the target at an arbitrary 

angle with respect to the vertical. The surface is 

Figure 4: Experimental facility showing the droplet generator, 

the target assembly, the high-speed video camera, and the 

lasers and photodiodes. 

Figure 5: Operation of the droplet generator. Step 1) Fill the 

liquid chamber with test liquid. Step 2) Close the inlet and vent 

ports. Step 3) Inject a well-defined air pulse into the air chamber 

to deflect the latex membrane and produce a desired droplet. 

Figure 6: Target assembly with interchangeable target surfaces, 

mounting holes for the lasers and photodiodes, and a high-speed 

video camera. 

- 15 -

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Kinematic Viscosityvs Percent Water 

;6 

t > 

;4 >--- - ------- • , l 

ii 

! 1 

0+---~-~-~~-~ 

Surface Tension vs Percent Alcohol at 

:60% Water 

:000 ©ro !loo 6Jro 'I.JOO 10000 aoo LOO l ll 

V ePemntWetHjl/j Vo!wne Penent Alcool 1%) 

,oo 

interchangeable to allow different surfaces to be investigated and prepared prior to each experiment. 

The impact speed of the droplet is measured by a pair of parallel laser beams held a fixed distance apart, 

aligned with the path of the droplet, and monitored with a pair of photodiodes. As the droplet passes 

through each laser beam the current output of each photodiode is interrupted from which the passage 

time of the droplet and hence the impact velocity is measured. 

Three different target surfaces were used 

during this research: glass, bathroom tile, and 

paper. The glass and tile surfaces were thoroughly 

Material glass tile paper 

 (m) 2.0 48. 224/292 

cleaned prior to each test. A fresh piece of paper Table 1: The measured roughness of the three types of 

was used for each test when paper was the target target surfaces used in this research. The roughness  is 

surface. The roughness of these surfaces was defined as the average deviation of the absolute value of 

measured using a standard surface profilometer the surface profile about the mean. The roughness of the 

paper surface depended on the direction along the surface. and the results for each surface are given in Table The first value is along the direction of travel of the droplet 

1. The roughness is the same in all directions for when it strikes the surface. The second larger value is for 

the glass and tile surfaces. However, the paper the transverse direction. 

surface has a directional dependence as indicated 

in the caption of Table 1. 

The primary data of interest in these experiments is the spreading behavior of the droplet as it 

spreads along the target surface. Images of this process were recorded using a Phantom Miro M120 

high-speed video camera mounted on the same movable arm as the target (see Figures 4, 6). The 

camera is held above the target surface and the movable arm ensures that the view angle of the camera 

is always 90° (normal) with respect to the plane of the surface even when the target surface is inclined. 

Finally, the initial droplet diameter assuming a spherical droplet was obtained by measuring the 

mass of the target surface before and after each droplet impact. A Mettler AE160 analytical balance 

was used for this measurement. 

2) Blood simulant 

Blood is both a viscoelastic and shear thinning fluid. However, for shear rates larger than 100 s-1 , 

which are typical in the droplet impact events 

seen in this experimental facility, it behaves 

as if it were a Newtonian fluid [18]. Thus, to 

simplify the experimental procedures a blood 

simulant was developed based on a mixture 

of water, glycerin, and alcohol. The resulting 

mixture matched the kinematic viscosity of 

blood at 4.15 cSt and the surface tension of 

blood at 62 mN/m as shown in the property 

curves of the mixture in Figure 7. Due to the 

temperature-dependent nature of the 

viscosity of water-glycerin mixtures, ambient 

Figure 7: Blood simulant property curves versus volume percent 

of water and alcohol. The red line indicates the desired 

properties of blood. 

- 16 -

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Droplet 

Target surface 

conditions were carefully monitored to ensure that test conditions and liquid properties were 

maintained at constant values. The simulant liquid was prepared and tested before each experimental 

run to verify that the properties were correct. The viscosity was measured using a Cannon-Fenske 

Routine viscometer, the surface tension was measured using the pendant-drop method [14], and the 

density was measured by weighing a sample of a given volume on the Mettler AE160 analytical balance. 

Assuming a temperature change of 0.5 °C, the relative uncertainly in the Reynolds number calculation 

for the blood simulant increased from 3.7% to 4.0% and the uncertainty in the Weber number did not 

change from 6.8%. Thus, this temperature effect was safely ignored. 

Note that using a Newtonian blood simulant also provides a good baseline study from which the 

non-Newtonian effects of blood can be explored in a later project. 

3) Numerical methods 

The numerical simulation of the droplet impact problem was designed from scratch using modern 

computing techniques optimized for parallel processing on a graphic processing unit (GPU). The 3-D 

time dependent simulation uses the fluid-flow governing equations for mass, momentum, and energy 

written in compressible form since this formulation is ideally suited for GPU parallelization. Air was 

treated as an ideal gas and an appropriate equation of state for liquid compressibility was used. The 

interface of the droplet was modeled using the level-set method. The spatial discretization of the 

equations is based on a fourth-order finite difference scheme with a wavelet adaptive multi-resolution 

grid to automatically resolve and capture the fine length scales of the motion as the system evolves in 

time. 

For fully compressible flows, a variety of explicit time integration methods can be selected by the 

user to evolve the governing equations in time. In the droplet impact problem, the effect of 

compressibility is very small in the liquid, but is important in the gas layer underneath the droplet [19, 

20]. This is addressed in the wavelet simulation through the use of a new implicit dual-time stepping 

scheme that integrates the acoustic pressure field on an extremely fast time scale to compute the bulk 

pressure experienced by each fluid as it moves. The net effect of the fast acoustic field is to maintain an 

incompressible flow in the domain of the liquid, i.e., no volume change in the liquid, while allowing for 

compressibility effects in the gas layer underneath the droplet. Thus, this GPU simulation with dual time 

stepping will compute an incompressible flow field in the liquid even though the equations are written in 

compressible form. Details of this simulation can be found 

in Forster [17]. 

4) Data analysis 

At the beginning of each test, the density ρ, viscosity μ, 

and surface tension σ of the blood simulant were measured. 

The angle of impact of the droplet (defined in Figure 8) 

was set on the experimental facility. A droplet was then 

generated and its impact velocity V was measured with the Figure 8: Sketch of droplet impact defining the 

laser/photodiode sensors. The initial droplet diameter D angle of impact. 

- 17 -

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based on an initial spherical droplet was determined by weighing the target before the test, weighing 

the droplet on the target after the test, and using the known density of the liquid. 

These dimensional parameters are combined using dimensional analysis to form two dimensionless 

parameters: the Reynolds number Re and the Weber number We, defined in equation (2). In the 

present experiments, these parameters vary over the ranges: 

1,200 < Re < 5,400, and 240 < We < 1,920. (6) 

These values are a subset of the ranges typically seen in forensics problems, shown in equations (3) and 

are typical of dripping and some blunt trauma situations. 

The high-speed video camera records the motion of the 

droplet as it impacts and spreads along the target surface. 

Of particular interest to the bloodstain problem is the shape 

of the droplet on the solid surface at its maximum extent, 

since this is the present definition of the stain left by a 

blood droplet on the target surface. An example of such a 

shape is shown in Figure 9. Here, a droplet of blood 

simulant has spread to its maximum extent on a glass 

surface at an impact angle of 40°. The droplet was moving 

1

4

2

3

W

L

Figure 9: A droplet of blood simulant at its point 

from left to right in the image. The current practice in of maximum spreading on a glass surface at an 

forensics bloodstain pattern analysis is to fit an ellipse to impact angle of 40°. The droplet was moving 

from left to right. Also shown is the blue-grey this shape as illustrated in Figure 9. The primary 

ellipse fitted to the shape of the spreading measurements of this maximal shape are the width W and 

droplet. In this case, four spines occur on the 

length L of the ellipse and the number of spines along the leading (right) edge of the droplet. 

periphery of the droplet. The aspect ratio of the ellipse is 

computed using the relation from equation (1), i.e., 

Ar = W/L. (7) 

The current practice in bloodstain pattern analysis is to use the measured aspect ratio of the ellipse 

to determine the angle of impact of the blood droplet  using the formula 

sin( )   Ar

(8) 

One of the concerns of this research is to evaluate the accuracy of this common approach. 

Another measure of the impact process is the spreading factor Sf, defined as the planar area of the 

elliptical shape of the stain over the cross-sectional area of the drop. Thus, 

2 2

/ 4

/ 4 f

LW LW S

D D





  . (9) 

- 18 -

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surfaces 90 

00 0 

00 Oo 0 

0.9 0 8 80 

0 8 & @ 0 

0.8 

70 

60 

"0 0 0 00 

0.7 "" 4: 

1: 50 

4: 00 

0.6 0 0 

@ 0 0 0 

·;;; 

"' 40 

0.5 30 0 glass 

00 0 

® 00 

0.4 

0 30 

0 40 

50 

0 60 

0 tile 

20 paper 

--commoo 

--best fit 

0 70 10 

0.3 ._ _ _.. __ ~--~-..... --~--~-..... --~-__, 10 20 30 40 50 60 70 80 90 

1000 1500 2000 2500 3000 3500 4000 4500 5000 55< Impact Angle 

Re 

Figure 10: The aspect ratio of a bloodstain on a tile 

surface versus the Reynolds number for various impact 

angles. 

III. Results 

1) Experimental work 

The experimental facility described above was used to perform 182 experiments with three different 

target surfaces: 78 on clean glass, 52 on bathroom tile, and 52 on paper. Typical results from these 

experiments are shown in Figure 10 for droplet impact on a tile surface for various impact angles and 

Reynolds numbers. For this range of Reynolds numbers, the stain aspect ratio is almost constant with 

Reynolds number for most impact angles. A small increase in the aspect ratio as the Reynolds number 

increases is observed for an impact angle of 30°. Figure 11 shows the aspect ratio versus the angle of 

impact for all Reynolds numbers and glass, tile, and paper surfaces. This figure shows that the common 

practice relation is fairly accurate for near normal impact angles, but that it would under-predict the 

impact angle for a given bloodstain aspect ratio for oblique angles less that about 40°. 

Figure 11: The arcsin of the aspect ratio of a bloodstain 

versus the impact angle in degrees for all surfaces and 

Reynolds numbers. The solid black line is the common 

practice relationship and the red line is the best fit curve 

of equation (10). 

The data from Figure 11 were fitted in a least-squares sense to a new curve based on the common 

practice relation with the form 

 2

      x c x x Ar 90 , asin( ) , (10) 

where x is an angle expressed in degrees. Here, x is the predictor or independent variable and  is the 

response or dependent variable. A comprehensive fit to all the data in Figure 11 gives c = 1/898. For 

reference, the values of the fitting constant c for all of the materials separately are shown in Table 2. 

The fourth column of this table gives the goodness-of-fit of equation (10) to the data for each material 

as measured by the coefficient of determination R2

. This coefficient gives the amount of the variation of 

the data captured by the model equation. For these data, the fit is very good. Note that is also better 

- 19 -

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0.9 

... 

E·7 

0 

C -o.6 

All inclined surfaces 

0 O 0 

We*Re<·2'5) (norm) 

that the corresponding fit of the data 

to the common practice relation of a 

straight line, given in the fifth column 

of Table 2. 

The relative uncertainty in the 

parameter 

asin( ) Ar

used in Figure 11 

Material c 1/c 2 R (10) 2 R (cp) 

Glass 6.71e-4 1490 0.982 0.970 

Tile 1.06e-3 941 0.984 0.952 

Paper 1.72e-3 583 0.915 0.819 

All data 1.11e-3 898 0.958 0.923 

can be estimated based on the Table 2: The constant c in the fitting function of equation (10) for each 

uncertainties in the measurements of of the materials used in this experiment. The column R2 (10) is the 

coefficient of determination for the fit of equation (10). The column R2 

the bloodstain length and width. 

(cp) is the coefficient of determination for the fit to the common When  = 70°, this relative uncertainty practice relation,  = asin(Ar). 

is about 6% and for  = 30°, it is about 

10%. The total relative variation in the data about the mean that is present in Figure 11 is 13% for  = 

70° and 22% for  = 30°. Thus, the relative variation in the data is about twice the uncertainty in the 

data. For this reason, the measurement error is assumed to be contained in the total variation of the 

data and not specifically mentioned in any of the subsequent statistical error analyses. 

The experimental data was also analyzed using ideas from Eggers et al. [15]. In that work, normal 

droplet impact was considered and it was shown that the maximum spreading diameter was governed 

by the transfer of the kinetic energy of the droplet to capillary energy (surface energy of the fully spread 

droplet) with some energy dissipation through a viscous boundary layer on the solid surface. Eggers et 

al. [15] formulated a relationship between the problem parameters that also holds in the present 

droplet impact problem. Here, the width of the spreading droplet in the lateral direction and the 

normal component of the impact velocity were used. The relationship is given by 

1/2

1/5 1 2/5

1/2

2

,

r n n n

c P W Re P We Re

c P

 

 



, (11) 

where is the dimensionless 

max / W W D r



maximum lateral spreading width of the droplet, 

/ Re V D n norm  

is the Reynolds number based 

on the normal impact velocity Vnorm, 

Figure 12: The experimental data for lateral droplet 

spreading normalized as shown in equation (11). The solid 

red line is the fit to equation (11) for the data on all 

surfaces. The lower, solid blue line is the fit to the results of 

the normal impact experiments in Laan et al. [16]. 

2

/ We V D n norm

  

is the Weber number based on 

1

the normal impact velocity, and the constants 

c

and 

2

c

are used to fit the data. Here, 

2/5 We Ren

is 

the predictor or independent variable and 

1/5 W Re r n

is the response or dependent variable. Figure 12 

shows the fitting result for all surfaces. The red 

curve is equation (11) with a fit to all of the present 

data of . The coefficient of 

1 2 [ , ] [1.01,1.07] c c 

determination of this fit is R2 = 0.342, which is 

- 20 -

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All Inclined surfaces 2~--~---~--~---~---~--~ 

1.8 

1.6 

I 1.4 0 

C: i1.2 

'in 

~ 

~ 0.8 

~ 

~ 0.6 

0.4 

0.2 

0 

O glass 

O tile 

0 paper 

--Best fit 

~ 

0 

o~--~---~--~---~---~--~ 

0 10 20 30 40 50 60 

We*Re<-215> (norm) 

expected because of the large variation of the data seen in Figure 12. Also shown is a blue curve which 

is the fit obtained by Laan et al. [16] for normal droplet impact on a variety of surfaces of 

. While the present data do not have a very large range in this parameter space, they 

1 2 [ , ] [1,1.24] c c 

still seem to be reasonably close to the expected fit from Laan et al. [16]. It is also clear that there is a 

dependence of the spreading width on the type of surface. 

Another parameter of interest is the eccentricity ratio of the bloodstain, defined as 

Ec L W D   ( ) /

(12) 

The eccentricity parameter can be scaled in a similar way to that shown in equation (11) to reflect the 

spreading physics involved. However, one difference is a factor of cos() used to include the effect of 

the inclination angle on the longitudinal spreading of the droplet. As  approaches 90° (normal impact), 

the eccentricity Ec should approach zero. This 

normalized parameter, 

1/5 / cos( ) Ec Ren 



, is 

plotted in Figure 13. The black line is a linear, leastsquares fit to a straight line for all of the data. It has 

a slope of -0.014 and a y-intercept of 0.83. Here, 

2/5 We Ren

is the predictor or independent variable 

and 

1/5 / cos( ) Ec Ren 



is the response or 

dependent variable. The coefficient of 

determination of this fit is R2 = 0.307. In this plot, 

the data for all of the surfaces and all of the 

inclination angles have at least collapsed into a 

single region spread out about the fitting line. This 

suggests that the scaling may have captured some of 

the appropriate physics. However, more data are 

needed to investigate the variability seen in the 

present results. 

Figure 14 is a plot of the spreading factor on a tile surface versus the impact angle for various 

Reynolds numbers. These data show that the impact angle only weakly influences the spreading factor, 

but that the effect increases as the Reynolds number increases. Using the same kind of scaling ideas as 

above, the spreading factor has a functional relationship as shown in equation (13) 

Figure 13: The eccentricity ratio for droplet spreading 

normalized as shown in equation (11). The solid black 

line is a linear, least-squares fit for all data on all 

surfaces. 

3/10 2/5 ( ) f

S Re f We Re

(13) 

The present data for all surfaces is scaled in this way and plotted in Figure 15. The black line in the 

figure is a linear, least-squares fit to all of the data. It has a slope of 4.6 and a y-intercept of 96. Here, 

2/5 We Ren

is the predictor or independent variable and 

3/10

f n S Re

is the response or dependent variable. 

The coefficient of determination of this fit is R2 = 0.517. These results have a better fit than the data for 

the eccentricity, although it is still not very good. There also appears to be a slight surface effect with 

some of the results for paper being smaller than those for glass. 

- 21 -

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necessarily reflect the official position or policies of the U.S. Department of Justice 
2/5 We Ren



 

 

 

 

 

 

 

 

 

45 

40 

35 

311 

I 

°6,25 

"' 

~20 

.! 

E 15 ::, 

z 10 

5 

0 

-5 

35 

30 

25 

20 

15 

~ 10 0 

0 

0 

0 

0 

1 

0 

0 

0 

6' 

Oo 0 

0 30 

0 40 

50 

0 60 

O 70 

o~-~-~-~--~-~-~-~~-~-~ 

1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 

Re 

Allaurfacn 

o a- 0 

0 ... 

0 paper 

0 

0 0 

0 

'o 

0 0 

0 10 20 311 40 50 60 

we•Re(-2/al (norm) 

All lndlnad aurfacln 460 .---....... ----,----.-----,----..----, 

400 

350 

150 

100 

50 L.-__ ...,__ __ __. ___ _._ __ _.. ___ .,_ __ _, 

D 10 20 30 40 50 80 

wa•Re(41&) (nonn) 

Figure 15: The experimental data for spreading factor Figure 14: The spreading factor of a bloodstain on a tile 

normalized as shown in equation (13). The solid black surface versus Reynolds number for various impact angles. line is a linear, least-squares fit for all data on all 

surfaces. 

When the impact velocity of the droplet is large enough, spines and/or satellite droplets can appear 

as shown in Figures 1 and 9. This indicates either the start or the presence of splashing. In the present 

experiment, the number of spines was counted and the data are plotted in Figure 16 using the same 

scaling as in equation (11). The lines in this figure are a linear, least-squares fit to the data for each 

Figure 16: The experimental data for the number of 

spines plotted using the scaling shown in equation (11). 

The solid lines are a linear, least-squares fit for the data 

on each surface. 

Material c1 c2 

2 R

Glass 0.329 -0.943 0.693 

Tile 0.748 -4.037 0.842 

Paper 0.530 0.156 0.824 

Table 3: The results of the linear least squares fit to the data 

of Figure 16. The fitting line is 

1 2 y c x c  

. The two 

constants for this fit are shown in columns 2 and 3 for each 

material. The column R2 is the coefficient of determination 

for the fit of this equation. 

material separately. For each line, is the predictor or independent variable and the number of 

spines is the response or dependent variable. The detailed results of these fits are shown in Table 3. 

This shows a clear effect of the type of surface on the number of spines that appear during spreading. 

However, the effect is not as straightforward as one might imagine. The glass surface is the smoothest 

and it has the fewest spines. The next smoothest surface is tile and it seems to have more spines than 

the roughest surface, which is paper. The surface roughness affects the spreading of the droplet and the 

subsequent instability of the droplet rim. For paper, there may also be an effect of absorption of the 

- 22 -

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Department of Justice. Opinions or points of view expressed are those of the author(s) and do not 

necessarily reflect the official position or policies of the U.S. Department of Justice 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Droplet radius versus time 

3.5 

R 2.5 

s 

1.5 

0.5 

0 

0 10 12 14 16 

:: I 1.5 

0.5 

0 e 0 0.5 1.5 2.5 3.5 0.5 1.5 2.5 3.5 

t = 5.4 t = 14.4

liquid into the paper. The mechanisms of these interactions are not clear and need to be studied in 

future work. 

Eggers et al. [15] also proposed a simple model for droplet spreading on a solid surface with a 

normal impact velocity. The model is based on the bulk acceleration of the droplet rim driven by a 

stagnation point flow in the thin film of liquid near the droplet center. In this thin film there is also a 

boundary layer flow that eventually arrests the stagnation point flow. The results of their model 

compared well to their own numerical simulations of axisymmetric, normal droplet impact. 

This model was investigated 

and improved in several ways in 

the present work. The results for 

one case of normal droplet 

impact with Re = 1807 and We = 

320, which is appropriate to 

blood spatter, is shown in Figure 

17. This model seems to be quite 

successful for normal impact as it 

follows the numerical simulations 

of Eggers et al. [15] for normal 

droplet impact and spreading. It 

seems likely that it can be (b) (c) 

extended to the situation of Figure 17: A numerical model of normal impact droplet spreading using the ideas 

oblique droplet impact that is of 

relevance to blood spatter. 

of Eggers et al. [15]. Here, Re = 1807 and We = 320. (a) is the time history of the 

normalized droplet radius, (b) is the droplet shape at maximum spreading, and 

(c) is the droplet shape just before full retraction. 

2) Numerical work 

The GPU-based, wavelet-adaptive, 3-D, multiphase flow simulation was only partially completed 

during this project. The level-set model for a multiphase flow was not finished during the time frame of 

this project. At present, the simulation can only solve for single phase flow fields under compressible 

and/or incompressible flow conditions. The wavelet grid allows it to provide fully resolved flow fields 

and the GPU programming provides extremely 

fast execution speeds. These capabilities are 

demonstrated in the following two example 

simulations. 

The first example is a compressible flow; the 

classic Richtmyer-Meshkov instability on a 

circular bubble in 2-D as shown in Figure 18. 

Here, a circular gas bubble is struck by a normal 

shock wave traveling from left to right in the 

figure. The shock wave (now located to the right 

of the bubble at the dark-orange/green 

(a) 

Figure 18: The density field in the Richtmyer-Meshkov 

instability arising from a 2-D, viscous, shock-bubble 

interaction. The top portion of the plot shows the waveletadaptive point representation of the density and the bottom 

shows the reconstructed density field on a uniform grid. 

- 23 -

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necessarily reflect the official position or policies of the U.S. Department of Justice 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.9 

1 ~ 

0.8 

0.7 

0.6 

{;0.5 

0.4 

0.3 

0.2 

0.1 

0 

0 0.2 0.4 0.8 0.8 1 

a:i 

boundary) causes the bubble to roll-up and break into two pieces that follow the shock wave as shown. 

Similar results are also seen in 3-D. 

A popular benchmark incompressible flow example is 

the flow in a 2-D, lid-driven cavity. In this system, the 

top wall of the cavity moves to the right at a constant 

speed and the remaining three walls are stationary. The 

resulting flow is a clockwise vortex in the cavity as shown 

in Figure 19. The flow is considered incompressible since 

the Mach number, the ratio of the flow speed to the 

sound speed, is always less than 0.001 in this flow 

domain. Compressible effects start to become important 

in a flow when the Mach number is larger than about 

0.3. This problem highlights the simulation’s ability to

solve for an incompressible flow even though the 

governing equations used in the simulation are the 

compressible flow equations. 

IV. Conclusions 

1) Discussion of findings 

The experimental findings shown in Figure 11 demonstrate that the common practice relation 

Figure 19: Contours of velocity magnitude in a liddriven cavity flow for Re = 1000 and Ma = 0.001. 

The top wall is moving to the right and all other 

walls are stationary. 

between the droplet impact angle and the bloodstain aspect ratio, i.e., 

sin( )   Ar

, is in significant 

error for shallow impact angle less than about 40°. A new correlation to correct this error is given in 

equation (10). The correlation was fitted to all of the data and to each surface type individually, with 

the results given in Table 2. These results show that the correction is greater for rougher surfaces, i.e., 

rougher surfaces produce smaller aspect ratios for the final bloodstain. Note that these results are also 

limited to a forensic parameter range typical of either dripping or blunt force trauma situations. 

The mechanistic ideas discussed in the work of Eggers et al. [15] indicate that the maximum droplet 

spreading normal to the impact vector is governed by the transfer of the kinetic energy of the droplet to 

capillary energy (surface energy of the fully spread droplet) with some energy dissipation through a 

viscous boundary layer on the solid surface. Figure 12 shows that when the experimental data are 

scaled using appropriate scaling parameters that reflect this balance the result is a collapse near a 

representative curve that compares well to the curve from Laan et al. [16]. Again, the roughness of the 

surface does appear to have some influence with rougher surfaces decreasing the lateral spreading of 

the droplet. 

Three other parameters were plotted using these same ideas; the eccentricity ratio in equation (12), 

the spreading factor from equation (9), and the number of spines on the droplet periphery. These 

results are shown in Figures 13, 15, and 16. The eccentricity ratio and the spreading factor seem to have 

collapsed into a single region, but there is still significant variability in the data. The results shown in 

Figure 14 for the spreading factor indicates that this variability is not due to variations in the impact 

angle. The results for the number of spines do collapse into a single curve for small values of the 

- 24 -

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Department of Justice. Opinions or points of view expressed are those of the author(s) and do not 

necessarily reflect the official position or policies of the U.S. Department of Justice 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

parameter P as defined in equation (11). However, there is a significant surface roughness effect as P 

increases. 

A primary limitation of this work is the variability seen in all of the data, which may be a result of 

how the droplets were generated. Any method of droplet generation will cause some droplet 

oscillations. If these oscillations are not damped out before the droplet strikes the surface, the 

deformed shape of the droplet may affect the spreading process. Another effect may be variable 

surface roughness. The tile and paper surfaces used do not have the same roughness, and furthermore, 

the roughness may not even be distributed uniformly over the surface. Even for the smooth glass 

surface, it is known that contamination can affect the droplet spreading process. To verify the source of 

the data variability, the experiments need to be repeated with more careful control or at least better 

characterization of the droplet generation process. There should also be better control on the 

uniformity and magnitude of the roughness of the impact surfaces. It would also be useful to have a 

larger number of impact surfaces covering a wider range of roughness magnitude. 

The phenomenological model for the normal impact of a droplet described by Eggers et al. [15] is 

based on the idea that the droplet rim is accelerated outward by a stagnation point flow produced by 

the impacting droplet. The results for an improved version of this model are shown in Figure 17. These 

results compared well with the numerical simulations of droplet spreading by Eggers et al. [15] and 

seem to do a good job of predicting the maximum spreading diameter of the droplet. 

The GPU-based, wavelet-adaptive, 3-D, flow simulation was completed during this project for single 

phase flows. The simulation was verified against a number of well characterized benchmark flow 

problems, including compressible flows and incompressible flows. The comparisons were excellent, 

with the simulation’s resolution self-adapting to the flow conditions to meet a user-specified error 

tolerance. 

However, the wavelet multiphase flow simulation was not completed during the time frame of this 

project. The inclusion of the level set model and its application to the droplet impact problem will be 

the subject of the future work discussed below. 

2) Implications for policy and practice 

Bloodstain pattern analysis is an important tool in the criminal justice community. The bloodstain 

problem of interest to this research is the impact of a blood droplet on a solid surface. The final 

bloodstain on the surface is the result of very complex fluid dynamical processes involved in the 

spreading and splashing of the droplet. Thus, it is not surprising that the current simple relations used 

to predict the droplet impact velocity and angle from the appearance of the final bloodstain do not work 

well in all cases. 

The results of this research have produced a new set of simple correlations for use in bloodstain 

pattern analysis. From the normal measurements of the length and width of a bloodstain, this work has 

produced a correction to the standard practice relation used to compute the impact angle of the blood 

droplet. The correction is significant for shallow impact angles of less than about 40°. These results also 

showed that this correction depends on the roughness of the surface, with rougher surfaces having a 

- 25 -

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Department of Justice. Opinions or points of view expressed are those of the author(s) and do not 

necessarily reflect the official position or policies of the U.S. Department of Justice 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

larger correction. This work also developed two correlations, one for the lateral spreading of the 

bloodstain and one for the eccentricity of the bloodstain that can be used with the correlation for the 

impact angle to determine the impact speed and diameter of the blood droplet. However, these 

predictions have significant error because of the variability of the data used for the correlations. If this 

variability can be quantified in some way as discussed in the next section, it is expected that the use of 

these correlations would allow for a more accurate assessment of the initial conditions related to a 

given bloodstain in a crime scene. This would be a significant benefit to the criminal justice community. 

3) Implications for further research 

The experimental results discussed above imply three main areas for future work. First, the scaling 

used in equation (11) produced the parameter 

2/5 P We Re n n



, which was the main independent 

variable used to plot the data. Figure 12 shows that this worked reasonably well, but that the bulk of 

the present data fell in the range between the two scaling limits of this parameter, i.e., very small P and 

very large P. This parameter written in terms of primitive parameters is 

2/5 8/5 3/5 ( / ) P    V D n

, 

where  is the kinematic viscosity of the fluid. Thus, to address these two limits, experiments should be 

performed for blood simulant droplets that are both smaller and slower, and larger and faster. 

The next two areas of future work are concerned with the variability seen in the present data. This 

research used glass, tile, and paper surfaces as representative of what would be seen in a typical crime 

scene. The results showed a significant effect of surface roughness on the droplet spreading process, 

the shape of the fully spread droplet, and the onset and number of spines. This effect can be explored 

and characterized with another set of experiments using surfaces of well-defined and uniform 

roughness. The surfaces can be made from etched glass and range from completely smooth to as rough 

as needed to explore the effect on spreading and splashing of the impacting droplets. The use of glass 

would eliminate any effects that could be attributed to a porous surface such as paper. 

The last area of experimental research is to examine the effect of droplet oscillations on the results. 

This is essentially a study of how the shape of an oscillating droplet just before impact affects the way 

the droplet spreads on the surface. This could be accomplished by acoustically forcing the droplet so 

that it oscillates in one of its fundamental modes of oscillation. The shape of the droplet just before 

impact could then be controlled by the acoustic signal to adjust the phase and amplitude of the droplet 

deformation to the desired point. 

These last two studies on the variability of the data using controlled droplet oscillations and surface 

roughness are very important with respect to the use of this work in forensics applications. At a crime 

scene, there is no control of either of these parameters. Thus, if these future studies can adequately 

quantify the effect of each of these parameters on the size and shape of the bloodstain, then these 

results can be used to estimate to expected error in the computation of the impact parameters for use 

in forensics. 

The GPU-based, wavelet-adaptive, single phase flow simulation was completed and verified in this 

project. The future work with this simulation will be to add the level set model for the simulation of 

- 26 -

This resource was prepared by the author(s) using Federal funds provided by the U.S. 

Department of Justice. Opinions or points of view expressed are those of the author(s) and do not 

necessarily reflect the official position or policies of the U.S. Department of Justice 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

multiphase flows. Once completed and verified, the simulation will be used for a comprehensive 

parameter study of droplet impact on an inclined solid surface with arbitrary roughness as appropriate 

to the blood spatter problem and a comparison of those simulations to the experimental results 

obtained in this project. This will include a closer examination of the dependence of the aspect ratio, 

the width ratio, the eccentricity ratio, and the spreading factor of the bloodstain on the Reynolds 

number, Weber number, and impact angle of the blood droplet, and the roughness of the surface. 

These simulations would also enable a detailed investigation of the physical mechanisms associated with 

droplet impact and how these mechanisms are affected by droplet deformation due to initial oscillations 

and the friction attributed to surface roughness. 

The fully resolved numerical simulation of droplet impact can also be used to more fully verify the 

simple droplet spreading model of Eggers et al. [15]. The verified normal impact model could then be 

extended in future work to produce an oblique droplet impact and spreading model. This would be a 

set of partial differential equations that describe the shape and spreading of a droplet on a solid surface. 

Using the idea that the maximum spreading of the droplet is the shape of the bloodstain, these 

equations would allow a quick determination of the shape of a bloodstain as a function of the droplet 

impact angle and speed, the droplet size and its physical parameters such as viscosity and surface 

tension, and the amount of surface roughness. The results from this model would be compared and 

validated against the experimental data on droplet shape and spreading factor and against the data 

from the fully resolved numerical simulation of droplet spreading. 

The results from this simple phenomenological model of droplet spreading verified by the fully 

resolved numerical simulations would assist in the development of simple correlations or computations 

that could be used by forensic practitioners in the field. These results would be fully justified on 

scientific grounds and have a rational measure of expected error. Their use in forensics would greatly 

enhance the ability of practitioners to reconstruct a crime scene based on the available blood spatter 

evidence. 

V. References 

[1] U. Buck, B. Kneubuehl, S. Nather, N. Albertini, L. Schmidt, and M. Thali, “3D Bloodstain Pattern 

Analysis: Ballistic Reconstruction of the Trajectories of Blood Drops and Determination of the 

Centres of Origin of the Bloodstains,” Forensic Science International, vol. 206, no. 1-3, pp. 22-28, 

2011. 

[2] P. A. Pizzola, S. Roth, and P. R. D. Forest, “Blood Droplet Dynamics,” Journal of Forensic Sciences, 

vol. 31, no. 1, pp. 36-49, 1986. 

[3] L. Hulse-Smith and M. Illes, “A Blind Trial Evaluation of a Crime Scene Methodology for Deducing 

Impact Velocity and Droplet Size from Circular Bloodstains,” Journal of Forensic Sciences, vol. 52, 

no. 1, pp. 65-69, 2007. 

[4] C. D. Adam, “Fundamental Studies of Bloodstain Formation and Characteristics,” Forensic Science 

International, vol. 219, no. 1-3, pp. 76-87, 2012. 

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This resource was prepared by the author(s) using Federal funds provided by the U.S. 

Department of Justice. Opinions or points of view expressed are those of the author(s) and do not 

necessarily reflect the official position or policies of the U.S. Department of Justice 
 

 

 

 

 

 

 

 

 

 

 

 

[5] C. Knock and M. Davison, “Predicting the Position of the Source of Blood Stains for Angled 

Impacts,” Journal of Forensic Sciences, vol. 52, no. 5, pp. 1044-1049, 2007. 

[6] M. Boue and M. Illes, “Robust Estimation for Area of Origin in Bloodstain Pattern Analysis via 

Directional Analysis,” Forensic Science International, vol. 226, no. 1-3, pp. 223-229, 2013. 

[7] V. Balthazard, R. Piedelievre, H. Desoille, and L. DeRobert, “Study of projected drops of blood,”

Ann Med Leg Criminol Police Sci Toxicol, vol. 19, pp. 265–323, 1939. 

[8] J. C. Bird, S. S. Tsai, and H. A. Stone, “Inclined to Splash: Triggering and Inhibiting a Splash with 

Tangential Velocity,” New Journal of Physics, vol. 11, no. 6, 2009. 

[9] K. Range and F. Feuillebois, “Influence of Surface Roughness on Liquid Droplet Impact,” Journal of 

Colloid and Interface Science, vol. 203, pp. 16-30, 1998. 

[10] A. Costello, F. Fances, and F. Verdu, “Bleach interference in forensic luminol tests on porous 

surfaces: More about the drying time effect,” Talanta, vol. 77, no. 4, pp. 1555-1557, 2009. 

[11] B. Karger, S. Rand, T. Fracasso, and H. Pfeiffer, “Bloodstain Pattern Analysis-Casework Experience,”

Forensic Science International, vol. 181, no. 1-3, pp. 15-20, 2008. 

[12] D. Attinger, C. Moore, A. Donaldson, A. Jafari, and H. A. Stone, “Fluid Dynamics Topics in 

Bloodstain Pattern Analysis: Comparative Review and Research Opportunities,” Forensic Science 

International, vol. 231, no. 1-3, pp. 375-396, 2013. 

[13] P. L. Carroll, “Results Obtained from Planar-Impact Experiment,” Summer Research Project, 

Georgia Institute of Technology, 2010. 

[14] J. Andreas, A. Hause, and W. Tucker, “Boundary Tension by Pendant Drops,” in Proceedings of the 

Fifteenth Colloid Symposium, Cambridge, 1938. 

[15] J. Eggers, M. A. Fontelos, C. Josserand, and S. Zaleski, “Drop dynamics after impact on a solid wall: 

Theory and simulations,” Physics of Fluids 22, 062101, 2010; doi: 10.1063/1.3432498. 

[16] N. Laan, K. G. de Bruin, D. Bartolo, C. Josserand, and D. Bonn, “Maximum Diameter of Impacting 

Liquid Droplets,” Physical Rev Applied 2, 044018, 2014. 

[17] C. J. Forster, “Parallel Wavelet-Adaptive Direct Numerical Simulations of Multi-Phase Flows With 

Phase Change, Ph.D. Thesis, Georgia Institute of Technology, August 2016. 

[18] T. Bodnár, A. Sequeira, and M. Prosi, “On the shear-thinning and viscoelastic effects of blood flow 

under various flow rates,” Applied Mathematics and Computation 217, 2011. 

[19] S. Mandre and M. P. Brenner, “The mechanism of a splash on a dry solid surface,” J. Fluid Mech. 

690 (2012) 148–172. 

[20] L. Xu, W. W. Zhang, and S. R. Nagel, “Drop splashing on a dry smooth surface, Phys. Rev. Lett. 94

(2005), pp. 184505:1–4. 

- 28 -

This resource was prepared by the author(s) using Federal funds provided by the U.S. 

Department of Justice. Opinions or points of view expressed are those of the author(s) and do not 

necessarily reflect the official position or policies of the U.S. Department of Justice 
 

 

 

 

VI. Dissemination of Research Findings 

1. Lockard, M., Neitzel, G. P., & Smith, M. K., “Droplet Impact Patterns on Inclined Surfaces with 

Variable Properties,” Sixty-Seventh Meeting of the American Physical Society - Division of Fluid 

Dynamics, San Francisco, CA, November 23–25, 2014. 

2. Lockard, M., “The Fluid Dynamics of Droplet Impacts on Inclined Surfaces with Application to 

Forensic Blood spatter Analysis,” M.S. Thesis, Georgia Institute of Technology, August 2015. 

3. Smith, M. K., Lockard, M., & Neitzel, G. P., “Droplet Impact on Inclined Surfaces for Forensic 

Bloodstain Analysis,” Sixty-Eighth Meeting of the American Physical Society - Division of Fluid 

Dynamics, Boston, MA, November 22–24, 2015. 

4. Forster, C. J., “Parallel Wavelet-Adaptive Direct Numerical Simulations of Multi-Phase Flows With 

Phase Change, Ph.D. Thesis, Georgia Institute of Technology, August 2016. 

5. Forster, C. J. and Smith, M. K. “GPU-based Wavelet-adaptive Multiphase Flow Simulation for All 

Mach Numbers. Part 1: Verification of High-speed Compressible Flow,” submitted to J. Comp. 

Physics, 2016. 

6. Forster, C. J. and Smith, M. K. “GPU-based Wavelet-adaptive Multiphase Flow Simulation for All 

Mach Numbers. Part 2: Verification of Low-speed Compressible Flow,” in preparation for submission

to J. Comp. Physics, 2017. 

- 29 -

This resource was prepared by the author(s) using Federal funds provided by the U.S. 

Department of Justice. Opinions or points of view expressed are those of the author(s) and do not 

necessarily reflect the official position or policies of the U.S. Department of Justice