Droplet Dynamics of Newtonian Fluids and Blood on Polyester Fabric

Karlijn Charlotte Maria Limpens 10615342

Bachelor Project Physics and Astronomy, 15 EC September 4, 2017 - 20th December 2017

Supervisor Second assessor Daily supervisor Prof. dr. D.Bonn dr. N.F. Shahidzadeh T.C. de Goede Msc Abstract The difficulty of blood impact on fabric lies in the complexities of blood and the varieties in fabrics. This report examines whether blood spreads as a Newtonian fluid on polyester fabrics. Using a high-speed camera the impact of blood, a water-glycerol mixture and water droplets on a smooth surface (stainless steel) and polyester fabric are compared. We show that the spreading of the fluids on fabric is less than the spreading on stainless steel. Furthermore, we found that the spreading of blood on fabric is similar to the spreading of water-glycerol mixture. We also show that the complexity of blood influences the fabric penetration dynamics during impact. Although we see a difference in the penetration through the fabric between blood and the water-glycerol mixture we conclude that the spreading of blood is similar to its Newtonian counterpart, as the difference in fabric penetration dynamics can be accounted for with the loss of volume due to fabric penetration during droplet spreading . Contents

1 Introduction 1

2 Theory 2 2.1 Viscosity ...... 2 2.2 Surface Tension ...... 3 2.3 Droplet Impact ...... 3 2.4 Physical Properties of Blood ...... 5

3 Methods 7 3.1 Setup ...... 7 3.2 Liquids and Surfaces ...... 7 3.3 Image Analysis ...... 9

4 Results and Discussion 11 4.1 Droplet Impact on Stainless Steel ...... 11 4.2 Drop impact on Textile ...... 12 4.2.1 Water ...... 12 4.2.2 Glycerol 6mPa·s vs Water ...... 15 4.2.3 Blood vs Glycerol 6mPa·s...... 16

5 Conclusion and Outlook 18

6 Dutch summary 19

References 20 1 Introduction

The impact of droplets is a field of research that continues to find new applications in fields like crop spraying [1], ink jet printing [2, 3] and blood pattern analysis [4–6]. Droplet impact is a phenomena which is still not completely understood. Although there have been numerous studies on the impact of droplets on solid surfaces [7–11], drop impact on porous media such as fabrics, is still rather unexplored. There have been studies about the effect of droplet dynamics on porous stones [12, 13] and the trampoline effect after droplet impact [14]. But the influence of fabric properties on droplet spreading seems to be underexposed, especially for complex fluids like blood.

The real-life importance of understanding blood droplet impact on fabric, becomes clear after looking at the legal case of David Camm 1. On the evening of September 28 2000, the Sellersburg Indiana State Police post received a call from David Camm, who reported the murder of his wife and two children. Upon arrival at the crime scene the police found Camm with blood spatters on his shirt. After initial research the State charged Camm with three counts of murder. During the trial in 2002, the prosecution claimed that the blood spatters found on Camm’s shirt were high velocity impact spatter resulting from a gunshot. The defence claimed that the spatters were transfer stains from when Camm carried his son out of the car to preform CPR. Camm was found guilty of the murder of his wife and two children based on the bloodstains on his shirt. It took until 2013 for Camm to be found not guilty of all charges due to, among other reasons, contradictory statements made by experts about the cause of the blood spatters on Camm’s shirt. This case highlights why understanding blood impact on fabrics is of critical importance.

Blood impact on fabrics is a complicated topic, since blood is a complex fluid and fabrics come with a variety of properties. In this research, we further the understanding of the field by studying whether blood impact on polyester fabrics can be compared to the impact of Newtonian fluids. We use high-speed imaging to record and compare droplet impact of different fluids on different substrates. The fabrics are made with a plain weave, with a single fiber per yarn so no wicking occurs.

This thesis is build up as follows: first, the theoretical background of fluid properties, droplet impact and blood will be discussed. Then we will describe the experimental setup, after which we will discuss the obtained result, finally the conclusions and possible further research will be stated.

1INDIANA COURT OF APPEALS, 2004. David Camm v. State of Indiana. Indiana Court of Appeals

1 2 Theory

In this section, the theoretical background of droplet impact will be discussed. First the fluid properties essentially for droplet impact will be defined. Then the impact of droplets on solid surfaces will be explained, along with model which to describe the process. Finally, we discuss the composition of blood and the influence of its different component on its physical properties.

2.1 Viscosity

(a) (b)

Figure 1: (a) Schematic overview of parallel plates system. Both plates have a surface area A. The bottom and top plate lie at a height of y = 0 and y = h, respectively. (b) The viscosity as a function of the shear rate of a shear thickening, Newtonian and shear thinning ﬂuid.

When a fluid flows it dissipates energy due to an internal friction described by the shear viscosity η. To determine the viscosity of a system, consider a fluid with viscosity η confined between two infinite parallel plates (Figure 1a) [15] with height difference h between the two plates and the bottom plate positioned at y = 0. When the top plate is moved by a constant force F , resulting in the plate moving with velocity v, a shear stress (τ ≡ F/A) is applied on the fluid.

As a result of the shear stress the ﬂuid will start moving with a high dependant velocity ux. Assuming that no wall slip occurs [16], we obtain two boundary conditions for the ﬂuid’s velocity:

ux(0) = 0, ux(h) = v (1)

These boundary conditions give a simple linear solution for ux: v u (y) = y (2) x h The derivative of this velocity to y is defined as the shear rateγ ˙ : ∂u v γ˙ ≡ x = (3) ∂y h The viscosity of a fluid can now be defined as the ratio between the shear rate and shear stress τ η = (4) γ˙ For simple fluids like water, the shear rate linearly increases with the shear stress and the viscosity is constant. Such fluids are known as Newtonian fluids. More complex fluids often show

2 non-Newtonian behaviour and can be shear thickening or thinning. For a shear thinning fluid the viscosity of the fluid decreases with increasing shear rate or stress. For a shear thickening fluid the the opposite applies, the fluid gets a higher viscosity when there is an increase in shear stress (Figure 1b).

2.2 Surface Tension

Figure 2: Schematic overview of cohesive forces (arrows) acting on liquid particles (black dots).

At the liquid gas interface the surface of the liquid has a surface tension σ. Liquid particles in the bulk (Figure 2), experience a net zero force as the surrounding particles pull with the same cohesive force in all directions. The particles at the liquid surface are not exposed to the same cohesive forces, because the gas particles are not as closely packet as the liquid particles. As a result, the particles at the surface are pulled inwards, reducing the surface area as much as possible. To increase the surface of the ﬂuid, energy needs to be put in the system. The total amount of Gibbs free energy needed to increase the area A of a ﬂuid is:

G = σA (5) The surface tension σ is deﬁned as the amount of Gibbs energy needed to increase the surface area by ∂A while the temperature T and pressure P are constant:

∂G σ = (6) ∂A T,P

2.3 Droplet Impact

When a droplet with diameter D0 hits a solid smooth surface with impact velocity vimp, it deforms into a pancake-like shape with a maximum diameter Dmax within a few milliseconds (Figure 3). The spreading of the droplet is determined by either the dissipation of the droplet’s kinetic energy into viscous energy (viscous regime) or the transformation into surface energy (capillary regime). Diﬀerent models [17–27] have been proposed that tried to describe droplet impact in either the capillary regime or in the viscous regime, were the either the capillary or viscous forces dominate. These models commonly use two dimensionless parameters: the Weber number, which is the ratio between the inertial and capillary forces:

2 ρD0v W e = imp (7) σ

3 And the Reynolds number, which describes the ratio between the inertial and viscous forces: ρD v Re = 0 imp (8) η

(a) (b)

Figure 3: Typical example of a droplet impact on a smooth surface (vimp ≈ 1.4 [m/s]). (a) Before impact, the droplet is spherical and has a diameter D0. (b) The droplet reaches a maximum spreading Dmax 2.6 [ms] after impact. The lamella spreads out to the rim of the droplet where most of the volume is gathered.

From energy conservation laws, models can be deduced to describe droplet spreading in the capillary and viscous regime. The transformation of the total inertial energy into surface energy gives a model for droplet impact in the capillary regime: D √ max ∝ W e (9) D0 The total dissipation of inertial energy into the viscous energy gives a model that describes the droplet impact for high velocities: D max ∝ Re1/5 (10) D0 Laan et al. showed that neither models for the capillary regime nor those for the viscous regime alone are sufficient for describing droplet impact [8]. During the spreading of droplets the kinetic energy is both dissipated in the viscous energy and transformed into surface energy. Using a first order Padéaproximant and Equations (9) and (10) as boundary conditions, Laan et al. were able to interpolate between the two regimes and find a relation between the spreading of a droplet, its impact velocity and fluid parameters: √ Dmax − 1 P Re 5 = √ (11) D0 1.24 + P −2/5 With P ≡ W e . The problem with this model is that for the limit vimp → 0, the droplet spreading also becomes zero, which is unphysical . Lee et al. [28] proposed a correction to the model by adding an energy correction in the low-velocity limit, Equation (9):

4 q √ 2 2 βmax − β0 = W e (12)

With the spreading ratio βmax ≡ Dmax/D0 and the correction term β0 representing the spreading ratio of a droplet at vimp = 0. Using this correction, Lee et al. [28] were able to adapt Equation 11 and include droplet spreading at low velocities: √ q 1 W e β2 − β2 = Re 5 √ (13) max 0 7.6 + W e The rescaling proposed by Lee et al. can be used to describe the maximum spreading of droplets on smooth and rough solid surfaces for high and low impact velocities.

2.4 Physical Properties of Blood Blood has four main components: plasma, red blood cells, white blood cells and platelets. Because white blood cells take up about 1% of the total blood volume, their influence on the physical properties of blood are neglected. Platelets are the component mainly responsible for the coagulation of blood. However, it is assumed that the spreading of blood droplets on a crime scene happens on such a small time frame that the influence of the coagulation on the physical properties of blood is negligible [29]. Plasma, the main component of blood, consists of water mixed with different kinds of enzymes and proteins. For a healthy person plasma is a Newtonian fluid with a viscosity between 1.10 and 1.35 mPa·s at 37◦C [30]. The volume fraction of red blood cells in the total blood volume is called the hematocrite value (Hct).. For men this value is approximately 43 ± 4% and for women around 39 ± 4% [31].

(a) (b)

Figure 4: (a) Schematic overview of a blood droplet spreading [32]. (b) Viscosity of blood and three Newtonian ﬂuids as a function of the shear rate [32].

Although plasma is a Newtonian fluid, blood is not. The red blood cells in blood cause the non-Newtonian behaviour of blood [31]. When the shear rate of the blood is low, red blood cells aggregate and stack upon one another in a rouleaux formation [33], causing a high viscosity [32]. Increasing the shear rate, the rouleaux formation will eventually break up and the viscosity decreases, finally settling at a constant value η∞ at high shear rate, which is defined as the high shear rate viscosity of blood (Figure 4a).

5 By approximating droplet spreading as a parallel plate system (Figure 4b) Laan [32] showed that the shear rate inside a spreading droplet is around the order of 107 [s−1]. Laan postulated, using the high shear rate, that blood during spreading could be considered Newtonian, with a wiscosity equal to η∞. He compared experimental data of blood and a water-glycerol mixture with a viscosity of 6 mPa·s to show that blood spreads like a Newtonian ﬂuid on solid surfaces [8].

6 3 Methods 3.1 Setup To capture droplet impact, a recording a high speed camera setup (Figure 5) was used. Since the droplets were accelerated√ by gravity, the impact velocity was tuned by changing the height h of the needle (vimp ∝ gh , with g the gravitational constant). Usually four impacts were measured at each height, by averaging the results cleaner data was obtain. A syringe pump (Model 200, kdScientiﬁc, Holliston, Massachusetts, USA) was used to create droplets at an expulsion speed of 5 [µl/minute], from a 0.4 mm diameter blunt tipped needle (Figure 5). To record the impact a high speed camera (Phantom Miro M310, Vision Research, Dey Rd. Wayne, New Jersey USA) with a frame rate of 8100 frames per second was used. To create a shadow image of the droplet (Figure 7a), a LED light (MultiLED LT, GSvitec GmbH, Gelnhausen, Germany) and light diﬀuser sheet were used. For every data set millimetre paper was used as reference length and placed it in the same focal plane as the droplet impact.

Figure 5: Schematic overview of the droplet impact setup

3.2 Liquids and Surfaces In this research three different liquids were compared, for which the surface tension, density and viscosity are given in Table 1. Water was used as reference. A water-glycerol mixture (glycerol 6mPa·s) was used because its viscosity is comparable to the high shear rate viscosity of blood. Blood was collected in vacutainers (4.5 [mL], BD Vacutainer, 9NC 0.15M, Buff.) with sodium citrate as an anticoagulant. The influence of the anticoagulant on the physical properties is negligible in these amounts [34]. The blood has an average Htc value of 38 ± 1% measured with a centrifuge (Haematokrit 210, Hettich zentrifugen, Germany). Between blood collection and the measurements, blood was stored in a refrigerator for up to four days. Before blood was used, the temperature was brought back to body temperature (37◦[C]). To make sure only fresh droplet were used, the needle was wiped clean of any remaining blood before forming a new droplet.

7 Table 1: Surface tension, density and viscosity values of water, glycerol 6mPa·s and blood [32]. Glycerol 6mPa·s is a water-glycerol mixture with a mass ratio of 1 : 1

Surface tension Density Viscosity [mN/m] [kg/m3] [mP a · s] Water 73 ± 2 998 1.0 Glycerol 6mPa·s 65.69 ± 0.07 1124 ± 2 6.0 Blood 60 ± 2 1055 ± 3 4.8

Stainless steel was used as smooth reference substrate. As fabrics, two simple polyester hydro- phobic fabrics were used, P150 and P45 (Gilson Company, inc., USA), respectively. Pore sizes and yarn diameters of P45 and P150 are given in Table 2. The fabrics are made with a plain weave and have one ﬁber per yarn (Figure 6a). Drop impact was measured on fabric both suspended in the air and placed on a smooth steel surface. In this study, both cases are deﬁned as Air-Textile-Air (ATA; Figure 6b) and Air-Textile-Surface (ATS; Figure 6c) measurements, respectively. To remove any surface contaminations, the stainless steel substrates were cleaned with acetone and ethanol and dried using paper tissues and a high pressure air gun. The pieces of fabric used as substrates for water were wiped and blown dry with a high pressure air gun, for glycerol and blood a clean new piece of fabric was used for every impact measurement.

Table 2: Yarn diameter and pore size of the polyester fabrics P45 and P150

Fabrics yarn diameter pore size [µm] [µm] P45 40 45 P150 80 150

(b)

(a) (c)

Figure 6: (a) Microscopic image of the polyester fabric, Y denotes the yarn diameter and p the pore size. (b), (c) Schematic representation of the Air-Textile-Air (ATA) substrate and Air-Textile-Surface (ATS), respectively.

8 3.3 Image Analysis The analysis of the high-speed images consisted of several steps. First the reference length is calculated from the scale image to convert data into SI units. Secondly a reference frame was made, the ﬁrst frame of every recording (Figure 7a) will be used as reference frame. When the droplet is visible in the reference frame it is removed (Figure 7b). The reference frame is used to extract the drop from the footage, after which each image gets binarized (Figure 7c). For every binarized image three coordinates were determined: the centre of the droplet given by the (xc,yc) coordinates, the coordinates of the top-left corner (x1,y1) and the right-bottom corner (x2,y2) of the bounding box that just encloses the entire droplet (Figure 7c).

(a) (b) (c)

Figure 7: From the ﬁrst frame of the movie (a), the droplet is removed, giving a reference frame (b). The extracted droplet (bianarised with the boudingbox (yellow) and the centroid (red)

The droplet’s diameters in the x and y direction (D0x and D0y, respectively) were determined for each frame by: D0x = x2 − x1 D0y = y2 − y1 (14)

D0 is determined for every measurement by taking the mean value of the D0x before impact. D0y is not used due to motion blur. Dmax is determined by the maximum value of D0x after impact. Dmax With these values the spreading ratio βmax, deﬁned as , was calculated for every measure- D0 ment. Finally, the average value of βmax per height was calculated.

The velocity of the droplet can be determined by dividing the difference in yc and the time t between two consecutive frames: y − y v = c,i+1 c,i (15) ti+1 − ti As shown in Figure 8, the velocity increases linearly in time. Near the moment of impact determ- ining the centroid of the drop becomes imprecise, due to optical effects with the substrate, creating fluctuations in the velocity data. Therefore, the velocity at the time of impact can not be used as the impact velocity vimp. Instead, a simple linear model describing the acceleration of the droplet by gravity was used:

v(t) = a · t + b (16) By fitting the linear model to the data before the fluctuations and finding the speed of the linear model at the time of impact, vimp was determined. Then Equation (16) is fitted to the data (Figure 8) to extrapolate vimp by using the time of impact.

9 Figure 8: The velocity data of a single measurement (blue circles) and the best fit of the linear model (red line). For the fitting the fluctuations of the last data point are left out.

10 4 Results and Discussion

First the impact on stainless steel will be shown and compared to the literature. Then the spreading of water on stainless steel will be compared to the spreading om fabrics. Finally the spreading on fabric of glycerol 6mPa·s will be compared to the spreading of blood.

4.1 Droplet Impact on Stainless Steel

Figure 9: Spreading ratio of water, glycerol 6mPa·s and blood on stainless steel as a function the impact velocity

The spreading ratio as function of the impact velocity for water, glycerol 6mPa·s and blood on stainless steel are given in Figure 9. At low velocities βmax overlaps for all three fluids, but as the impact velocity increases, the spreading of glycerol 6mPa·s and blood starts to deviate from the spreading of water. This is expected, as droplet spreading at higher impact velocities is more dependent on the viscous properties of the fluid. The similar spreading between glycerol 6mPa·s and blood confirms that blood can be considered as a Newtonian fluid, in line with the observation by Laan et al. [8]. To further investigate the similarities between our measurements and the literature, the data is rescaled the same way as Lee et al. [28]. To determine β0 in Equation (13), the equation is rewritten to:

√ !2 1 W e 2 2 Re 5 √ = β + β (17) 7.6 + W e max 0 When comparing Equation (17) to a simple linear model as y = x+b, where b is the intersection with the x-axis, then the slope of a linear fit through the data should be 1 and the intersection of a 2 2 linear fit represents β0 . By plotting the left side of Equation (17) against βmax and fitting a linear model with slope 1 to the data (Figure 10a) β0 is found. For all three fluids, β0 was determined and used to rescale the data with Equation (13) shown in Figure 10b. The rescaled data fits to the curve in a similar way as the literature [28], confirming the reproducibility of the rescaling.

11 (a) (b)

Figure 10: (a) A linear ﬁt (red solid line) through the water data rescaled to Equation (17), as a 2 function of βmax (blue circles). (b) Rescaled data for stainless steel and Equation (13) (solid line). The error bars are not plotted for clarity reasons.

For the impact of droplets on stainless steel we found that blood and glycerol 6mPa·s spread the same way, conﬁrming that blood spreads like a Newtonian ﬂuid during impact. By applying the rescaling of Lee et al. [28] we see that the data collapse to the same line as found in the literature.

4.2 Drop impact on Textile Having investigated droplet impact on smooth surfaces, we will now consider droplet impact on the polyester fabrics.

4.2.1 Water Figure 11 shows high-speed images of water droplets at maximum spreading for diﬀerent substrates and impact velocities. For droplet impact on stainless steel (Figure 11 a-c), the droplet spreads radially outward with an smooth rim. On P150 ATS (Figure 11 d-f) the spreading for low velocities is similar to the spreading on stainless steel, while the drop spreads less at higher impact velocities. The spreading of the droplet with the low impact velocity on P150 ATA (Figure 11 g) is also comparable to the spreading on P150 ATS and stainless steel. But for the droplets at higher impact velocities (Figure 11h and 11i) the water penetrates through the fabric, resulting in the break up of the droplet volume underneath the textile while the droplet is at maximum spreading.

In Figures 12a and 12b the spreading ratios of water on stainless steel, P150 and P45 as a function of the impact velocity is shown. When comparing the spreading on ATS to the spreading on stainless steel (Figure 12), we see a deviation between the data sets that increases for higher velocities. The diﬀerence between stainless steel and ATS is bigger for the impact on P150 than for the impact on P45. We can explain this by considering that P45 has smaller a pore size and yarn diameter, the substrate is smoother and more similar to the stainless steel substrate than P150. This implies that the fabrics have a certain roughness that inﬂuences the spreading of the droplet.

12 (a) (b) (c)

(d) (e) (f)

(g) (h) (i)

Figure 11: Maximum spreading for water on (a-c) stainless steel, (d-f) fabric on substrate and (g-i) fabric without substrate. The pore size of the fabric with and without substrate is 150 [µm].

(a) (b)

Figure 12: (a) Maximum spreading ratio βmax of water on stainless steel (circles), P150 ATS (dia- monds) and P150 ATA (triangles) as a function of the impact velocity. The orange triangles show the spreading ratio ATA with a correction for the lost volume. The purple line marks the minimal velocity necessary for the ﬂuid to penetrate through the fabric. (b) Measured maximum spreading ratio βmax of water on stainless steel (circles), P45 ATS (squares) and P45 ATA (triangles), as a function of the impact velocity. The blue line mark the minimal velocity necessary for the ﬂuid to penetrate through the fabric.

13 On fabric the spreading at low impact velocities is the same for ATS and ATA. Above the velocity at which we see the droplet penetrating thought the fabrics in the ATA system (solid lines; Figure 12b and 12c), the results begin to deviate. On P150 ATA the penetration through the fabric happens at a impact velocity of 0.64 [m/s], for P45 ATA the penetration velocity is much higher 1.31 [m/s]. The P150 ATA data stays at a constant value after the fluid penetrates through the fabric, but βmax still increases for P45 with an increasing impact velocity. The differences between the spreading on P150 and P45 has to be caused by either the pore size or yarn diameter of the fabric. Since in this research, the two are not varied independently, we cannot provide conclusive answers. For the P45 ATA data sets we see larger error bars for the high velocities. For these velocities we saw that the fabric sometimes started to vibrate at the impact op the droplets causing a trampoline like effect. The vibrating of the fabric is a new way for the system to dissipate energy, which causes the bigger error bars for P45 ATA. For P150 this trampoline effect was not observed because the yarns where thicker and thus less flexible.

In Figure 11 we compared water spreading on ATS and ATA to spreading on stainless steel and saw that for ATA, water penetrates through the fabric if the impact velocity is high enough. The penetration of water though the fabric leads to a loss of volume which could explain difference is spreading between ATS and ATS. When we consider that the effective volume of the drop is reduced by the volume which penetrates through the fabric, we can introduce a correction to D0 which takes the lost of volume into account. The shape of the fluid volume underneath the fabric is estimated to be a paraboloid (Figure 13). By subtracting the volume of the paraboloid from the ∗ volume of the initial droplet, a corrected initial diameter (D0), as a function of the height h and base radius r of the paraboloid, is found by: q ∗ 3 3 2 D0 = D0 − 3r h (18)

By recalculating βmax using the corrected initial diameter, the corrected ATA spreading data (Figure 12a; orange triangles) now overlaps with the ATS data. This implies that the only diﬀer- ence between the spreading on ATS or ATA is due to the volume loss when the droplet penetrates through the fabric.

Figure 13: The shape of the volume fraction of the droplet that penetrated through the fabric estimated as a paraboloid with height h and radius r.

For the impact of water on fabric, we have shown that without a substrate water can penetrate through the fabric, resulting is an eﬀective loss in volume on top of the fabric. When we correct for the lost volume, we observe a similar spreading for ATS and ATA. We show that for smaller pore size and yarn diameter water needs a higher velocity to penetrate through the fabric. Finally we showed that there is a bigger diﬀerence between the spreading on stainless steel and ATS when the fabric has larger a pore size and yarn diameter.

14 4.2.2 Glycerol 6mPa·s vs Water To investigate the influence of the viscosity on droplet spreading on fabrics, a comparison is made between water and glycerol 6mPa·s for both P150 (Figure 14a) and P45 (Figure 14b) Similar to stainless steel (Figure 9), the droplet spreading of water and glycerol 6mPa·s overlaps at lower velocities, and glycerol deviates from water for higher impact velocities. In the ATS data sets a similar deviation between water and glycerol 6mPa·s occurs. Due to the higher viscosity of glycerol 6mPa·s it spreads less at higher velocities. For the ATA data sets something different happens. Glycerol 6mPa·s needs a higher impact velocity to penetrate through the fabric, on P150 the impact speeds has to be at least 0.77 [m/s] (dashed green line; Figure 14a) and on P45 the minimal velocity has to be 1.6 [m/s] (dashed green line; Figure 14b). This implies that the viscosity of a fluid influences the process of penetration through the fabric, causing a bigger spreading for glycerol 6mPa·s on ATA because there is a smaller loss in volume that penetrated through the fabric.

(a) (b)

Figure 14: (a) Spreading of water and glycerol on P150 ATS and ATA. The blue solid line marks the velocity at which water penetrates through the fabric and the green dashed line marks the velocity at which glycerol penetrated through the fabric. (b) Spreading of water and glycerol on P45, ATS and ATA. The purple solid line marks the velocity at which water penetrates through the fabric and the green dashed line marks the velocity at which glycerol penetrated through the fabric

When comparing the results for glycerol on P45 and P150, the values start to deviate beyond the velocity at which the fluids penetrates through the fabric. For P45 a higher impact velocity is needed to penetrate through the fabric and thus the deviation between ATS and ATA also happens at a higher velocity. Because the data has larger error due to the trampoline effect of P45 and the penetration of the fluids through the fabric happening at a higher velocity, it is hard to draw definitive conclusions about the deviation between ATS and ATA on P45. To see more distinct differences between the ATS and ATA data on P45, droplet spreading at higher impact velocity needs to be considered.

The comparison between water and glycerol 6mPa·s on the fabrics shows that the impact of

15 water and glycerol 6mPa·s droplets on fabrics that lie on a substrate have a similar deviation at high velocities as the impact on stainless steel. For higher impact velocities the spreading on fabric is less than the spreading on stainless steel. We also showed that the penetration through a fabric depends on the viscosity of the ﬂuid.

4.2.3 Blood vs Glycerol 6mPa·s

(a) (b)

Figure 15: (a) Spreading of glycerol and blood on P150 ATS and ATA, the green dashed line marks the velocity at which glycerol penetrates through the fabric, the orange solid line marks the velocity at which blood penetrates through the fabric. (b) Spreading of glycerol and blood on P45 ATS and ATA, the green dashed line marks the velocity at which glycerol penetrates through the fabric, the pink solid line marks the velocity at which blood penetrates through the fabric.

In Figures 15a and 15b, the measured maximum spreading ratio of glycerol 6mPa·s and blood on P150 and P45 respectively, are shown as a function of the impact velocity. Again, the spreading of both ﬂuids is similar for both ATS and ATA at low impact velocities. We also see that for blood to penetrate through the fabrics, the velocity has to be 0.93 [m/s] (solid orange line; Figure 15a) for P150 and to penetrate though P45, a higher impact velocity of 1.74 [m/s] (solid pink line; Figure 15b) is necessary. The minimal velocity for penetrating through the fabric for blood is a higher compared to glycerol 6mPa·s. Blood needs more energy to penetrate through the pores of the fabric.

At higher impact velocities, there is a difference between blood and glycerol 6mPa·s for the impact on P150 ATA. Because blood needs a higher velocity to penetrate through the fabric than glycerol 6mPa·s, the deviation between ATS and ATA happens at higher impact velocities for blood. For P45 the deviation between ATS and ATS for blood does not occur for the measured impact velocities. For P150 there appears to be a significant difference between the blood and glycerol data. To verify that the data collected for the impact of blood on P150 ATA is reproducible the experiment was repeated, which yielded the same results.

The difference between the blood and glycerol 6mPa·s impact on P150 ATA does not imply that blood spreads different on fabrics suspended in the air. As shown in Figure 12 the difference

16 between ATS and ATA is the lost of volume due to penetration through the fabric. The diﬀerence between ATS and ATA shows that the way blood penetrates through the fabric is diﬀerent from the way glycerol 6mPa·s does.

For the impact of blood on fabric we have shown that blood spreads the same as glycerol 6mPa·s does on polyester fabric that lies on a substrate. The comparison between blood and glycerol 6mPa·s on polyester fabrics suspended in the air showed that blood penetrates through the fabric at a higher velocity than glycerol 6mPa·s. Due to the higher velocity necessary for blood to penetrate through the fabric the deviation between P150 ATA and ATS happens at a higher velocity causing blood to spread more once penetrated through the fabric. This does not imply that blood spreads different than a Newtonian fluid because we have shown that the difference between ATA and ATS is the lost of volume that penetrated through the fabric.

17 5 Conclusion and Outlook

In this thesis we investigated whether blood can be approximated as a Newtonian ﬂuid on polyester fabrics. Using high-speed imaging, we measured droplet impact of water, a water-glycerol mixture and blood on a stainless steel and polyester fabrics.

For smooth surfaces we confirmed that blood behaves as a Newtonian fluid during droplet spreading. By investigating Newtonian fluid droplets impacting on fabrics, we found that for high impact velocities the spreading on fabric on a substrate was smaller than the spreading on stainless steel. For fabrics suspended in the air we found that the spreading was the same as the spreading of droplets on fabric on a substrate until the velocity at which the fluids penetrated through the fabric. From the moment fluids penetrated through the fabric a sharp deviation between the two data sets occurs. We showed that for both the penetration and spreading with the fabric was influence by the viscosity of the fluid and the properties of the fabric. We found that the difference between spreading on fabric suspended in the air and on a substrate is due to the loss of droplet volume that penetrated through the fabric.

Comparing the droplet impact of blood and glycerol 6mPa·s, we ﬁnd that droplet spreading is similar when impacting fabrics on a substrate. However, for fabrics without a substrate, the fact that blood needs a higher velocity to penetrate the fabric compared to its Newtonian counter part, indicates that the complex nature of blood is important for understanding fabric penetration. However, as we showed that the diﬀerence in spreading on fabric can be accounted for with the volume loss that occurs due to fabric penetration, we therefore conclude that blood behaves as a Newtonian liquid for impact on simple polyester fabrics.

As shown the fabric properties have a significant influence on both the spreading and penetration of the fabric. Therefore, the influence of fabric properties on the spreading of Newtonian fluids on fabric is an interesting subject for research. By systematically varying in pore size and yarn diameter of fabrics the influence of these fabric properties on the penetration velocity can be found. A broader impact velocity range should be examined to also investigate the spreading behaviour of fluids that penetrate though fabrics with small pore sizes. The ratio between pore size and yarn diameter could also be interesting for the spreading behaviour of fluids that penetrate though fabrics.

Why the penetration of blood through the fabrics happens at a higher velocity than for its Newtonian counterpart is also an interesting problem for further research. Because of the complexity of blood, there are a few plausible factors that could explain the difference between blood and the water-glycerol mixture during fabric penetration. The red blood cells could block the flow of blood through the pores of the fabric, or the flow dynamics in the pores could reduce the shear rate and thus viscosity of the blood, which would make it more difficult for blood to penetrate through the pores of the fabric. To study this, we propose investigating a fluid with the same shear tinning properties as blood but without the presence of red blood cells. This way the influence of red blood cells and the influence of shear thinning on the penetration though the fabric can be examined.

18 6 Dutch summary

In de forensische wereld wordt er gebruikt gemaakt van bloedspoorpatroon om te achterhalen wat er zich heeft voorgedaan op een plaats delict, zoals Dexter (Figure 16). Voor deze analyse wordt tot op heden gebruik gemaakt van alleen de druppels die op droge harde ondergronden terecht zijn gekomen. Terwijl er op de meeste plaatsen delict ook veel stoﬀen ondergronden zijn: zoals kleding, bekleed meubilair en gordijnen. De bloeddruppels die op stoﬀen ondergronden terecht komen worden niet mee genomen in de patroon analyse omdat de mechanieken die een rol spelen bij het uitspreiden van druppels op stof nog onderbelicht zijn. Zo spreidt een druppel op stof nog verder uit na inslag omdat de vloeistof door de stof wordt opgenomen.

Het onderwerp van spreiding van bloed op stoffen is erg complex. Bloed is een vloeistof waarvan de stroperigheid afneemt naarmate de vloeistof sneller stroomt. Bij simpelere vloeistoffen zoals water blijft de stroperigheid constant. Ook bestaat bloed uit verschillende vloeibare en vaste stoffen die invloed kunnen hebben op het gedrag van bloed. Daarnaast maakt de grote variabiliteit in stoffen zoals de materialen en de manier van weven het probleem nog complexer.

Dit onderzoek kijkt naar de impact van druppels van Newtoniaanse vloeistoffen en bloed op simpele polyester stoffen. Het doel van dit onderzoek is het vast stellen of bloeddruppels op een soortgelijke manier uitspreiden op simpele polyester stoffen als een Newtoniaanse vloeistof. Door een simpele polyester stof te gebruiken wordt de complexiteit van het vraagstuk gereduceerd. Aan de hand van high-speed camera opnames wordt data verzameld over de impact van verschillende druppels op verscheidene ondergronden. Door bloed te vergelijken met een Newtoniaanse vloeistof die vergelijkbare kenmerken heeft als bloed tijdens impact wordt vastgesteld of bloed zich tijdens impact op polyester stoffen gedraag als een Newtoniaanse vloeistof.

Figure 16: Van de serie Dexter.

Acknowledgement

First of all I would like to thank Thijs de Goede for all the support and feedback in which he provided. I would also like to thank Jan Wormmeester, because he was always available when I needed to get blood out of my body. And Finally I like to thank the Soft Matter Group, especially Luci for all the fun and fascinating conversation during the lunch brakes and for making me feel like a full member of the group.

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