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

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.