We thank Susantha Wijesinghe who designed and constructed the image compression system we use. We acknowledge support from the NSF grant DMR-1208990.

<ol>
	<li>Marcus, G., Parsa, S., Kramel, S., Ni, R., Voth, G. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Measurements+of+the+Solid-body+Rotation+of+Anisotropic+Particles+in+3D+Turbulence.">Measurements of the Solid-body Rotation of Anisotropic Particles in 3D Turbulence.</a> New J. Phys. 16, 102001 (2014).</li><li>Bretherton, F. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=The+motion+of+rigid+particles+in+a+shear+flow+at+low+Reynolds+number.">The motion of rigid particles in a shear flow at low Reynolds number.</a> J. Fluid Mech. 14 (02), 284-304 (1962).</li><li>Oullette, N., Xu, H., Bodenschatz, E. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=A+quantitative+study+of+three-dimensional+Lagrangian+particle+tracking+algorithms.">A quantitative study of three-dimensional Lagrangian particle tracking algorithms.</a> Exp. in Fluids. 40 (2), 301-313 (2006).</li><li>Parsa, S., Calzavarini, E., Toschi, F., Voth, G. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Rotation+Rate+of+Rods+in+Turbulent+Fluid.">Rotation Rate of Rods in Turbulent Fluid.</a> Phys. Rev. Lett. 109 (13), 134501 (2012).</li><li>Parsa, S., Voth, G. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Inertial+Range+Scaling+in+Rotations+of+Long+Rods+in+Turbulence.">Inertial Range Scaling in Rotations of Long Rods in Turbulence.</a> Phys. Rev. Lett. 112 (2), 024501 (2014).</li><li>Tsai, R. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=A+versatile+camera+calibration+technique+for+high-accuracy+3d+machine+vision+metrology+using+off-the-shelf+tv+cameras+and+lenses.">A versatile camera calibration technique for high-accuracy 3d machine vision metrology using off-the-shelf tv cameras and lenses.</a> IEEE Journal of Robotics and Automation. 3 (4), 323-344 (1987).</li><li>Blum, D., Kunwar, S., Johnson, J., Voth, G. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Effects+of+nonuniversal+large+scales+on+conditional+structure+functions+in+turbulence.">Effects of nonuniversal large scales on conditional structure functions in turbulence.</a> Phys. Fluids. 22 (1), 015107 (2010).</li><li>Mann, J., Ott, S., Andersen, J. 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Instrum. 78 (2), 023704 (2007).</li><li>Goldstein, H., Poole, C., Safko, J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Classical Mechanics, 3rd Edition. , 134-180 (2002).</li><li>Parsa, S. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Rotational dynamics of rod particles in fluid flows. , (2013).</li><li>Wijesinghe, S. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Measurement of the effects of large scale anisotropy on the small scales of turbulence. , (2012).</li><li>Wallace, J., Foss, J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=The+Measurement+of+Vorticity+in+Turbulent+Flows.">The Measurement of Vorticity in Turbulent Flows.</a> Annu. 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Fluid Mech. 528, 87-118 (2005).</li><li>Frish, M., Webb, W. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Direct+measurement+of+vorticity+by+optical+probe.">Direct measurement of vorticity by optical probe.</a> J. Fluid Mech. 107, 173-200 (1981).</li><li>Zimmerman, R., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Tracking+the+dynamics+of+translation+and+absolute+orientation+of+a+sphere+in+a+turbulent+flow.">Tracking the dynamics of translation and absolute orientation of a sphere in a turbulent flow.</a> Rev. Sci. Instrum. 82 (3), 033906 (2011).</li><li>Zimmerman, R., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Rotational+Intermittency+and+Turbulence+Induced+Lift+Experienced+by+Large+Particles+in+a+Turbulent+Flow.">Rotational Intermittency and Turbulence Induced Lift Experienced by Large Particles in a Turbulent Flow.</a> Phys. Rev. Lett. 106 (15), 154501 (2011).</li><li>Klein, S., Gibert, M. a. t. h. i. e. u., B&#233;rut, A., Bodenschatz, E. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Simultaneous+3D+measurement+of+the+translation+and+rotation+of+finite-size+particles+and+the+flow+field+in+a+fully+developed+turbulent+water+flow.">Simultaneous 3D measurement of the translation and rotation of finite-size particles and the flow field in a fully developed turbulent water flow.</a> Meas. Sci. Technol. 24 (2), 1-10 (2013).</li><li>Bellani, G., Byron, M., Collignon, A., Meyer, C., Variano, E. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Shape+effects+on+turbulent+modulation+by+large+nearly+neutrally+buoyant+particles.">Shape effects on turbulent modulation by large nearly neutrally buoyant particles.</a> J. Fluid Mech. 712, 41-60 (2012).</li></ol>

The authors have no competing financial interests to disclose.

Measurements of the vorticity and rotation of particles in turbulent fluid flow have long been recognized as important goals in experimental fluid mechanics. The solid-body rotation of small spheres in turbulence is equal to half the fluid vorticity, but the rotational symmetry of spheres has made direct measurement of their solid-body rotation difficult. Traditionally, the fluid vorticity has been measured using complex, multi-sensor, hot-wire probes14. But these sensors only get single-point vorticity measurements in airflows that have large mean velocity. Other vorticity measurement methods have been developed. For example, Su and Dahm used flow field velocimetry based on scalar images15 and L&#252;thi, Tsinober, and Kinzelbach used 3D particle tracking velocimetry16. Measurements of vorticity in turbulence by tracking rotations of single particles were pioneered by Frish and Webb, who measured the rotations of solid spherical particles using a vorticity optical probe17. This probe uses small particles with planar crystals embedded that act as mirrors to create a beam whose direction changes as the particle rotates. Recently, methods have been developed for measuring the rotational motion of large spherical particles using imaging of patterns painted on the particles18,19 or fluorescent particles embedded in transparent hydrogel particles20. To track anisotropic particles, Bellani et al. have used custom-molded hydrogel particles21. Parsa et al. have tracked the rotations of segments of nylon threads5,6,12. The methods for measuring vorticity and particle rotations presented in this paper have advantages over these alternative methods. 3D-printed anisotropic particles can be small, with arm thicknesses down to 0.3 mm in diameter, and their rotations can still be resolved very accurately. Other methods traditionally require larger particles because they involve the resolution of structures on or within the particles themselves. In addition, the use of image compression systems allows for many more particle trajectories to be recorded and measured than would otherwise be reasonable. Having more measurements makes it possible to study rare events like those with very high rotation rates in Figure 5, which reveal intermittency phenomena of great interest to researchers.
Particle concentrations in these experiments were about 5 x 10-3 cm-3, which meant that typically only about 20% of images from the cameras had a particle. To study rare events, thousands of particle trajectories are typically required, which meant that hundreds of thousands of images of particles were needed. With these low concentrations, therefore, millions of images needed to be recorded to obtain an adequate volume of data. If real-time image compression systems were not used to facilitate data acquisition, this would require hundreds of TB of data storage and the analysis would be much more computationally intensive. Image compression systems decrease this load by factors of several hundred10. However, standard video recording would be adequate for higher particle densities and if data storage space is not an issue. If 100,000 particles of each type were ordered instead of 10,000, fewer images would, in principle, be needed to capture the same statistics. However, at higher particle densities particles begin to shadow one another more often. That is, there will be more times when there are particles between the laser and the particle in view, or between the particle in view and the camera. These shadowing events make measuring orientations throughout a track across the viewing volume more difficult and less reliable. For these reasons, lower particle concentrations were chosen for these experiments and image compression systems were therefore necessary.
There may be times when arm shadowing will affect the results of the nonlinear search algorithm. For certain orientations of the jack, arm shadowing causes there to be multiple minima in Euler angle space, which lead to indeterminacies in the measured orientations. This reduces the accuracy of orientation measurements for these particular orientations and occasionally leads to erroneously high measurements of the solid-body rotation rate, which pushes additional probability density towards the tail of the PDF in Figure 5. For jacks, whose arms are perpendicular to each other, this issue could be decreased by changing the angles of the cameras with respect to one another to be farther away from 90&#176;. If the configuration of the apparatus makes this change difficult to implement, one alternative is to change the geometry of the particles to decrease shadowing. This was the reason tetrads were chosen for experiments after those with jacks had been completed, and recent tetrad measurements have shown significantly improved orientation accuracy when compared to jacks.
The methods of 3D particle tracking presented here are not confined to this particular flow or the particle sizes and shapes we use. We have already begun experiments tracking tetrads and triads with much larger sizes using similar techniques. The use of high-speed cameras to measure particle orientations and rotations can be extended to a wide array of shapes and can be used for inertial particles as well as in the neutrally buoyant case presented here. Using more cameras would allow for an even wider array of potential particle shapes, as the primary limitations to this method are the resolution of the cameras and particles&#39; self-shadowing, as discussed in the previous paragraph.
In step 5.1.6 of the Protocol, we smooth Euler angles measurements by assuming that a particle would not rotate by more than half of an angle between arms over the course of two frames &#8212; that is, we assume that the accurate orientation measurement at frame i+1 retains the chosen symmetric orientation found for frame i. If the particle had rotated by more than half of one of these interior angles, then smoothing in this way would result in a sudden and incorrect reversal of the direction of rotation. In Ref. 5 we show that an upper limit on particle tumbling rate is:
<img alt="Equation 5" src="/files/ftp_upload/53599/53599eq5.jpg" />
So the largest tumbling rate (<img alt="Equation 6" src="/files/ftp_upload/53599/53599eq6.jpg" />) is <img alt="Equation 7" src="/files/ftp_upload/53599/53599eq7.jpg" /> which for <img alt="Equation 8" src="/files/ftp_upload/53599/53599eq8.jpg" /> sec is 16.2 sec-2. This is a root mean square (RMS) tumbling rate of 4.0 sec-1. Since we record images at 450 frames per second, particles would then typically rotate 0.009 radians between frames. The smallest interior angle of any of the particles in these experiments was <img alt="Figure 5" src="/files/ftp_upload/53599/53599divident.jpg" />, so this smoothing method would fail if particles tumble more than <img alt="Figure 5" src="/files/ftp_upload/53599/53599equal.jpg" /> radians between frames. Thus, we can accurately track particles with tumbling rates of more than 80 times the RMS, which is much faster than the&#160;<img alt="Equation 6" src="/files/ftp_upload/53599/53599squareroot.jpg" /> times the RMS that we actually observe in Figure 5.

In a recent publication, we introduced the use of particles made from multiple slender arms for measuring rotational motion of particles in turbulence1. These particles can be fabricated using 3D printers, and it is possible to accurately measure their position, orientation, and rotation rate using multiple cameras. Using tools from slender body theory, it can be shown that these particles have corresponding effective ellipsoids2, and the rotational motions of these particles are identical to those of their respective effective ellipsoids. Particles with symmetric arms of equal length rotate like spheres. One such particle is a jack, which has three mutually perpendicular arms attached at its center. Adjusting the relative lengths of the arms of a jack can form a particle equivalent to any tri-axial ellipsoid. If the length of one arm is set equal to zero, this creates a cross, whose equivalent ellipsoid is a disk. Particles made of slender arms take up a small fraction of the solid volume of their solid ellipsoidal counterparts. As a result, they sediment more slowly, making them easier to density match. This allows the study of much larger particles than is convenient with solid ellipsoidal particles. Additionally, imaging can be performed at much higher particle concentrations because the particles block a smaller fraction of the light from other particles.
In this paper, methods for fabrication and tracking of 3D-printed particles are documented. Tools for tracking the translational motion of spherical particles from particle positions as seen by multiple cameras have been developed by several groups3,4. Parsa et al.5 extended this approach to track rods using the position and orientation of the rods seen by multiple cameras. Here, we present methods for fabricating particles of a wide variety of shapes and reconstructing their 3D orientations. This offers the possibility to extend 3D tracking of particles with complex shapes to a wide range of new applications.
This technique has great potential for further development because of the wide range of particle shapes that can be designed. Many of these shapes have direct applications in environmental flows, where plankton, seeds, and ice crystals come in a vast array of shapes. Connections between particle rotations and fundamental small-scale properties of turbulent flows6 suggest that study of rotations of these particles provides new ways to look at the turbulent cascade process.

<table border="1" fo:keep-together.within-page="1" fo:keep-with-next.within-page="always">
	<tbody>
		<tr>
			<td>Condor Nd:YAG 50W laser</td>
			<td>Quantronics</td>
			<td>532-30-M</td>
			<td></td>
		</tr>
		<tr>
			<td>High speed camera</td>
			<td>Basler</td>
			<td>A504k</td>
			<td></td>
		</tr>
		<tr>
			<td>High speed camera</td>
			<td>Mikrotron</td>
			<td>EoSens Mc1362</td>
			<td></td>
		</tr>
		<tr>
			<td>Rhodamine-B</td>
			<td>ScienceLab.com</td>
			<td>SLR1465</td>
			<td></td>
		</tr>
		<tr>
			<td>Sodium Hydroxide</td>
			<td>Macron</td>
			<td>7708</td>
			<td>Pellets.</td>
		</tr>
		<tr>
			<td>500 Connex 3D printer</td>
			<td>Objet</td>
			<td></td>
			<td>Used to make smaller particles. Particles ordered from RP+M (rapid prototyping plus manufacturing).</td>
		</tr>
		<tr>
			<td>VeroClear</td>
			<td>Stratasys</td>
			<td>RGD810</td>
			<td>Objet build material.</td>
		</tr>
		<tr>
			<td>Form 1+ 3D printer</td>
			<td>Formlabs</td>
			<td></td>
			<td>Used to make larger particles.</td>
		</tr>
		<tr>
			<td>Clear Form 1 Photopolymer Resin</td>
			<td>Formlabs</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>Cylindrical and spherical lenses</td>
			<td></td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>200, 100, 50 mm macro camera lenses</td>
			<td></td>
			<td></td>
			<td>F-mount.</td>
		</tr>
		<tr>
			<td>Ultrasonic bath</td>
			<td>Sonicator</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>Calcium Chloride</td>
			<td>Spectrum Chemical Mfg. Corp.</td>
			<td>CAS 10043-52-2</td>
			<td>Pellets.</td>
		</tr>
		<tr>
			<td>LabVIEW System Design Software</td>
			<td>National Instruments</td>
			<td></td>
			<td>Used to trigger cameras, control grid, and trigger laser.</td>
		</tr>
		<tr>
			<td>XCAP Software</td>
			<td>EPIX</td>
			<td></td>
			<td>Used with LabVIEW to trigger cameras.</td>
		</tr>
		<tr>
			<td>MATLAB</td>
			<td>Mathworks</td>
			<td></td>
			<td>Used for all image and data analysis. Programs for extracting 3D orientations from multiple images are included with this publication.</td>
		</tr>
		<tr>
			<td>OpenPTV: Open Source Particle Tracking Velocimetry</td>
			<td>OpenPTV Consortium</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>ParaView</td>
			<td>Kitware</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>AutoCAD</td>
			<td>AutoDesk</td>
			<td></td>
			<td>Used to design all particles. Screenshots of particle designs are all of AutoCAD.</td>
		</tr>
		<tr>
			<td>Mesh with 0.040 x 0.053 inch holes</td>
			<td>Industrial Netting</td>
			<td>XN5170&#8211;43.5</td>
			<td></td>
		</tr>
		<tr>
			<td>Camera filters</td>
			<td>Schneider Optics</td>
			<td>B+W 040M</td>
			<td></td>
		</tr>
	</tbody>
</table>

methods for measuring the orientation and rotation rate of 3d-printed particles in turbulence

Experimental methods are presented for measuring the rotational and translational motion of anisotropic particles in turbulent fluid flows. 3D printing technology is used to fabricate particles with slender arms connected at a common center. Shapes explored are crosses (two perpendicular rods), jacks (three perpendicular rods), triads (three rods in triangular planar symmetry), and tetrads (four arms in tetrahedral symmetry). Methods for producing on the order of 10,000 fluorescently dyed particles are described. Time-resolved measurements of their orientation and solid-body rotation rate are obtained from four synchronized videos of their motion in a turbulent flow between oscillating grids with R&#955; = 91. In this relatively low-Reynolds number flow, the advected particles are small enough that they approximate ellipsoidal tracer particles. We present results of time-resolved 3D trajectories of position and orientation of the particles as well as measurements of their rotation rates.

Figure 3a shows an image of a tetrad from one of our cameras above a plot of the Euler angles obtained from a section of its trajectory (Figure 3c). In Figure 3b, the results of the orientation-finding algorithm, described in Protocol 5 - 5.3, are superimposed on the tetrad image. The arms of the tetrad in Figure 3a do not follow the simple intensity distributions that are used to create the model (Protocol 5.1.3.1). This is true for all of the particles. The observed intensity furthermore has a non-trivial dependence on the angles between the arms, the illumination, and the viewing direction12. The models do not include any of these factors but nonetheless produce very accurate measurements of particle orientations.
Once an orientation is found with a least-squares fit, the 3D coordinates of the particle center and the three Euler angles,&#160;(&#966;,&#160;&#952;,&#160;&#968;) , that specify its orientation matrix11 are saved. This is done for every frame where the particle is in view of all four cameras. These data enable the reconstruction of the complete trajectory of the particle across the viewing volume, as are shown in Figure 4 for a cross and a jack. Figure 4 was made using the Paraview open source visualization package and is based on measurements made with images from the experiments.
<img alt="Figure 3" src="/files/ftp_upload/53599/53599fig3.jpg" /> 
Figure 3. Reconstructed particle orientations from measured images. a) A sample image from one of the four cameras. The object shown is a tetrad, which has four arms at 109.5&#176; interior angles to one another. b) The same tetrad shown with the results of our orientation-finding algorithm. c) Measured Euler angles plotted as a function of time for a single trajectory. <a href="https://www-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/53599/53599fig3large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 4" src="/files/ftp_upload/53599/53599fig4.jpg" /> 
Figure 4. Reconstructed trajectories of a cross (a) and a jack (b) in three-dimensional turbulence. (a) The two different color sheets trace the path of the two arms of the particle through space over time. The length of the track is 336 frames, or 5.7&#160;&#964;&#951;, and a cross is shown every 15 frames. (b) The blue, orange, and blue-green paths trace the paths of the three arms of the jack as the particle rotates and moves through the fluid. The dark green line denotes the path of the jack&#39;s center. The length of the particle track is 1,025 frames, or 17.5&#160;&#964;&#951;, and a jack is shown every 50 frames. (Note: Neither the crosses nor the jacks above are drawn to scale.) Figure from 1, where it is Figure 3. <a href="https://www-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/53599/53599fig4large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
Two different but related quantities based on particle orientations are calculated over the entire trajectory: tumbling rate and solid-body rotation rate. Tumbling rate, <img alt="Equation 1" src="/files/ftp_upload/53599/53599pdot.jpg" /> , is the rate of change of the unit vector defining the orientation of the particle. In previous measurements of rods, <img alt="Equation 1" src="/files/ftp_upload/53599/53599p.jpg" /> was defined as the axis of symmetry along the rod; for crosses and triads,&#160;<img alt="Equation 1" src="/files/ftp_upload/53599/53599p.jpg" /> is normal to the plane of the arms; for jacks and tetrads,&#160;<img alt="Equation 1" src="/files/ftp_upload/53599/53599p.jpg" /> is along one of the arms. Because rotation along the axis of rods cannot be directly measured, studies of the rotations of rods in turbulence have largely been limited to measuring the tumbling rate. This is not an issue for any of the particles in these experiments. All rotations of these particles can be measured and, with orientation measurements smoothed along a particle&#39;s trajectory, the full solid-body rotation rate vector,&#160;<img alt="Equation 1" src="/files/ftp_upload/53599/53599ws.jpg" /> , can be found.
To extract the solid-body rotation rate from measured particles orientations, smoothing needs to be done over several time steps. The problem is to find the rotation matrix <img alt="Equation 1" src="/files/ftp_upload/53599/53599R.jpg" /> that relates an initial orientation&#160;<img alt="Figure 5" height="19" src="/files/ftp_upload/53599/53599oti.jpg" width="37" />&#160; to the measured orientations <img alt="Figure 5" src="/files/ftp_upload/53599/53599ot.jpg" /> at a sequence of time steps:
<img alt="Equation 1" src="/files/ftp_upload/53599/53599eq1.jpg" />
where&#160; <img alt="Figure 5" src="/files/ftp_upload/53599/53599tf.jpg" /> is the period between images and&#160;<img alt="Figure 5" src="/files/ftp_upload/53599/53599ti.jpg" /> is the time of the initial frame. In Marcus et al.1, we used a nonlinear least-squares fit to determine the six Euler angles defining the initial orientation matrix, <img alt="Figure 5" height="19" src="/files/ftp_upload/53599/53599oti.jpg" width="37" />, and the rotation matrix over a single time step,&#160;<img alt="Equation 1" src="/files/ftp_upload/53599/53599R.jpg" />, that best match the measured orientation matrices as a function of time. More recent work has shown that this algorithm sometimes has difficulty when the rotation rate is small because the nonlinear search is exploring the region where the Euler angles are approximately equal to zero and are degenerate. In the case where the rotation in a time step is sufficiently small, <img alt="Equation 1" src="/files/ftp_upload/53599/53599R.jpg" /> can be linearized using&#160;<img alt="Equation 2" src="/files/ftp_upload/53599/53599eq2.jpg" />, where &#937; is a rotation rate matrix. As described in the Discussion below, these experiments are in this low rotation limit, so &#937; can be found from the measured <img alt="Figure 5" src="/files/ftp_upload/53599/53599ot.jpg" /> using a linear least squares fit.
From the measured rotation matrix over a time step, <img alt="Equation 1" src="/files/ftp_upload/53599/53599R.jpg" />, we can extract the solid-body rotation rate and the tumbling rate. By Euler&#39;s theorem11 <img alt="Equation 1" src="/files/ftp_upload/53599/53599R.jpg" /> can be decomposed as a rotation by an angle&#160;&#934; about the solid-body rotation axis,&#160;<img alt="Figure 5" src="/files/ftp_upload/53599/53599wns.jpg" />. The magnitude of the solid-body rotation rate is&#160;<img alt="Equation 3" src="/files/ftp_upload/53599/53599eq3.jpg" />. The tumbling rate is the component of the solid-body rotation rate perpendicular to the orientation of the particle, and so it can be calculated as&#160;<img alt="Equation 4" src="/files/ftp_upload/53599/53599eq4.jpg" />. Figure 5 compares PDFs of the measured mean square tumbling rate for crosses and jacks to direct numerical simulations of spheres. Small jacks rotate just like spheres in fluid flows1, so the fact that the PDF for jacks agrees with the simulated PDF for spheres demonstrates that the experiments are able to capture the rare high rotation events that occur in turbulent flows.
<img alt="Figure 5" src="/files/ftp_upload/53599/53599fig5.jpg" /> 
Figure 5. PDF of mean-square tumbling rate. The probability density function of the measured mean-square tumbling rate for our crosses (red squares) and jacks (blue circles) as well as direct numerical simulations of spheres (solid line). Error bars include the random error due to limited statistical sampling estimated by dividing the data set into subsets, as well as the systematic error that results from the fit length dependence of the tumbling rate, which is estimated by performing the analysis at a range of fit lengths. Figure from 1 where it is Figure 5. <a href="https://www-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/53599/53599fig5large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>

Watch this Scientific Journal Video about Methods for Measuring the Orientation and Rotation Rate of 3D-printed Particles in Turbulence at JoVE.com

Methods for Measuring the Orientation and Rotation Rate of 3D-printed Particles in Turbulence

We use 3D printing to fabricate anisotropic particles in the shapes of jacks, crosses, tetrads, and triads, whose alignments and rotations in turbulent fluid flow can be measured from multiple simultaneous video images.

Experimental methods are presented for measuring the rotational and translational motion of anisotropic particles in turbulent fluid flows. 3D printing ...

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10.0K Views.  Wesleyan University. We use 3D printing to fabricate anisotropic particles in the shapes of jacks, crosses, tetrads, and triads, whose alignments and rotations in turbulent fluid flow can be measured from multiple simultaneous video images.

Video: Methods for Measuring the Orientation and Rotation Rate of 3D-printed Particles in Turbulence

Encapsulation and Permeability Characteristics of Plasma Polymerized Hollow Particles

In this protocol, core-shell nanostructures are synthesized by plasma enhanced chemical vapor deposition. We produce an amorphous barrier by plasma polymerization of isopropanol on various solid substrates, including silica and potassium chloride. This versatile technique is used to treat nanoparticles and nanopowders with sizes ranging from 37 nm to 1 micron, by depositing films whose thickness can be anywhere from 1 nm to upwards of 100 nm. Dissolution of the core allows us to study the rate of permeation through the film. In these experiments, we determine the diffusion coefficient of KCl through the barrier film by coating KCL nanocrystals and subsequently monitoring the ionic conductivity of the coated particles suspended in water. The primary interest in this process is the encapsulation and delayed release of solutes. The thickness of the shell is one of the independent variables by which we control the rate of release. It has a strong effect on the rate of release, which increases from a six-hour release (shell thickness is 20 nm) to a long-term release over 30 days (shell thickness is 95 nm). The release profile shows a characteristic behavior: a fast release (35% of the final materials) during the first five minutes after the beginning of the dissolution, and a slower release till all of the core materials come out.

We have used plasma enhanced chemical vapor deposition to deposit thin films ranging from a few nm to several 100 nm on nano-sized particles of various materials. We subsequently etch the core material to produce hollow nanoshells whose permeability is controlled by the thickness of the shell. We characterize the permeability of these coatings to small solutes and demonstrate that these barriers can provide sustained release of the core material over several days.

In this protocol, core-shell nanostructures are synthesized by plasma enhanced chemical vapor deposition. We produce an amorphous barrier by plasma ...

Experimental Measurement of Settling Velocity of Spherical Particles in Unconfined and Confined Surfactant-based Shear Thinning Viscoelastic Fluids

An experimental study is performed to measure the terminal settling velocities of spherical particles in surfactant based shear thinning viscoelastic (VES) fluids. The measurements are made for particles settling in unbounded fluids&#160;and fluids between parallel walls. VES fluids over a wide range of rheological properties are prepared and rheologically characterized. The rheological characterization involves steady shear-viscosity and dynamic oscillatory-shear measurements to quantify the viscous and elastic properties respectively. The settling velocities under unbounded conditions are measured in beakers having diameters at least 25x the diameter of particles. For measuring settling velocities between parallel walls, two experimental cells with different wall spacing are constructed. Spherical particles of varying sizes are gently dropped in the fluids and allowed to settle. The process is recorded with a high resolution video camera and the trajectory of the particle is recorded using image analysis software. Terminal settling velocities are calculated from the data.
The impact of elasticity on settling velocity in unbounded fluids is quantified by comparing the experimental settling velocity to the settling velocity calculated by the inelastic drag predictions of Renaud et al.1&#160;Results show that elasticity of fluids can increase or decrease the settling velocity. The magnitude of reduction/increase is a function of the rheological properties of the fluids and properties of particles. Confining walls are observed to cause a retardation effect on settling and the retardation is measured in terms of wall factors.

This paper demonstrates the experimental procedure to measure terminal settling velocities of spherical particles in surfactant-based shear thinning viscoelastic fluids. Fluids over a wide range of rheological properties are prepared and settling velocities are measured for a range of particle sizes in unbounded fluids and fluids between parallel walls.

An experimental study is performed to measure the terminal settling velocities of spherical particles in surfactant based shear thinning viscoelastic ...

Automation of Mode Locking in a Nonlinear Polarization Rotation Fiber Laser through Output Polarization Measurements

When a laser is mode-locked, it emits a train of ultra-short pulses at a repetition rate determined by the laser cavity length. This article outlines a new and inexpensive procedure to force mode locking in a pre-adjusted nonlinear polarization rotation fiber laser. This procedure is based on the detection of a sudden change in the output polarization state when mode locking occurs. This change is used to command the alignment of the intra-cavity polarization controller in order to find mode-locking conditions. More specifically, the value of the first Stokes parameter varies when the angle of the polarization controller is swept and, moreover, it undergoes an abrupt variation when the laser enters the mode-locked state. Monitoring this abrupt variation provides a practical easy-to-detect signal that can be used to command the alignment of the polarization controller and drive the laser towards mode locking. This monitoring is achieved by feeding a small portion of the signal to a polarization analyzer measuring the first Stokes parameter. A sudden change in the read out of this parameter from the analyzer will occur when the laser enters the mode-locked state. At this moment, the required angle of the polarization controller is kept fixed. The alignment is completed. This procedure provides an alternate way to existing automating procedures that use equipment such as an optical spectrum analyzer, an RF spectrum analyzer, a photodiode connected to an electronic pulse-counter or a nonlinear detecting scheme based on two-photon absorption or second harmonic generation. It is suitable for lasers mode locked by nonlinear polarization rotation. It is relatively easy to implement, it requires inexpensive means, especially at a wavelength of 1550 nm, and it lowers the production and operation costs incurred in comparison to the above-mentioned techniques.

A protocol to detect and automate mode locking in a pre-adjusted nonlinear polarization rotation fiber laser is presented. The detection of a sudden change in the output polarization state when mode locking occurs is used to command the alignment of an intra-cavity polarization controller in order to find mode-locking conditions.

When a laser is mode-locked, it emits a train of ultra-short pulses at a repetition rate determined by the laser cavity length. This article outlines a ...

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow

3D-PTV is a quantitative flow measurement technique that aims to track the Lagrangian paths of a set of particles in three dimensions using stereoscopic recording of image sequences. The basic components, features, constraints and optimization tips of a 3D-PTV topology consisting of a high-speed camera with a four-view splitter are described and discussed in this article. The technique is applied to the intermediate flow field (5 &#60;x/d &#60;25) of a circular jet at Re &#8776; 7,000. Lagrangian flow features and turbulence quantities in an Eulerian frame are estimated around ten diameters downstream of the jet origin and at various radial distances from the jet core. Lagrangian properties include trajectory, velocity and acceleration of selected particles as well as curvature of the flow path, which are obtained from the Frenet-Serret equation. Estimation of the 3D velocity and turbulence fields around the jet core axis at a cross-plane located at ten diameters downstream of the jet is compared with literature, and the power spectrum of the large-scale streamwise velocity motions is obtained at various radial distances from the jet core.

A three-dimensional particle tracking velocimetry (3D-PTV) system based on a high-speed camera with a four-view splitter is described here. The technique is applied to a jet flow from a circular pipe in the vicinity of ten diameters downstream at Reynolds number Re &#8776; 7,000.

3D-PTV is a quantitative flow measurement technique that aims to track the Lagrangian paths of a set of particles in three dimensions using stereoscopic ...

Frequency Mixing Magnetic Detection Scanner for Imaging Magnetic Particles in Planar Samples

The setup of a planar Frequency Mixing Magnetic Detection (p-FMMD) scanner for performing Magnetic Particles Imaging (MPI) of flat samples is presented. It consists of two magnetic measurement heads on both sides of the sample mounted on the legs of a u-shaped support. The sample is locally exposed to a magnetic excitation field consisting of two distinct frequencies, a stronger component at about 77 kHz and a weaker field at 61 Hz. The nonlinear magnetization characteristics of superparamagnetic particles give rise to the generation of intermodulation products. A selected sum-frequency component of the high and low frequency magnetic field incident on the magnetically nonlinear particles is recorded by a demodulation electronics. In contrast to a conventional MPI scanner, p-FMMD does not require the application of a strong magnetic field to the whole sample because mixing of the two frequencies occurs locally. Thus, the lateral dimensions of the sample are just limited by the scanning range and the supports. However, the sample height determines the spatial resolution. In the current setup it is limited to 2 mm. As examples, we present two 20 mm &#215; 25 mm p-FMMD images acquired from samples with 1 &#181;m diameter maghemite particles in silanol matrix and with 50 nm magnetite particles in aminosilane matrix. The results show that the novel MPI scanner can be applied for analysis of thin biological samples and for medical diagnostic purposes.

A scanner for imaging magnetic particles in planar samples was developed using the planar frequency mixing magnetic detection technique. The magnetic intermodulation product response from the nonlinear nonhysteretic magnetization of the particles is recorded upon a two-frequency excitation. It can be used to take 2D images of thin biological samples.

The setup of a planar Frequency Mixing Magnetic Detection (p-FMMD) scanner for performing Magnetic Particles Imaging (MPI) of flat samples is presented. ...

A High Performance Impedance-based Platform for Evaporation Rate Detection

This paper describes the method of a novel impedance-based platform for the detection of the evaporation rate. The model compound hyaluronic acid was employed here for demonstration purposes. Multiple evaporation tests on the model compound as a humectant with various concentrations in solutions were conducted for comparison purposes. A conventional weight loss approach is known as the most straightforward, but time-consuming, measurement technique for evaporation rate detection. Yet, a clear disadvantage is that a large volume of sample is required and multiple sample tests cannot be conducted at the same time. For the first time in literature, an electrical impedance sensing chip is successfully applied to a real-time evaporation investigation in a time sharing, continuous and automatic manner. Moreover, as little as 0.5 ml of test samples is required in this impedance-based apparatus, and a large impedance variation is demonstrated among various dilute solutions. The proposed high-sensitivity and fast-response impedance sensing system is found to outperform a conventional weight loss approach in terms of evaporation rate detection.

This paper presents an impedance-based apparatus for evaporation rate detection of solutions. It offers clear advantages over a conventional weight loss approach: a fast response, high-sensitivity detection, a small sample requirement, multiple sample measurements, and easy disassembly for cleaning and reuse purposes.

This paper describes the method of a novel impedance-based platform for the detection of the evaporation rate. The model compound hyaluronic acid was ...

Subsurface Defect Localization by Structured Heating Using Laser Projected Photothermal Thermography

The presented method is used to locate subsurface defects oriented perpendicularly to the surface. To achieve this, we create destructively interfering thermal wave fields that are disturbed by the defect. This effect is measured and used to locate the defect. We form the destructively interfering wave fields by using a modified projector. The original light engine of the projector is replaced with a fiber-coupled high-power diode laser. Its beam is shaped and aligned to the projector&#39;s spatial light modulator and optimized for optimal optical throughput and homogeneous projection by first characterizing the beam profile, and, second, correcting it mechanically and numerically. A high-performance infrared (IR) camera is set up according to the tight geometrical situation (including corrections of the geometrical image distortions) and the requirement to detect weak temperature oscillations at the sample surface. Data acquisition can be performed once a synchronization between the individual thermal wave field sources, the scanning stage, and the IR camera is established by using a dedicated experimental setup which needs to be tuned to the specific material being investigated. During data post-processing, the relevant information on the presence of a defect below the surface of the sample is extracted. It is retrieved from the oscillating part of the acquired thermal radiation coming from the so-called depletion line of the sample surface. The exact location of the defect is deduced from the analysis of the spatial-temporal shape of these oscillations in a final step. The method is reference-free and very sensitive to changes within the thermal wave field. So far, the method has been tested with steel samples but is applicable to different materials as well, in particular to temperature sensitive materials.

This method aims at locating vertical subsurface defects. Here, we couple a laser with a spatial light modulator and trigger its video input to heat a sample surface deterministically with two anti-phased modulated lines while acquiring highly resolved thermal images. The defect position is retrieved from evaluating thermal wave interference minima.

The presented method is used to locate subsurface defects oriented perpendicularly to the surface. To achieve this, we create destructively interfering ...

A 3D-printed Chamber for Organic Optoelectronic Device Degradation Testing

In this manuscript, we outline the manufacture of a small, portable, easy-to-use atmospheric chamber for organic and perovskite optoelectronic devices, using 3D-printing. As these types of devices are sensitive to moisture and oxygen, such a chamber can aid researchers in characterizing the electronic and stability properties. The chamber is intended to be used as a temporary, reusable, and stable environment with controlled properties (including humidity, gas introduction, and temperature). It can be used to protect air-sensitive materials or to expose them to contaminants in a controlled way for degradation studies. To characterize the properties of the chamber, we outline a simple procedure to determine the water vapor transmission rate (WVTR) using relative humidity as measured by a standard humidity sensor. This standard operating procedure, using a 50% infill density of polylactic acid (PLA), results in a chamber that can be used for weeks without any significant loss of device properties. The versatility and ease of use of the chamber allows it to be adapted to any characterization condition that requires a compact-controlled atmosphere.

Here, we present a protocol for the design, manufacture, and use of a simple, versatile 3D-printed and controlled atmospheric chamber for the optical and electrical characterization of air-sensitive organic optoelectronic devices.

In this manuscript, we outline the manufacture of a small, portable, easy-to-use atmospheric chamber for organic and perovskite optoelectronic devices, ...

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses

We demonstrate the use of two nuclear-based analytical methods that can follow the modifications of microstructural arrangement of iron-based metallic glasses (MGs). Despite their amorphous nature, the identification of hyperfine interactions unveils faint structural modifications. For this purpose, we have employed two techniques that utilize nuclear resonance among nuclear levels of a stable 57Fe isotope, namely M&#246;ssbauer spectrometry and nuclear forward scattering (NFS) of synchrotron radiation. The effects of heat treatment upon (Fe2.85Co1)77Mo8Cu1B14 MG are discussed using the results of ex situ and in situ experiments, respectively. As both methods are sensitive to hyperfine interactions, information on structural arrangement as well as on magnetic microstructure is readily available. M&#246;ssbauer spectrometry performed ex situ describes how the structural arrangement and magnetic microstructure appears at room temperature after the annealing under certain conditions (temperature, time), and thus this technique inspects steady states. On the other hand, NFS data are recorded in situ during dynamically changing temperature and NFS examines transient states. The use of both techniques provides complementary information. In general, they can be applied to any suitable system in which it is important to know its steady state but also transient states.

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses

Here, we present a protocol to describe ex situ and in situ investigations of structural transformations in metallic glasses. We employed nuclear-based analytical methods which inspect hyperfine interactions. We demonstrate the applicability of M&#246;ssbauer spectrometry and nuclear forward scattering of synchrotron radiation during temperature-driven experiments.

We demonstrate the use of two nuclear-based analytical methods that can follow the modifications of microstructural arrangement of iron-based metallic ...

Applicability Analysis of Assessment Methods for Morphological Parameters of Corroded Steel Bars

The irregular and uneven residual sections along the length of a corroded steel bar substantially change its mechanical properties and significantly dominate the safety and performance of an existing concrete structure. As a result, it is important to measure the geometry and amount of corrosion of a steel bar in a structure properly to assess the residual bearing capacity and service life of the structure. This paper introduces and compares five different methods for measuring the geometry and amount of corrosion of a steel bar. A single 500 mm long and 14 mm diameter steel bar is the specimen that is subjected to accelerated corrosion in this protocol. Its morphology and the amount of corrosion were carefully measured before and after using mass loss measurements, a Vernier caliper, drainage measurements, 3D scanning, and X-ray micro-computed tomography (XCT). The applicability and suitability of these different methods were then evaluated. The results show that the Vernier caliper is the best choice for measuring the morphology of a non-corroded bar, while 3D scanning is the most suitable for quantifying the morphology of a corroded bar.

This paper measures the geometry and the amount of corrosion of a steel bar using different methods: mass loss, calipers, drainage measurements, 3D scanning, and X-ray micro-computed tomography (XCT).

The irregular and uneven residual sections along the length of a corroded steel bar substantially change its mechanical properties and significantly ...