The authors are thankful to unknown referees for valuable advice and to Sukyung Choi, Byeongwoo Ko and Baekkyoung Shin for the collaboration in setting up the experiments. This work was supported by the Brain Busan 21 Project in 2017.

1. Incipient Particle Motion in the Creeping Flow Limit.
NOTE: The measurements are conducted in a rotational rheometer that has been modified for this specific application.
<ol>
	<li>Preparing the Rheometer.
	<ol>
		<li>Connect the air supply to the rheometer in order to avoid damaging the air bearings. Open the valve besides the air filters until a pressure of approximately 5 bars in the system is achieved.</li>
		<li>Connect the fluid circulator to the measuring plate. En...

The authors have nothing to disclose

We present two different experimental methods for characterizing the incipient particle motion as a function of the sediment bed geometry. For that purpose, we use a monolayer of spheres regularly arranged according to a triangular or quadratic symmetry in such a way that the geometrical parameter simplifies to a single geometry. In the creeping flow limit, we describe the experimental method using a rotational rotameter to induce the laminar shear flow as in previous studies39,<sup cla...

Incipient particle motion is encountered in a wide range of industrial and natural processes. Environmental examples include the initial process of sediment transport in river and oceans, bed erosion or dune formation among others 1,2,3. Pneumatic conveying4, removal of pollutants or cleaning of surfaces5,6 are typical industrial applications involving the onset of particle motion.
Due to the broad range of applications, the onset of particle motion has been extensively studied over a century, mostly under turbulent conditions7,8,9,10,11,12,13,14,15. Many experimental approaches have been applied to determine the threshold for the onset of motion. The studies include parameters such as the particle Reynolds number13,16,17,18,19,20, the relative flow submergence21,22,23,24 or geometrical factors as the angle of repose16,18,25, exposure to the flow26,27,28,29, relative grain protrusion29 or streamwise bed slope30.
The current data for the threshold including turbulent conditions are broadly scattered12,31 and the results often seem inconsistent24. This is mostly due to the inherent complexity of controlling or determining flow parameters under turbulent conditions13,14. Besides, the threshold for sediment motion strongly depends on the mode of motion, i.e. sliding, rolling or lifting17 and the criterion to characterize the incipient motion31. The latter may be ambiguous in an erodible sediment bed.
During the last decade, experimental researchers have studied incipient particle motion in laminar flows32,33,34,35,36,37,38,39,40,41,42,43,44, where the wide spectrum of length scales interacting with the bed is avoided45. In many practical scenarios implying sedimentation, the particles are quite small and the particle Reynolds number remains lower than about 546. On the other hand, laminar flows are able to generate geometric patterns as ripples and dunes as turbulent flows do42,47. Similitudes in both regimens have been shown to reflect analogies in the underlying physics47 so important insight for the particle transport can be obtained from a better controlled experimental system48.
In laminar flow, Charru et al. noticed that the local rearrangement of a granular bed of uniformly sized beads, so-called bed armouring, resulted in a progressive increase of the threshold for the onset of motion until saturated conditions were achieved32. Literature, however, reveals different thresholds for saturated conditions in irregularly arranged sediment beds depending on the experimental set-up36,44. This scattering may be due to the difficulty of controlling particle parameters such as orientation, protrusion level and compactness of the sediments.
The main goal of this manuscript is to describe in detail how to characterize the incipient motion of single spheres as a function of geometrical properties of the horizontal sediment bed. For that purpose, we use regular geometries, consisting of monolayers of fixed beads regularly arranged according to triangular or quadratic configurations. Regular substrates similar to that we use are found in applications such as for the template-assembly of particles in microfluidic assays49, self-assembly of microdevices in confined structured geometries50 or intrinsic particle-induced transport in microchannels51. More importantly, using regular substrates allows us to highlight the impact of local geometry and orientation and to avoid any dubiety about the role of the neighborhood.
In laminar flow, we observed that the critical Shields number increased by 50% only depending on the spacing between the substrate spheres and thus on the exposure of the bead to the flow38. Similarly, we found that the critical Shields number changed by up to a factor of two depending on the orientation of the substrate to the flow direction38. We noticed that immobile neighbors only affect the onset of the mobile bead if they were closer than about three particle diameters41. Triggered by the experiment findings, we have recently presented a rigorous analytical model that predicts the critical Shields number in the creeping flow limit40. The model covers the onset of motion from highly exposed to hidden beads.
The first part of this manuscript deals with the description of the experimental procedure used in previous studies at shear Reynolds number, Re*, lower than 1. The laminar flow is induced with a rotational rheometer with a parallel configuration. In this low Reynolds number limit, the particle is not supposed to experience any velocity fluctuation20 and the system matches the so-called hydraulically smooth flow where the particle is submerged within the viscous sublayer.
Once incipient motion at laminar flow is established, the role of turbulence can become clearer. Motivated by this idea, we introduce a novel experimental procedure in the second part of the protocol. Using a G&#246;ttingen low-speed wind tunnel with open jet test section, the critical Shields number can be determined in a wide range of Re* including the hydraulically transitional flow and the turbulent regime. The experimental results can provide important insight about how forces and torques act on a particle due to the turbulent flow depending on the substrate geometry. Besides, these results can be used as a benchmark for more sophisticated models at high Re* in a similar way that past work in laminar flow has been used to feed semi probabilistic models52 or to validate recent numerical models53. We present some representative examples of applications at Re* ranging from 40 to 150.
The incipient criterion is established as the motion of the single particle from its initial equilibrium position to the next one. Image processing is used to determine the mode of onset of motion, i.e. rolling, sliding, lifting39,41. For that purpose, the angle of rotation of mobile spheres that were manually marked is detected. The algorithm tracks the position of the marks and compares it with the center of the sphere. A preliminary set of experiments was conducted in both experimental set-ups to clarify that the critical Shields number remains independent of finite size effects of the set-up and relative flow submergence. The experimental methods are thus designed to exclude any other parameter dependent on the critical Shields number beyond Re* and geometrical properties of the sediment bed. The Re* is varied using different fluid-particle combinations. The critical Shields number is characterized as a function of the burial degree, <img alt="Equation 01" src="/files/ftp_upload/57238/57238eq001.jpg" />, defined by Martino et al.37 as <img alt="Equation 02" src="/files/ftp_upload/57238/57238eq002.jpg" /> where <img alt="Equation 03" src="/files/ftp_upload/57238/57238eq003.jpg" /> is the angle of repose, i.e. the critical angle at which motion occurs54, and <img alt="Equation 04" src="/files/ftp_upload/57238/57238eq004.jpg" /> is the exposure degree, defined as the ratio between the cross-sectional area effectively exposed to the flow to the total cross-sectional area of the mobile bead.

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		<tr height="21">
			<td height="21" style="height:21px;width:368px;">MCR 302 Rotational Rheometer</td>
			<td style="width:255px;">Antoon Par</td>
			<td style="width:471px;">Induction of shear laminar flow</td>
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		<tr height="21">
			<td height="21" style="height:21px;width:368px;">Measuring Plate PP25</td>
			<td style="width:255px;">Antoon Par</td>
			<td>Induction of shear laminar flow</td>
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		<tr height="21">
			<td height="21" style="height:21px;width:368px;">Peltier System P-PTD 200</td>
			<td style="width:255px;">Antoon Par</td>
			<td>Keep temperature of silicon oils constant in the system at laminar flow</td>
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			<td height="42" style="height:42px;width:368px;">Silicone oils with viscosities of approx. 10 and 100 mPas</td>
			<td style="width:255px;">Basildon Chemicals</td>
			<td>Fluid used to induced the shear in the particles</td>
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		<tr height="21">
			<td height="21" style="height:21px;width:368px;">Soda-lime glass beads of (405.9 &#177; 8.7) &#956;m</td>
			<td style="width:255px;">The Technical Glass Company</td>
			<td>Construction of the regular substrates for laminar flow conditions</td>
		</tr>
		<tr height="42">
			<td height="42" style="height:42px;width:368px;">Opto Zoom 70 Module 0.3x-2.2x</td>
			<td style="width:255px;">WEISS IMAGING AND SOLUTIONS GmbH</td>
			<td>Imaging system for recording the bead motion in the rheometer</td>
		</tr>
		<tr height="42">
			<td height="42" style="height:42px;width:368px;">2 x TV-Tube 1.0x, D=35 mm, L=146.5 mm</td>
			<td style="width:255px;">WEISS IMAGING AND SOLUTIONS GmbH</td>
			<td>Imaging system for recording the bead motion in the rheometer</td>
		</tr>
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			<td height="42" style="height:42px;width:368px;">UI-1220SE CMOS Camera</td>
			<td style="width:255px;">IDS Imaging Development Systems GmbH</td>
			<td>Imaging system for recording the bead motion in the rheometer</td>
		</tr>
		<tr height="42">
			<td height="42" style="height:42px;width:368px;">UI-3590CP CMOS Camera</td>
			<td style="width:255px;">IDS Imaging Development Systems GmbH</td>
			<td>Imaging system for recording the bead motion in the rheometer</td>
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		<tr height="21">
			<td height="21" style="height:21px;width:368px;">Volpi IntraLED 3 - LED light source&#160;</td>
			<td style="width:255px;">Volpi USA</td>
			<td>Imaging system for recording the bead motion in the rheometer</td>
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		<tr height="21">
			<td height="21" style="height:21px;width:368px;">Active light guide diameter 5mm</td>
			<td style="width:255px;">Volpi USA</td>
			<td>Imaging system for recording the bead motion in the rheometer</td>
		</tr>
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			<td height="21" style="height:21px;width:368px;">300 Watt Xenon Arc Lamp</td>
			<td style="width:255px;">Newport Corporation</td>
			<td>Imaging system for recording the bead motion in the rheometer</td>
		</tr>
		<tr height="42">
			<td height="42" style="height:42px;width:368px;">Wind-tunnel with open jet test section, G&#246;ttingen type&#160;</td>
			<td style="width:255px;">Tintschl BioEnergie und Str&#246;mungstechnik AG</td>
			<td>Induction of turbulent flow</td>
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		<tr height="21">
			<td height="21" style="height:21px;width:368px;">Glass spheres of (2.00 &#177; 0.10) mm</td>
			<td style="width:255px;">Gloches South Korea</td>
			<td>Construction of the regular substrates for turbulent flow conditions</td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;width:368px;">Alumina spheres of (5.00 &#177; 0.25) mm</td>
			<td style="width:255px;">Gloches South Korea</td>
			<td>Targeted bead for experiments</td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;width:368px;">CTA Anemometer DISA 55M01</td>
			<td style="width:255px;">Disa Elektronik A/S&#160;</td>
			<td>Measurement of&#160; flow velocity in the wind tunnel</td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;width:368px;">Miniaure Wire Probe Type 55P15</td>
			<td style="width:255px;">Dantec Dynamics</td>
			<td>Measurement of&#160; flow velocity in the wind tunnel</td>
		</tr>
		<tr height="42">
			<td height="42" style="height:42px;width:368px;">HMO2022 Digital Oscilloscope, 2 Analogue. Ch., 200MHz</td>
			<td style="width:255px;">Rohde &#38; Schwarz</td>
			<td>Measurement of&#160; flow velocity in the wind tunnel</td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;width:368px;">Phantom Miro eX1 High-speed Camera</td>
			<td style="width:255px;">Vision Research IncVis</td>
			<td>Imaging system for recording the bead motion in the wind-tunnel</td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;width:368px;">Canon ef 180mm f/3.5 l usm macro lens</td>
			<td style="width:255px;">Canon</td>
			<td>Imaging system for recording the bead motion in the wind-tunnel</td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;width:368px;">Table LED Lamp</td>
			<td style="width:255px;">Gloches South Korea</td>
			<td>Imaging system for recording the bead motion in the wind-tunnel</td>
		</tr>
	</tbody>
</table>

visually based characterization of the incipient particle motion in regular substrates: from laminar to turbulent conditions

Two different experimental methods for determining the threshold of particle motion as a function of geometrical properties of the bed from laminar to turbulent flow conditions are presented. For that purpose, the incipient motion of a single bead is studied on regular substrates that consist of a monolayer of fixed spheres of uniform size that are regularly arranged in triangular and quadratic symmetries. The threshold is characterized by the critical Shields number. The criterion for the onset of motion is defined as the displacement from the original equilibrium position to the neighboring one. The displacement and the mode of motion are identified with an imaging system. The laminar flow is induced using a rotational rheometer with a parallel disk configuration. The shear Reynolds number remains below 1. The turbulent flow is induced in a low-speed wind tunnel with open jet test section. The air velocity is regulated with a frequency converter on the blower fan. The velocity profile is measured with a hot wire probe connected to a hot film anemometer. The shear Reynolds number ranges between 40 and 150. The logarithmic velocity law and the modified wall law presented by Rotta are used to infer the shear velocity from the experimental data. The latter is of special interest when the mobile bead is partially exposed to the turbulent flow in the so-called hydraulically transitional flow regime. The shear stress is estimated at onset of motion. Some illustrative results showing the strong impact of the angle of repose, and the exposure of the bead to shear flow are represented in both regimes.

Figure 1(a) represents a sketch of the experimental set-up used to characterize the critical Shields number in the creeping flow limit, Section 1 of the protocol. The measurements are conducted in a rotational rheometer that was modified for this specific application. A transparent Plexiglas plate of 70 mm in diameter was carefully fixed to a parallel plate of 25 mm in diameter. The inertia of the measuring system was therefore readjusted bef...

Watch this Scientific Journal Video about Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions at JoVE.com

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions

Two different methods for characterizing the incipient particle motion of a single bead as a function of the sediment bed geometry from laminar to turbulent flow are presented.

Two different experimental methods for determining the threshold of particle motion as a function of geometrical properties of the bed from laminar to ...

The goal of this experimental procedure is to quantify the impact of sediment bed geometry on incipient particle motion by using regular substrates that consist of monolayers of fixed beads regularly arranged according to triangular or quadratic configurations. Incipient particle motion is found in a wide range of industrial applications such as cleaner surfaces, removal of pollutants, filtration processes, or microfluidics, including template assembly of microparticles. The main advantage of using regular substrates is that we can analyze the impact of a local sediment bed geometry orientation, avoiding any dubiety about the role of the neighborhood.We propose two different methods to cover a broad range of particle Reynolds number, from the creeping flow limit, to the hydraulically rough flow. The results of this method can also help us understand the impact of the local bed geometry in nature processes, such as sediment transport, or grain bed erosion. Visual demonstration of this method is important since the use of a rotational rheometer, for instance, may not be common for particle hydrodynamic applications.Demonstrating the method with the wind tunnel will be Jiwon Han, a graduate student from our lab that just finished her master thesis on this topic. These measurements take place in a rotational rheometer. The rheometer is modified to include a customized circular transparent container.There is an embedded microscope slide to improve imaging. The bottom of the container has a regular substrate, examples of which are in this schematic, which provides an overview of the setup, including its two digital cameras, and two light sources. Have the rheometer ready for normal operation.Then place a customized adapter on the rheometer plate, also mount the container with substrate on top of the plate. Ensure the microscope slide faces the camera. Start the rheometer and its software, initialize it, and set its temperature.Next, get the customized rotating disk. This is the 70 millimeter diameter transparent acrylic glass plate fixed to a 25 millimeter diameter plate. Mount this and set its height reference point.Then lift the rotating disk and remove it. Complete preparation by filling the container with silicon oil. Begin to work with the imaging system.This includes a CMOS camera and objective lens with an overhead view into the container. A second high speed camera has a side-view into the container. The view is through the microscope slide.Turn on and adjust the Xenon lamp and the LED to illuminate the container. Use imaging software in the CMOS camera to visualize the substrate. Adjust the vertical stage to bring it into focus.After focusing, identify the center of the substrate. Place a carefully marked soda-lined glass sphere at the position. Continue by remounting the rotating disk on the rheometer two millimeters above the height reference point.Finally, make any adjustments to the side-view camera. Enter the rotational speed range, program a linear increase in rotational speed, and start the measurements. Start recording a video sequence from both cameras, and observe the live video from one of them.When the bead displaces from its equilibrium position, stop the measurement and note the rotational speed, which is the critical rotating speed. Then, stop recording the videos. During data analysis, load recorded videos into a custom image processing routine to help determine the mode of incipient motion.Perform turbulent regime measurements in a customized low-speed wind tunnel. It has an open-jet test section with a regular substrate centered within it. Linear, vertical, and horizontal stages support an anemometer and other instrumentation in the test section.The high-speed camera with macro lens is mounted at one side. This schematic provides an overview of the equipment. Note that the anemometer signal is input to an oscilloscope and computer.Locate where on the substrate to place a marked alumina bead. Identify the point along the substrate's central axis and 110 millimeters from the leading edge and place the bead there. Use the high-speed camera, and adjust an LED light-source to achieve a clear, focused image of the bead and its marks.Start the wind tunnel's fan well below the approximate critical fan speed. Monitor the bead and increase the fan speed four to six RPM every 10 seconds. Start recording with the imaging software when close to incipient conditions.Stop increasing the fan speed when incipient motion occurs, and note the critical speed value, and stop the video. Again, for data analysis, use custom software to analyze the recorded video, and determine the mode of incipient motion of the bead. Now, work with the anemometer with a miniature hot-wire probe.Switch its control function to stand-by and adjust the resistance for an overheat ratio of 65%Remove the marked bead from the substrate. Move the anemometer to place the hot-wire probe in its initial position. To calibrate the anemometer, the probe should be in the free stream zone.Here, the probe must be at least 10 millimeters above the substrate. Run the probe, and start the fan at a rotational speed of 200 RPM. Then employ an impeller anemometer in the air stream.Read and record the stream-wise velocity from the impeller anemometer. In addition, read and record the hot-wire probe voltage on the oscilloscope. Repeat recording the anemometer readings for increments of 50 RPM in the rotational speed up to 450 RPM.Use the data to establish a calibration curve. Monitor the probe with the camera, and lower it as close as possible to the substrate surface without touching it. Start the fan at the mean speed for incipient motion and begin collecting probe data.After each data set, increase the height of the probe, and repeat data collection. These top-view snapshots are of a marked bead on a quadratic surface during incipient motion in laminar flow. Software tracks features on the particle and the center of mass.The data allow determination of the angle of rotation as a function of the trajectory, and closely follow the expectations of pure rolling motions indicated by the dotted line. These are analogous side-view snapshots for a marked alumina bead on a quadratic surface in turbulent flow. In this case, the bead seems to carry out a pure rolling motion only early in its motion.A plot of the time averaged stream-wise velocity profile, the circles, is possible using data from the constant temperature anemometer. Here, the solid line is a fit using the logarithmic log law, and the blue Xs are for a fit using the modified wall law. The shear velocity needed to determine the critical shields number is inferred from the fits.Here, both wall laws suggest similar values for the shear velocity. Here is a plot of the root mean square stream-wise velocity profile within a small height range. The measured viscus sub-layer is about 1/4 of a millimeter, indicating that the mobile bead is mainly exposed to a turbulent flow.Each measurement in the rheometer doesn't take more than five minutes if it is performed properly. Experiments in the wind tunnel, however, may take about five hours, since the measurement of the boundary layer is a complex process. The proper setting of the gap in the rheometer is critical to avoid any systematic error when calculating the critical shear rate and the critical shields numbers.In the wind tunnel, the animal with the calibration wants to be carefully conduct to determine the shear velocity. It is recommended to perform a calibration before and after measurement, to ensure that no significant changes occurred in the course of the measurement. Following the procedure in the wind tunnel, other criteria beyond the classical shields one can be used to signify incipient motion.The inputs or energy criteria can be adopted since the duration of events can be measured by thermal anemometer. The results can provide important insight into how forces and torques act on a particular due to turbulent flow depending on the substrate geometry. The results can be used as a benchmark for more sophisticated models.After watching this video, you should have a good understanding of how we can systematically quantify the inference of sediment bed geometry on the incipient particle motion.

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8.6K 조회수.  University of Erlangen-Nuremberg. The goal of this experimental procedure is to quantify the impact of sediment bed geometry on incipient particle motion by using regular substrates that consist of monolayers of fixed beads regularly arranged according to triangular or quadratic configurations. Incipient particle motion is found in a wide range of industrial applications such as cleaner surfaces, removal of pollutants, filtration processes, or microfluidics, including template assembly of microparticles. The main advantage of...