Experimental validation of a numerical model for predicting the trajectory of blood drops in typical crime scene conditions, including droplet deformation and breakup, with a study of the effect of indoor air currents and wind on typical spatter drop trajectories.

Bloodstain Pattern Analysis (BPA) provides information about events during an assault, e.g. location of participants, weapon type and number of blows. To extract the maximum information from spatter stains, the size, velocity and direction of the drop that produces each stain, and forces acting during flight, must be known. A numerical scheme for accurate modeling of blood drop flight, in typical crime scene conditions, including droplet oscillation, deformation and in-flight disintegration, was developed and validated against analytical and experimental data including passive blood drop oscillations, deformation at terminal velocity, cast-off and impact drop deformation and breakup features. 4th order Runge-Kutta timestepping was used with the Taylor Analogy Breakup (TAB) model and Pilch and Erdman's (1987) expression for breakup time. Experimental data for terminal velocities, oscillations, and deformation was obtained via digital high-speed imaging. A single model was found to describe drop behavior accurately in passive, cast off and impact scenarios. Terminal velocities of typical passive drops falling up to 8m, distances and times required to reach them were predicted within 5%. Initial oscillations of passive blood drops with diameters of 1mm<d<6mm falling up to 1.5m were studied. Predictions of oscillating passive drop aspect ratio were within 1.6% of experiment. Under typical crime scene conditions, the velocity of the drop within the first 1.5m of fall is affected little by drag, oscillation or deformation. Blood drops with diameter 0.4-4mm and velocity 1-15m/s cast-off from a rotating disk showed low deformation levels (Weber number<3). Drops formed by blunt impact 0.1-2mm in diameter at velocities of 14-25m/s were highly deformed (aspect ratios down to 0.4) and the larger impact blood drops (∼1-1.5mm in diameter) broke up at critical Weber numbers of 12-14. Most break-ups occurred within 10-20cm of the impact point. The model predicted deformation levels of cast-off and impact blood drops within 5% of experiment. Under typical crime scene conditions, few cast-off drops will break up in flight. However some impact-generated drops were seen to break up, some by the vibration, others by bag breakup. The validated model can be used to gain deep understanding of the processes leading to spatter stains, and can be used to answer questions about proposed scenarios, e.g. how far blood drops may travel, or how stain patterns are affected by winds and draughts.

[1]  A. W. Green,et al.  An Approximation for the Shapes of Large Raindrops , 1975 .

[2]  John William Strutt,et al.  Scientific Papers: On the Instability of Cylindrical Fluid Surfaces , 2009 .

[3]  H. Macdonell Flight characteristics and stain patterns of human blood , 1974 .

[4]  Sanjeev Chandra,et al.  Deducing drop size and impact velocity from circular bloodstains. , 2005, Journal of forensic sciences.

[5]  John Tsamopoulos,et al.  Nonlinear oscillations of inviscid drops and bubbles , 1983, Journal of Fluid Mechanics.

[6]  G. Luxford Experimental and modelling investigation of the deformation, drag and break-up of drizzle droplets subjected to strong aerodynamics forces in relation to SLD aircraft icing , 2005 .

[7]  Peter J. O'Rourke,et al.  The TAB method for numerical calculation of spray droplet breakup , 1987 .

[8]  Osman A. Basaran,et al.  Nonlinear oscillations of viscous liquid drops , 1992, Journal of Fluid Mechanics.

[9]  S. Chandrasekhar The Oscillations of a Viscous Liquid Globe , 1959 .

[10]  A. Wierzba,et al.  Deformation and breakup of liquid drops in a gas stream at nearly critical Weber numbers , 1990 .

[11]  R. Clift,et al.  Bubbles, Drops, and Particles , 1978 .

[12]  J. van Boxel,et al.  Numerical model for the fall speed of raindrops in a rainfall simulator , 1998 .

[13]  B. Kneubuehl,et al.  Response to “3D bloodstain pattern analysis: Ballistic reconstruction of the trajectories of blood drops and determination of the centres of origin of the bloodstains” by Buck et al. [Forensic Sci. Int. 206 (2011) 22–28] , 2012 .

[14]  Efstathios E. Michaelides,et al.  The Magnitude of Basset Forces in Unsteady Multiphase Flow Computations , 1992 .

[15]  V. N. Bringi,et al.  Drop Axis Ratios from a 2D Video Disdrometer , 2005 .

[16]  L. Rayleigh,et al.  XIX. On the instability of cylindrical fluid surfaces , 1892 .

[17]  Joanna Kathleen Wells Investigation of factors affecting the region of origin estimate in bloodstain pattern analysis , 2006 .

[18]  Larry F. Bliven,et al.  Field observations of multimode raindrop oscillations by high-speed imaging , 2006 .

[19]  Stefan A. Krzeczkowski,et al.  MEASUREMENT OF LIQUID DROPLET DISINTEGRATION MECHANISMS , 1980 .

[20]  E. Michaelides Particles, Bubbles And Drops: Their Motion, Heat And Mass Transfer , 2006 .

[21]  Ross Gardner,et al.  Bloodstain Pattern Analysis: With an Introduction to Crime Scene Reconstruction, Second Edition , 1997 .

[22]  R. Gunn,et al.  THE TERMINAL VELOCITY OF FALL FOR WATER DROPLETS IN STAGNANT AIR , 1949 .

[23]  M. Illes,et al.  A Blind Trial Evaluation of a Crime Scene Methodology for Deducing Impact Velocity and Droplet Size from Circular Bloodstains * , 2007, Journal of forensic sciences.

[24]  M. Jermy,et al.  Blood drop size in passive dripping from weapons. , 2013, Forensic science international.

[25]  A. Best Empirical formulae for the terminal velocity of water drops falling through the atmosphere , 1950 .

[26]  N. Kabaliuk Dynamics of Blood Drop Formation and Flight , 2014 .

[27]  M. Pilch,et al.  Use of breakup time data and velocity history data to predict the maximum size of stable fragments for acceleration-induced breakup of a liquid drop , 1987 .

[28]  G. Faeth,et al.  Drop deformation and breakup due to shock wave and steady disturbances , 1994 .

[29]  U. Gösele,et al.  Theory of bimolecular reaction rates limited by anisotropic diffusion , 1976 .

[30]  T. Kowalewski,et al.  Experimental and theoretical investigation of large-amplitude oscillations of liquid droplets , 1991, Journal of Fluid Mechanics.

[31]  H. Pruppacher,et al.  A Semi-Empirical Determination of the Shape of Cloud and Rain Drops , 1971 .

[32]  Daniel S. Isenschmid Review of: Medical-Legal Aspects of Alcohol, Fourth Edition , 2005 .

[33]  Sergey Y. Matrosov,et al.  Cloud Layers, Particle Identification, and Rain-Rate Profiles from ZRVf Measurements by Clear-Air Doppler Radars , 1992 .

[34]  Karla G. de Bruin,et al.  Improving the Point of Origin Determination in Bloodstain Pattern Analysis , 2011, Journal of forensic sciences.

[35]  The Mechanics of Bloodstain Pattern Formation , 2012 .

[36]  Lars Schmidt,et al.  3D bloodstain pattern analysis: ballistic reconstruction of the trajectories of blood drops and determination of the centres of origin of the bloodstains. , 2011, Forensic science international.

[37]  R. Reitz,et al.  Structure of High-Pressure Fuel Sprays , 1987 .

[38]  B. Massey,et al.  Mechanics of Fluids , 2018 .

[39]  M A Raymond,et al.  Oscillating blood droplets--implications for crime scene reconstruction. , 1996, Science & justice : journal of the Forensic Science Society.

[40]  E. Kvašňák,et al.  Temperature dependence of blood surface tension. , 2007, Physiological research.

[41]  Guifu Zhang,et al.  Experiments in Rainfall Estimation with a Polarimetric Radar in a Subtropical Environment , 2002 .

[42]  R. Schmehl Advanced Modeling of Droplet Deformation and Breakup for CFD Analysis of Mixture Preparation , 2002 .

[43]  Michael C. Taylor,et al.  The effect of firearm muzzle gases on the backspatter of blood , 2011, International Journal of Legal Medicine.

[44]  Daniel Attinger,et al.  Fluid dynamics topics in bloodstain pattern analysis: comparative review and research opportunities. , 2013, Forensic science international.

[45]  R. Reitz,et al.  Modeling the effects of drop drag and breakup on fuel sprays. Technical paper , 1993 .

[46]  S. Charm,et al.  Viscometry of Human Blood for Shear Rates of 0-100,000 sec−1 , 1965, Nature.

[47]  O. Levenspiel,et al.  Drag coefficient and terminal velocity of spherical and nonspherical particles , 1989 .

[48]  K. Beard,et al.  A New Model for the Equilibrium Shape of Raindrops , 1987 .