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Droplet Dynamics of Newtonian Fluids and Blood on Polyester Fabric

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Droplet Dynamics of Newtonian Fluids and Blood on Polyester Fabric 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 p 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.
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