Name: the diffusion of passive tracers in laminar shear flow
Uploaded: 2018-05-01T13:30:00.000+00:00
Duration: 8 min 1 s
Description: Watch this Scientific Journal Video about The Diffusion of Passive Tracers in Laminar Shear Flow at JoVE.com

We acknowledge funding from the Office of Naval Research (grant DURIP N00014-12-1-0749) and the National Science Foundation (grants RTG DMS-0943851, CMG ARC-1025523, DMS-1009750, and DMS-1517879). Additionally, we acknowledge the work of Sarah C. Burnett who helped develop an early version of the experimental setup and protocol.

1 . Prepare the parts to build the experimental setup
<ol>
	<li>Utilize the 3D CAD drawings attached (.stl format) to 3D-print an injector post, a reservoir, a hexagonal connector, and two plates to be used as mounts for the pipes (two for each geometry). 
	NOTE: Alternatively, certain parts of the setup can be laser-cut. In this report, the square thick pipe has been mounted with laser-cut plates, while the rectangular thin pipe has been mounted with 3D-printed plates.</li>
	<li>Obtain smooth glass capillary pipes of the desired geometry. 
	NOTE: In this report, two pipe geometries are used: 30 cm-long pipe of square cross-section - internal cross-section 1 mm x 1 mm and wall thickness 0.2 mm; 30 cm-long pipe of rectangular cross-section - internal cross-section 1 mm x 10 mm and wall thickness 0.7 mm. The square pipe is henceforth referred to as the thick pipe, whereas the rectangular pipe is referred to as the thin pipe.</li>
</ol>
2 . Assembly of the experimental setup
<ol>
	<li>Tapping of the 3D-Printed parts
	<ol>
		<li>Tap the injector post on both sides with a 1/8&#34; (0.32 cm) NPT tap where the injection needle and dye input will be installed. Tap the reservoir in the back with a 10-32 tap where the draining tube will be installed.</li>
		<li>Tap the four screw holes with a 6-32 tap on the front of the reservoir. Tap the hexagonal connector piece on the top and bottom with a 6-32 tap.</li>
	</ol>
	</li>
	<li>Prepare the tapped 3D-printed parts
	<ol>
		<li>Injector post
		<ol>
			<li>Cover the threads of a barbed hose fitting with PTFE sealing tape. Screw the prepared fitting onto the back hole of the injector post. Cut a 30 cm-long piece of plastic tubing (inner diameter 3.30 mm). Insert the tube on the hose adaptor.</li>
			<li>Cover the threads of the stainless-steel dispensing needle (outer diameter 0.71 mm) with PTFE sealing tape. Screw the stainless-steel dispensing needle on the front (large) hole onto the injector post.</li>
		</ol>
		</li>
		<li>Reservoir
		<ol>
			<li>Cover the threads of a small barbed hose fitting with PTFE sealing tape. Screw the prepared fitting onto the back hole of the reservoir (smaller hole).</li>
			<li>Cut a 30 cm-long piece of plastic tubing (inner diameter 3.30 mm). Insert the tube onto the hose adaptor. Close the other end of the tube with a small cap. 
			NOTE: This will be the draining system for the reservoir.</li>
			<li>Place a rubber O-Ring (Oil-Resistant Buna-N O-Ring, 1/16&#34; (0.16 cm) Fractional Width, Dash Number 016) in the circular recession on the pipe side of the reservoir.</li>
		</ol>
		</li>
		<li>Hexagonal connector
		<ol>
			<li>Cover the threads of a small barbed hose fitting with PTFE sealing tape. Screw the prepared fitting onto the bottom hole of the hexagonal connector.</li>
			<li>Cut a 30 cm-long piece of plastic tubing (inner diameter 3.30 mm). Insert the tube on the hose adaptor.</li>
			<li>Cover a hose adaptor with PTFE sealing tape. Make sure to cover the hose adaptor going against the threads.</li>
			<li>Cut a 4 cm-long piece of plastic tubing (inner diameter 3.30 mm). Insert the tube on the hose adaptor.</li>
		</ol>
		</li>
	</ol>
	</li>
	<li>Prepare the pipe
	<ol>
		<li>Distribute a thin layer of RTV rubber sealant 2 mm away from each end of the pipe. Spread the sealant evenly around the outside of the pipe and make sure not to obstruct the pipe access with the sealant.</li>
		<li>Mount the pipe onto the 3D-printed plates by inserting it carefully into the pre-cut holes on the 3D-printed pipe adapters. Make sure to push the pipe in at least 2 mm so that the sealant along each side contacts with the plates.</li>
		<li>Carefully spread the sealant onto the edge of the plate so that the pipe gets sealed into the cutout. Wait at least 12 h for the sealant to fully vulcanize thus sealing the pipe onto the plates.</li>
	</ol>
	</li>
	<li>Measure 0.40 g of fluorescein powder to prepare the dye solution. Dilute powder into 0.50 L of distilled water to obtain the desired dye concentration (0.80 g/L concentration). 
	NOTE: The diffusivity of fluorescein in water is estimated by performing a least-squares fit of the analytical expression for the second moment of the cross-sectionally averaged tracer distribution in the circular pipe geometry14 to the experimental measurement of the same quantity. The molecular diffusion coefficient is estimated to be &#954; = 5.7 x 10-6 cm2/s, consistent with previously published values of diffusivity of fluorescein in pure water.</li>
	<li>Assembly
	<ol>
		<li>Syringe pump A setup
		<ol>
			<li>Fill a 12 mL plastic syringe with a rubber plunger with distilled water. Insert a plastic dispensing tip onto the syringe. Mount the syringe onto syringe pump A. Connect the syringe to the 30 cm-long tube inserted at the bottom of the hexagonal connector.</li>
			<li>Fill a 1 mL plastic syringe with a rubber plunger with distilled water. Mount the syringe onto syringe pump A. Cut a 30 cm-long piece of plastic tubing (inner diameter 3.30 mm). Attach it to the 1 mL plastic syringe. 
			NOTE: Both syringes filled with distilled water are mounted on syringe pump A. As the pump is activated, water will be ejected from both syringes. The first one to be used is the 12 mL syringe, so the 1 mL syringe needs to be connected to a draining tube to avoid water spills. This step is not necessary for the thin rectangular pipe.</li>
		</ol>
		</li>
		<li>Injector Setup
		<ol>
			<li>Fill a 3 mL plastic syringe with a rubber plunger with the fluorescein solution. Insert a plastic dispensing tip onto the syringe.</li>
			<li>Attach the tube connected to the back of the injector to the dye syringe.</li>
			<li>Fill the injector post with the dye solution by manually injecting dye through the syringe while holding the injector post horizontally (i.e. with the needle oriented upwards and above the syringe). Keep pushing on the syringe until the injector is completely full of dye and no air is trapped inside.</li>
			<li>Mount the syringe onto syringe pump B. Clamp the injector post to the edge of the lab bench in a way that it is reachable by the tube connected to the syringe pump.</li>
			<li>Insert small washers on four long screws (Stainless Pan Head Phillips Machine Screws 6-32 Thread, 2-1/4&#34; (5.76 cm) length). Insert the four screws in the four holes surrounding the needle. 
			NOTE: Make sure the head of the screw is on the back of the injector post (on the same side as the tube connected to the dye syringe).</li>
		</ol>
		</li>
		<li>Hexagonal connector
		<ol>
			<li>Place two O-Rings (Oil-Resistant Buna-N O-Ring, 1/16&#34; (0.16 cm) Fractional Width, Dash Number 016) in the circular cutouts on each side of the hexagonal connector.</li>
			<li>Attach the hexagonal connector to the injector post by aligning its holes to the four screws and inserting it on them. Make sure to have the side with the larger hole facing the injector post. Check and ensure that the O-Ring does not move out of place when clamped between the two parts.</li>
		</ol>
		</li>
		<li>Pipe
		<ol>
			<li>Attach one of the end-plates connected to the pipe to the hexagonal connector by aligning its holes to the four screws and inserting it onto them. Pay close attention to the needle which needs to enter the pipe as it is being mounted.</li>
			<li>Secure the four long screws to compress together the injector, the hexagonal connector, and the pipe-adapter plate by attaching four 6-32 stainless steel nuts to the end of the long bolts. Ensure that the O-Rings do not move out of place when clamped between the parts.</li>
			<li>Attach the opposite end of the pipe to the reservoir by using four short screws and washers (Stainless Pan Head Phillips Machine Screws 6-32 Thread, 1/2&#34; (1.27 cm) length). Check that the O-Ring does not move out of place when compressed between the two parts.</li>
		</ol>
		</li>
		<li>Clamp the reservoir to the table. Make sure the reservoir is aligned with the injector post to not bend the pipe.</li>
		<li>Air extraction system: Insert a plastic dispensing tip into the tube connected to the top of the hexagonal connector. Attach a 3 mL syringe to the plastic tip. 
		NOTE: This syringe will be used to extract any air bubbles trapped in the system.</li>
		<li>Lights and Camera
		<ol>
			<li>Place two 61 cm-long UV-A tube lights on each side of the experimental setup. 
			NOTE: There is a specifically designed track on each side of both the injector and reservoir. The experiment should be run in the dark with the UV-A tube lights turned on.</li>
			<li>Place a camera with memory card above the experimental setup facing down. 
			NOTE: The camera should be positioned at least 1 m above the pipe. In this way, the frame will include the entire pipe length. A DSLR camera was used with a lens of adjustable focal length, 24 - 120 mm.</li>
			<li>Program the camera using a remote trigger to take pictures every 1 s with aperture 5.6f, shutter speed 5, and ISO 200.</li>
		</ol>
		</li>
	</ol>
	</li>
</ol>
3 . Experimental run
<ol>
	<li>Setup
	<ol>
		<li>Fill the reservoir with distilled water to a level slightly above the pipe. Fill pipe with distilled water by pushing on the syringe pump. Turn on the UV-A tube lights and pull the blackout curtains.</li>
		<li>Run the programmable syringe pump A to flush the pipe of any residual dye.</li>
		<li>Take a single reference image of the pipe filled with pure distilled water. 
		NOTE: This is the reference&#160;shot that will be used in the data processing steps later. This picture needs to be taken in the dark in conditions as similar as possible to the experimental run.</li>
		<li>Switch the tube connecting to the injector post to the 1 mL syringe mounted on syringe pump A. Connect the 12 mL syringe to the draining tube (previously connected to the 1 mL syringe). 
		NOTE: This step is not necessary for the thin rectangular pipe.</li>
	</ol>
	</li>
	<li>Initial Condition
	<ol>
		<li>Inject a 1 mm-thick dollop of dye (3 mm-thick for the thin rectangular tube) in the pipe by running the analog syringe pump B. 
		NOTE: This step creates the dye initial condition. The amount of dye injected depends on the geometry of the pipe used. The thin tube requires a larger amount of dye because its cross-sectional area is larger. Before the experimental run, the dye will have to diffuse across the cross-section and injecting a larger amount of dye ensures that it will be bright enough to be captured in photographs even after it has diffused.</li>
		<li>Program syringe pump A to inject distilled water at the very slow flow rate of 0.193 mL/h for the thick square pipe (the flow rate is 1.93 mL/h for the thin rectangular pipe). Run the syringe pump for 5 min to allow the bolus of dye to be transported down the pipe away from the needle. 
		NOTE: After 5 min, the dye should be approximately 1 cm away from the needle. The increase in the flow rate by one order of magnitude for the thin pipe is because the volume of the thin pipe is 10 times that of the thick pipe.</li>
		<li>Pull the dye syringe backwards manually, making sure the dye does not reach the needle. 
		NOTE: This will ensure that there is distilled water at the end of the needle so that no more dye will be dispersed into the pipe during the experimental run.</li>
		<li>Wait for a time tw &#62; t*d for the dye bolus to diffuse across the cross-section of the pipe. 
		NOTE: The diffusive time t*d = b2/&#954; considers the characteristic length b to be half the long cross-sectional side. This way of computing the wait time is generalizable to any cross-section with an appropriate choice of b. For our representative results, the wait time was 15 min for the thick square pipe and 15 h for the thin rectangular pipe.</li>
	</ol>
	</li>
	<li>Flow
	<ol>
		<li>Program syringe pump A to the desired flow rate of 1.93 mL/h for the thick square pipe and 19.3 mL/h for the thin rectangular pipe.</li>
		<li>Start the syringe pump and the remote trigger on the camera at the same time. Run the experiment for 5 min, with an interval between pictures of 1 s.</li>
		<li>Turn the room lights on and take an image of a&#160;ruler placed at the same height as the pipe and parallel to it. 
		NOTE: This will help determine the length scale (pixels/mm) used in data processing.</li>
	</ol>
	</li>
</ol>
4. Data Processing
<ol>
	<li>Extract the memory card from the camera and download the data to a computer where image processing software will be used to analyze it.</li>
	<li>MATLAB analysis
	<ol>
		<li>First subtract the reference image shot (snapped in step 3.1.3) from the first experimental image.</li>
		<li>Crop the image along the upper and lower edges of the pipe. Make sure to rotate the image if the pipe is not aligned with the frame.</li>
		<li>Sum the intensity reading of the green channel vertically in the resulting image. 
		NOTE: This is proportional to the total cross-sectional dye intensity as a function of the length along the pipe.</li>
		<li>Convert the units of length from pixels to mm by using the physical length scale from the calibration image (see step 3.3.3).</li>
		<li>Repeat for all remaining images. This results in a time sequence of the curves measuring the total dye concentration along the length of the pipe.</li>
	</ol>
	</li>
</ol>

<ol>
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The authors have nothing to disclose.

After injecting dye into the pipe, the bolus is transported away from the injection needle using a steady flow. Then, it is necessary to wait long enough for the dye to diffuse across the cross-section of the channel. In this way, a uniform Gaussian-like distribution is obtained and will serve as the initial condition for the experiment. Hence, a laminar background flow is created with the programmable syringe pump. The experimental run lasts for 5 min with photos taken every second.
The most common issues in the setup come from the connection of the parts and the pipes. The various 3D-printed parts need to be sealed properly when connected to avoid leaking. The glass pipes are very delicate and must be handled and installed with care.
An issue we encountered when transitioning from the thin rectangular pipe to the thick square pipe was related to the fact that the pipe volume was reduced by a factor of 10. To maintain the same cross-sectional average flow speed with the mounted 12 mL syringe, the plunger speed in syringe pump A would have needed to be extremely low. At this programmed speed, the plunger velocity was not uniform anymore and a steady flow cannot be guaranteed throughout the experimental run. Therefore, we switched to a much smaller 1 mL syringe when working with the thick square pipe in step 2.5.1.
Also, one should verify that the average intensity along the vertical dimension of the pipe in the initial condition is approximately uniform. If not, a filtering mask needs to be applied across all frames to account for this discrepancy.
The least repeatable part of the experiment is the dye injection (and consequently the width of the initial distribution). As illustrated earlier, it is not a concern for matching with the Monte Carlo simulations, as the experimental initial condition can be recreated using the analysis of the initial photograph. The dye injection and consequent manual withdrawing may not always produce dye plugs of precisely the same width. Particular care needs to be applied when setting up the initial dye bolus. The experiment becomes more repeatable as researchers gain experience in this part of the protocol, but future improvements could certainly be made.
When comparing the setup with microfluidic devices, the only parameter that appear in the governing equation when appropriately nondimensionalized is the P&#233;clet number Pe if the tracer is passive, i.e. the tracer evolution is uncoupled from the flow. Dynamic similarity is implicit in the assumption of low Reynolds (Re &#60;&#60; 1) which ensures stable laminar flows u(y,z). These two parameters are setting the full similarity between microfluidic setups and the scales of our experiment. In practice, the physical length of the pipe only restricts the nondimensional times we can safely reach with our setup. For very late non-dimensional times, the necessary length of the pipe could become prohibitively long for a fixed P&#233;clet number in this large-scale setup.
An obvious limitation of this experimental protocol is that the data collected is a projected 2D representation of 3D geometry as the pictures are taken top-down on the pipe. The current process only allows to obtain the evolution of the cross-sectionally averaged dye distribution. Obtaining a distribution defined at each location in the tube rather than on its cross-sectional average and comparison with theoretical and numerical predictions are the subject of ongoing research.
All the experimental setup parts have technical drawings available for download which makes the setup easily accessible and customizable by any interested researcher. Building on the current results, the same setup will be used to study more complex and unexplored pipe geometries as well as different flow regimes.

In recent years, substantial efforts have been focused on developing microfluidic and lab-on-chip devices that can reduce the costs and increase the productivity of chemical preparation and diagnostics for a range of applications. One of the main features of microfluidic devices is the pressure-driven transport of fluids and dissolved solutes through microchannels. In this context, it has become increasingly important to better understand the controlled delivery of solutes at the microscale. In particular, applications such as chromatographic separation1,2&#160;and microfluidic flow injection analysis3,4&#160;require improved control and understanding of solute delivery. Researchers in microfluidics have studied and documented the influence of the channel&#39;s cross-sectional shape on solute spreading5,6,7,8, and the role of the channel&#39;s aspect ratio9,10.
Analytical and numerical studies of solute spreading along channels have recently lead to the identification of a correlation between the pipe cross-sectional geometry and the shape of the distribution9,10. At early timescales, the distribution strongly depends on the geometry: rectangular pipes break symmetry almost immediately, while elliptical pipes retain their initial symmetry much longer9. On the other hand, progressing into longer timescales the asymmetries in the solute distribution no longer differentiate ellipses from rectangles, and are set solely by the cross-sectional aspect ratio &#955; (ratio of the short to long side). Considering &#34;pipes&#34; of elliptical cross-sections and &#34;ducts&#34; of rectangular cross-sections, predictions from numerical simulations and asymptotic analysis were benchmarked with laboratory experiments. Thin channels (aspect ratio &#60;&#60; 1) produce solutes arriving with sharp fronts and tapering tails, while thick channels (aspect ratio ~ 1) present the opposite behavior10. This robust effect is relatively insensitive to the initial conditions and can be used to help select the solute distribution profile required for any application.
The behavior outlined above of sorting thin versus thick domains happens before the classical &#34;Taylor dispersion&#34; regime is reached. Taylor dispersion refers to the enhanced spreading of passive solutes in laminar flow (stable at low Reynolds number, Re) with a boosted effective diffusivity, inversely proportional to the solute&#39;s molecular diffusivity &#954;11. This enhancement is observed only after long, diffusive timescales, when the solute has diffused across the channel. Such diffusive timescale is defined in terms of the characteristic length scale a of the geometry, as td = a2/&#954;. The P&#233;clet number is a nondimensional parameter which measures the relative importance of fluid advection to diffusion effects. We define this parameter in terms of the shortest length scale as Pe = Ua/&#954;, where U is the characteristic flow speed. (The Reynolds number can be defined in terms of the P&#233;clet number as Re = Pe &#954;/&#957;, where&#160;&#957; is the kinematic viscosity of the fluid.) Typical P&#233;clet number values for microfluidic applications12&#160;vary between 10 and 105, with molecular diffusivities ranging from 10-7 to 10-5 cm2/s. Hence, given the flow speeds and length scales of interest, it is critical to understand the behavior of solutes for intermediate-to-long timescales (relative to the diffusive timescale), well past the initial observations of geometry-driven behavior and into the cross-section-driven regimes universal for a large class of geometries.
Given the interest in microfluidic applications, the choice of a large scale experimental setup may at first seem unnatural. The experiments reported herein are at the millimeter scale, not at the microscale as in true microfluidic devices. However, the same physical behaviors characterize both systems and a quantitative study of the relevant phenomena can still be achieved by properly scaling the governing equations, just as scale models of aircraft are assessed in wind tunnels during the design phase. In particular, matching relevant nondimensional parameters (such as the P&#233;clet number for our experiment) ensures the adaptability of the experimental model. Working at such larger scales, while maintaining a laminar pressure-driven flow, offers several advantages over a traditional microscale setup. In particular, the equipment required to manufacture, perform, and visualize the present experiments is easier to operate and less costly. Furthermore, other common challenges of working with microchannels, such as frequent clogging and the enhanced influence of manufacturing tolerances, are mitigated with the larger setup. Another possible use for this experimental setup is for studies of residence time distribution (RTD) in laminar flows13.
The asymmetries arising in the solute distribution downstream can be analyzed via its statistical moments; in particular, the skewness, which is defined as the centered, normalized third moment, is the lowest order integral statistic measuring the asymmetry of a distribution. The sign of the skewness typically indicates the shape of the distribution, i.e. if it is front-loaded (negative skewness) or back-loaded (positive skewness). Focusing on the aspect-ratios of the channels, there exists a clear correlation of thin geometries with front-loaded distributions, and thick geometries with back-loaded distributions10. Additionally, a critical aspect ratio separating these two opposite behaviors can be calculated for both elliptical pipes and rectangular ducts. Such crossover aspect ratios are remarkably similar for standard geometries, in particular, &#955;* = 0.49031 for pipes, and &#955;* = 0.49038 for ducts, suggestive of the universality of the theory10.
The experimental setup and method described in this paper are used to study the spreading of a pressure-driven passive solute in laminar fluid flows throughout glass capillaries of various cross-sections. The simplicity and reproducibility of the experiment defines a robust method of analysis for understanding the connection between a pipe&#39;s geometrical cross-section and the resulting shape of the injected solute distribution as it is transported downstream. The method discussed in this work has been developed to readily benchmark mathematical and numerical results in a physical laboratory setting.
A simple experimental procedure is described which highlights the definitive role played by a fluidic channel&#39;s cross-sectional aspect-ratio in setting the shape of a solute distribution downstream. The experimental setup requires a programmable syringe pump to produce a laminar steady flow, smooth glass pipes of various cross-sections, a second syringe pump to inject the diffusing solute (e.g. fluorescein dye) into the surrounding laminar flow, and UV-A lights and a camera to record the solute evolution. CAD files are provided for all the custom parts of the setup and such files can be used to 3D-print the experimental parts prior to assembly.

<table><tbody><tr><td>Flourescein Dye</td><td>Flinn Scientific&amp;nbsp;</td><td>LOT: 118362&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; CAS NO: 518-47-8</td><td></td></tr><tr><td>PhD ULTRA Hpsi Syringe Pump</td><td>Harvard Apparatus</td><td>703111</td><td>programmable digital syringe pump</td></tr><tr><td>Compact Infusion Pump Model 975</td><td>Harvard Apparatus</td><td>55-1689</td><td></td></tr><tr><td>Form 2 SLA 3D Printer</td><td>Formlabs</td><td>100-240</td><td></td></tr><tr><td>Glass pipes</td><td>VitroCom</td><td>4410 and 8100</td><td></td></tr><tr><td>PTFE sealing tape</td><td>Teflon</td><td>4934A12</td><td></td></tr><tr><td>PVC tubing (1/8&quot; ID)</td><td>McMaster</td><td>5231K144</td><td>5 Foot Length</td></tr><tr><td>Reusable Stainless Steel Dispensing Needle 22 Gauge, .016&quot; ID, .028&quot; OD, 1/8&quot; NPT Thrd, 2&quot; Lg&amp;nbsp;</td><td>McMaster</td><td>7590A45&amp;nbsp;</td><td>1 Required</td></tr><tr><td>RTV silicone rubber sealant</td><td>McMaster</td><td>74945A69</td><td></td></tr><tr><td>Plastic Syringe Manual, w/ Luer Lock Connection, .34 oz Capacity, Packs of 10&amp;nbsp;</td><td>McMaster</td><td>7510A653&amp;nbsp;</td><td>1 required</td></tr><tr><td>Plastic Syringe Manual, w/ Luer Slip Connection, .034 oz Cap, Packs of 10&amp;nbsp;</td><td>McMaster</td><td>7510A603&amp;nbsp;</td><td>1 required</td></tr><tr><td>Plastic Syringe Manual, w/ Luer Lock Connection, 0.1 oz Capacity, Packs of 10&amp;nbsp;</td><td>McMaster</td><td>7510A651&amp;nbsp;</td><td>2 required</td></tr><tr><td>Plastic dispensing tip</td><td>McMaster</td><td>6699A1&amp;nbsp;</td><td>3 required</td></tr><tr><td>6&quot; C-Clamps</td><td>McMaster</td><td>5133A18</td><td>2 required</td></tr><tr><td>Type 18-8 Stainless Steel Flat Washer Number 6 Screw Size, 0.156&quot; ID, 0.312&quot; OD, Packs of 100&amp;nbsp;</td><td>McMaster</td><td>92141A008&amp;nbsp;</td><td>8 required</td></tr><tr><td>18-8 SS Pan Head Phillips Machine Screw 6-32 Thread, 2-1/4&quot; Length, Packs of 50&amp;nbsp;</td><td>McMaster</td><td>91772A167&amp;nbsp;</td><td>4 required</td></tr><tr><td>Oil-Resistant Buna-N Multipurpose O-Ring 1/16 Fractional Width, Dash Number 016, Packs of 100&amp;nbsp;</td><td>McMaster</td><td>9452K6&amp;nbsp;</td><td>3 required</td></tr><tr><td>Type 18-8 Stainless Steel Hex Nut 6-32 Thread Size, 5/16&quot; Wide, 7/64&quot; High, Packs of 100&amp;nbsp;</td><td>McMaster</td><td>91841A007&amp;nbsp;</td><td>4 required</td></tr><tr><td>18-8 SS Pan Head Phillips Machine Screw 6-32 Thread, 1/2&quot; Length, Packs of 100&amp;nbsp;</td><td>McMaster</td><td>91772A148&amp;nbsp;</td><td>4 required</td></tr><tr><td>24&quot; Black Light Fixture with bulb</td><td>American DJ</td><td>B0002F5544</td><td>2 required</td></tr><tr><td>DSLR camera&amp;nbsp;</td><td>Nikon&amp;nbsp;</td><td>D300</td><td></td></tr><tr><td>24-120 mm lens</td><td>Nikon</td><td>2193</td><td></td></tr><tr><td>Remote programmable trigger</td><td>Nikon</td><td>4917</td><td>remote programmable trigger</td></tr><tr><td>Memory Card</td><td>SanDisk&amp;nbsp;</td><td>SDCFX-032G-E61</td><td></td></tr><tr><td>Metric ruler</td><td>McMaster</td><td>20345A35</td><td></td></tr></tbody></table>

the diffusion of passive tracers in laminar shear flow

A simple method to experimentally observe and measure the dispersion of a passive tracer in a laminar fluid flow is described. The method consists of first injecting fluorescent dye directly into a pipe filled with distilled water and allowing it to diffuse across the cross-section of the pipe to obtain a uniformly distributed initial condition. Following this period, the laminar flow is activated with a programmable syringe pump to observe the competition of advection and diffusion of the tracer through the pipe. Asymmetries in the tracer distribution are studied and correlations between the pipe cross-section and the shape of the distribution is shown: thin channels (aspect ratio &#60;&#60; 1) produce tracers arriving with sharp fronts and tapering tails (front-loaded distributions), while thick channels (aspect ratio ~1) present the opposite behavior (back-loaded distributions). The experimental procedure is applied to capillary tubes of various geometries and is particularly relevant to microfluidic applications by dynamical similarity.

The experimental setup after assembly is shown in Figure 1. Images produced in MATLAB show the experimental data above the processed evolution of the concentration curve (Figure 2) for three non-dimensional times. We have verified that there is a linear relation between the tracer&#39;s intensity and concentration. The shape of the distribution changes as time passes and the dye bolus moves downstream. Figure 2 shows such evolution in the case of the thin rectangular duct geometry. The initial dye distribution is narrow and symmetric (Gaussian-like with respect to the longitudinal direction and nearly uniform in the cross-section, Figure 2 left), but the symmetry is broken almost immediately as the background flow starts. The distribution breaks symmetry by presenting a sharp front and long tapering tails (Figure 2, middle and right).
The experimental results are confirmed by Monte Carlo simulations performed matching the initial distribution and flow rate (Figure 3). The fitted value for the dye diffusivity &#954; was determined in an independent experiment (step 2.4 in protocol) and used in this comparison. Monte Carlo methods are often used to simulate the evolution of advection-diffusion problems involving complex geometries as the boundary conditions (homogeneous Neumann in this case) can be simply input as billiard like reflection rules. The approach is to sample realizations of the equivalent stochastic differential equation underlying the advection-diffusion equation in nondimensional form:
<img alt="Equation 1" src="/files/ftp_upload/57205/57205eq1v2.jpg" />
where T(x,y,z,t) is the tracer distribution, &#964; is the nondimensional time normalized by td, x is the longitudinal spatial coordinate, y is the short transverse coordinate, and z is the long transverse coordinate, all normalized by the short side a. The fluid flow u(y,z) is the laminar steady-state solution to the Navier-Stokes equations with no-slip boundary conditions (no flow at the wall), driven by a negative pressure gradient. A Gaussian initial data in the pipe longitudinal direction with a desired variance can be obtained by considering only diffusion (Pe = 0) and evolving the particles for the desired time to match the width of the experimental initial data9,10. These representative results were obtained using the flow rate values specified in the protocol, however we expect the loading phenomena observed to hold in general for the laminar regime10&#160;(Figure 3).
<img alt="Figure 1" class="xfigimg" src="/files/ftp_upload/57205/57205fig1.jpg" /> 
Figure 1: Experimental setup. (A) Diagram of the experimental setup. This figure has been modified from Aminianet al.10. (B) Presentation of the actual setup. <a href="https://cloudflare.jove.com/files/ftp_upload/57205/57205fig1large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 2" class="xfigimg" src="/files/ftp_upload/57205/57205fig2.jpg" /> 
Figure 2: Snapshots of processed data at various times. Top row: photo of the dye concentration diffused along the cross-section of the tube observed normally to the long cross-sectional direction at increasing non-dimensional times. The vertical axis has been scaled 5 times for the sake of clarity. Bottom: intensity of the dye concentration computed summing along the long cross-sectional direction. The peak value is normalized. <a href="https://cloudflare.jove.com/files/ftp_upload/57205/57205fig2large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 3" class="xfigimg" src="/files/ftp_upload/57205/57205fig3.jpg" /> 
Figure 3: Comparison of the concentration distribution between Monte Carlo simulations and experiments. The evolution of the cross-sectionally averaged dye concentration along the longitudinal length of the pipe is shown at two instants in time: &#964; = 0.15&#160; and &#964; = 0.30. The dashed lines are the simulation results, while the solid lines represent the experimental data. Top: comparison in the thick (square) channel; bottom: comparison in the thin (rectangular) channel. The area under each curve is normalized to be one and x = 0 corresponds to the center of the initial plug of dye. This figure has been modified from Aminianet al.10. <a href="https://cloudflare.jove.com/files/ftp_upload/57205/57205fig3large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
Supplementary File 1. Included CAD drawings of 3D Hexagonal Connector (<a href="https://cloudflare.jove.com/files/ftp_upload/57205/hex_connector_3D.STL" target="_blank">hex_connector_3D.STL</a>)
Supplementary File 2. Included CAD drawings of 3D Injector Post (<a href="https://cloudflare.jove.com/files/ftp_upload/57205/injector_post_3D.STL" target="_blank">injector_post_3D.STL</a>)
Supplementary File 3. Included CAD drawings of 3D Reservoir (<a href="https://cloudflare.jove.com/files/ftp_upload/57205/reservoir_3D.STL" target="_blank">reservoir_3D.STL</a>)
Supplementary File 4. Included CAD drawings of 3D Thick Pipe Plates (<a href="https://cloudflare.jove.com/files/ftp_upload/57205/plate_thick_3D.STL" target="_blank">plate_thick_3D.STL</a>)
Supplementary File 5. Included CAD drawings of 3D Thin Pipe Plates (<a href="https://cloudflare.jove.com/files/ftp_upload/57205/plate_thin_3D.STL" target="_blank">plate_thin_3D.STL</a>)

Watch this Scientific Journal Video about The Diffusion of Passive Tracers in Laminar Shear Flow at JoVE.com

The Diffusion of Passive Tracers in Laminar Shear Flow

A protocol for the study of the diffusion of passive tracers in laminar pressure-driven flow is presented. The procedure is applicable to various capillary pipe geometries.

A simple method to experimentally observe and measure the dispersion of a passive tracer in a laminar fluid flow is described. The method consists of ...

the-diffusion-of-passive-tracers-in-laminar-shear-flow

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8.4K Views.  University of North Carolina at Chapel Hill. A protocol for the study of the diffusion of passive tracers in laminar pressure-driven flow is presented. The procedure is applicable to various capillary pipe geometries.

Video: The Diffusion of Passive Tracers in Laminar Shear Flow

Confocal Imaging of Confined Quiescent and Flowing Colloid-polymer Mixtures

The behavior of confined colloidal suspensions with attractive interparticle interactions is critical to the rational design of materials for directed assembly1-3, drug delivery4, improved hydrocarbon recovery5-7, and flowable electrodes for energy storage8. Suspensions containing fluorescent colloids and non-adsorbing polymers are appealing model systems, as the ratio of the polymer radius of gyration to the particle radius&#160;and concentration of polymer control the range and strength of the interparticle attraction, respectively. By tuning the polymer properties and the volume fraction of the colloids, colloid fluids, fluids of clusters, gels, crystals, and glasses can be obtained9.&#160;Confocal microscopy, a variant of fluorescence microscopy, allows an optically transparent and fluorescent sample to be imaged with high spatial and temporal resolution in three dimensions. In this technique, a small pinhole or slit blocks the emitted fluorescent light from regions of the sample that are outside the focal volume of the microscope optical system. As a result, only a thin section of the sample in the focal plane is imaged. This technique is particularly well suited to probe the structure and dynamics in dense colloidal suspensions at the single-particle scale: the particles are large enough to be resolved using visible light and diffuse slowly enough to be captured at typical scan speeds of commercial confocal systems10. Improvements in scan speeds and analysis algorithms have also enabled quantitative confocal imaging of flowing suspensions11-16,37.&#160;In this paper, we demonstrate confocal microscopy experiments to probe the confined phase behavior and flow properties of colloid-polymer mixtures. We first prepare colloid-polymer mixtures that are density- and refractive-index matched. Next, we report a standard protocol for imaging quiescent dense colloid-polymer mixtures under varying confinement in thin wedge-shaped cells. Finally, we demonstrate a protocol for imaging colloid-polymer mixtures during microchannel flow.

Confocal microscopy is used to image quiescent and flowing colloid-polymer mixtures, which are studied as model systems for attractive suspensions. Image analysis algorithms are used to calculate structural and dynamic metrics for the colloidal particles that measure changes due to geometric confinement.

The behavior of confined colloidal suspensions with attractive interparticle interactions is critical to the rational design of materials for directed ...

Chemistry

Parallel-plate Flow Chamber and Continuous Flow Circuit to Evaluate Endothelial Progenitor Cells under Laminar Flow Shear Stress

The overall goal of this method is to describe a technique to subject adherent cells to laminar flow conditions and evaluate their response to well quantifiable fluid shear stresses1.
Our flow chamber design and flow circuit (Fig. 1) contains a transparent viewing region that enables testing of cell adhesion and imaging of cell morphology immediately before flow (Fig. 11A, B), at various time points during flow (Fig. 11C), and after flow (Fig. 11D). These experiments are illustrated with human umbilical cord blood-derived endothelial progenitor cells (EPCs) and porcine EPCs2,3.
This method is also applicable to other adherent cell types, e.g. smooth muscle cells (SMCs) or fibroblasts.
The chamber and all parts of the circuit are easily sterilized with steam autoclaving. In contrast to other chambers, e.g. microfluidic chambers, large numbers of cells (&gt; 1 million depending on cell size) can be recovered after the flow experiment under sterile conditions for cell culture or other experiments, e.g. DNA or RNA extraction, or immunohistochemistry (Fig. 11E), or scanning electron microscopy5. The shear stress can be adjusted by varying the flow rate of the perfusate, the fluid viscosity, or the channel height and width. The latter can reduce fluid volume or cell needs while ensuring that one-dimensional flow is maintained. It is not necessary to measure chamber height between experiments, since the chamber height does not depend on the use of gaskets, which greatly increases the ease of multiple experiments. Furthermore, the circuit design easily enables the collection of perfusate samples for analysis and/or quantification of metabolites secreted by cells under fluid shear stress exposure, e.g. nitric oxide (Fig. 12)6.

We are describing a method to subject adherent cells to laminar flow shear stress in a sterile continuous flow circuit. The cells' adhesion, morphology can be studied through the transparent chamber, samples obtained from the circuit for metabolite analysis and cells harvested after shear exposure for future experiments or culture.

The overall goal of this method is to describe a technique to subject adherent cells to laminar flow conditions and evaluate their response to well ...

Bioengineering

In Situ Monitoring of Diffusion of Guest Molecules in Porous Media Using Electron Paramagnetic Resonance Imaging

A method is demonstrated to monitor macroscopic translational diffusion using electron paramagnetic resonance (EPR) imaging. A host-guest system with nitroxide spin probe 3-(2-Iodoacetamido)-2,2,5,5-tetramethyl-1-pyrrolidinyloxy (IPSL) as a guest inside the periodic mesoporous organosilica (PMO) aerogel UKON1-GEL as a host and ethanol as a solvent is used as an example to describe the protocol. Data is shown from a previous publication, where the protocol has been applied to both IPSL and Tris(8-carboxy-2,2,6,6-perdeutero-tetramethyl-benzo[1,2-d:4,5-d&#8242;]bis(1,3)dithiole) methyl (Trityl) as guest molecules and UKON1-GEL and SILICA-GEL as host systems. 
A method is shown to prepare aerogel samples that cannot be synthesized directly in the sample tube for measurement due to a size change during synthesis. The aerogel is attached to sample tubes using heat shrink tubing and a pressure cooker to reach the necessary temperature without evaporating the solvent in the process. The method does not assume a clearly defined initial distribution of guest molecules at the start of the measurement. Instead, it requires a reservoir on top of the aerogel and experimentally determines the influx rate during data analysis.
The diffusion is monitored continually over a period of 20 hr by recording the 1d spin density profile within the sample. The spectrometer settings for the imaging experiment are described quantitatively. Data analysis software is provided to take the resonator sensitivity profile into account and to numerically solve the diffusion equation. The software determines the macroscopic translational diffusion coefficient by least square minimization of the difference between the experiment and the numerical solution of the diffusion equation.

In Situ Monitoring of Diffusion of Guest Molecules in Porous Media Using Electron Paramagnetic Resonance Imaging

A protocol for the in situ monitoring of the diffusion of guest molecules in porous media using electron paramagnetic resonance (EPR) imaging is presented.

A method is demonstrated to monitor macroscopic translational diffusion using electron paramagnetic resonance (EPR) imaging. A host-guest system with ...

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.

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 ...

A Permanent Window for Investigating Cancer Metastasis to the Lung

Metastasis, accounting for ~90% of cancer-related mortality, involves the systemic spread of cancer cells from primary tumors to secondary sites such as the bone, brain, and lung. Although extensively studied, the mechanistic details of this process remain poorly understood. While common imaging modalities, including computed tomography (CT), positron emission tomography (PET), and magnetic resonance imaging (MRI), offer varying degrees of gross visualization, each lacks the temporal and spatial resolution necessary to detect the dynamics of individual tumor cells. To address this, numerous techniques have been described for intravital imaging of common metastatic sites. Of these sites, the lung has proven especially challenging to access for intravital imaging owing to its delicacy and critical role in sustaining life. Although several approaches have previously been described for single-cell intravital imaging of the intact lung, all involve highly invasive and terminal procedures, limiting the maximum possible imaging duration to 6-12 h. Described here is an improved technique for the permanent implantation of a minimally invasive thoracic optical Window for High-Resolution Imaging of the Lung (WHRIL). Combined with an adapted approach to microcartography, the innovative optical window facilitates serial intravital imaging of the intact lung at single-cell resolution across multiple imaging sessions and spanning multiple weeks. Given the unprecedented duration of time over which imaging data can be gathered, the WHRIL can facilitate the accelerated discovery of the dynamic mechanisms underlying metastatic progression and numerous additional biologic processes within the lung.

Here, we present a protocol for the surgical implantation of a permanently indwelling optical window for the murine thorax, which enables high-resolution, intravital imaging of the lung. The permanence of the window makes it well-suited to the study of dynamic cellular processes in the lung, especially those that are slowly evolving, such as metastatic progression of disseminated tumor cells.

Metastasis, accounting for ~90% of cancer-related mortality, involves the systemic spread of cancer cells from primary tumors to secondary sites such as ...

Cancer Research

Analyzing Mixing Inhomogeneity in a Microfluidic Device by Microscale Schlieren Technique

In this paper, we introduce the use of microscale schlieren technique to measure mixing inhomogeneity in a microfluidic device. The microscale schlieren system is constructed from a Hoffman modulation contrast microscope, which provides easy access to the rear focal plane of the objective lens, by removing the slit plate and replacing the modulator with a knife-edge. The working principle of microscale schlieren technique relies on detecting light deflection caused by variation of refractive index1-3. The deflected light either escapes or is obstructed by the knife-edge to produce a bright or a dark band, respectively. If the refractive index of the mixture varies linearly with its composition, the local change in light intensity in the image plane is proportional to the concentration gradient normal to the optical axis. The micro-schlieren image gives a two-dimensional projection of the disturbed light produced by three-dimensional inhomogeneity.
To accomplish quantitative analysis, we describe a calibration procedure that mixes two fluids in a T-microchannel. We carry out a numerical simulation to obtain the concentration gradient in the T-microchannel that correlates closely with the corresponding micro-schlieren image. By comparison, a relationship between the grayscale readouts of the micro-schlieren image and the concentration gradients presented in a microfluidic device is established. Using this relationship, we are able to analyze the mixing inhomogeneity from associate micro-schlieren image and demonstrate the capability of microscale schlieren technique with measurements in a microfluidic oscillator4. For optically transparent fluids, microscale schlieren technique is an attractive diagnostic tool to provide instantaneous full-field information that retains the three-dimensional features of the mixing process.

Herein, we describe a procedure that employs microscale schlieren technique to measure mixing inhomogeneity in a microfluidic device. Through calibration, distribution of concentration gradient can be derived from the micro-schlieren image.

In this paper, we introduce the use of microscale schlieren technique to measure mixing inhomogeneity in a microfluidic device. The microscale schlieren ...

Fluorescence Recovery after Merging a Droplet to Measure the Two-dimensional Diffusion of a Phospholipid Monolayer

We introduce a new method to measure the lateral diffusivity of a surfactant monolayer at the fluid-fluid interface, called fluorescence recovery after merging (FRAM). FRAM adopts the same principles as the fluorescence recovery after photobleaching (FRAP) technique, especially for measuring fluorescence recovery after bleaching a specific area, but FRAM uses a drop coalescence instead of photobleaching dye molecules to induce a chemical potential gradient of dye molecules. Our technique has several advantages over FRAP: it only requires a fluorescence microscope rather than a confocal microscope equipped with high power lasers; it is essentially free from the selection of fluorescence dyes; and it has far more freedom to define the measured diffusion area. Furthermore, FRAM potentially provides a route for studying the mixing or inter-diffusion of two different surfactants, when the monolayers at a surface of droplet and at a flat air/water interface are prepared with different species, independently.

We present a new technique to measure the lateral diffusion of a surface active species at the fluid-fluid interface by merging a droplet monolayer onto a flat monolayer.

We introduce a new method to measure the lateral diffusivity of a surfactant monolayer at the fluid-fluid interface, called fluorescence recovery after ...

Controlling Flow Speeds of Microtubule-Based 3D Active Fluids Using Temperature

We present a method for using temperature to tune the flow speeds of kinesin-driven, microtubule-based three-dimensional (3D) active fluids. This method allows for tuning the speeds in situ without the need to manufacture new samples to reach different desired speeds. Moreover, this method enables the dynamic control of speed. Cycling the temperature leads the fluids to flow fast and slow, periodically. This controllability is based on the Arrhenius characteristic of the kinesin-microtubule reaction, demonstrating a controlled mean flow speed range of 4&#8211;8 &#181;m/s. The presented method will open the door to the design of microfluidic devices where the flow rates in the channel are locally tunable without the need for a valve.

The goal of this protocol is to use temperature to control the flow speeds of three-dimensional active fluids. The advantage of this method not only allows for regulating flow speeds in situ but also enables dynamic control, such as periodically tuning flow speeds up and down.

We present a method for using temperature to tune the flow speeds of kinesin-driven, microtubule-based three-dimensional (3D) active fluids. This method ...

Quantifying Mixing using Magnetic Resonance Imaging

Mixing is a unit operation that combines two or more components into a homogeneous mixture. This work involves mixing two viscous liquid streams using an in-line static mixer. The mixer is a split-and-recombine design that employs shear and extensional flow to increase the interfacial contact between the components. A prototype split-and-recombine (SAR) mixer was constructed by aligning a series of thin laser-cut Poly (methyl methacrylate) (PMMA) plates held in place in a PVC pipe. Mixing in this device is illustrated in the photograph in Fig. 1. Red dye was added to a portion of the test fluid and used as the minor component being mixed into the major (undyed) component. At the inlet of the mixer, the injected layer of tracer fluid is split into two layers as it flows through the mixing section. On each subsequent mixing section, the number of horizontal layers is duplicated. Ultimately, the single stream of dye is uniformly dispersed throughout the cross section of the device.
 Using a non-Newtonian test fluid of 0.2% Carbopol and a doped tracer fluid of similar composition, mixing in the unit is visualized using magnetic resonance imaging (MRI). MRI is a very powerful experimental probe of molecular chemical and physical environment as well as sample structure on the length scales from microns to centimeters. This sensitivity has resulted in broad application of these techniques to characterize physical, chemical and/or biological properties of materials ranging from humans to foods to porous media 1, 2. The equipment and conditions used here are suitable for imaging liquids containing substantial amounts of NMR mobile 1H such as ordinary water and organic liquids including oils. Traditionally MRI has utilized super conducting magnets which are not suitable for industrial environments and not portable within a laboratory (Fig. 2). Recent advances in magnet technology have permitted the construction of large volume industrially compatible magnets suitable for imaging process flows. Here, MRI provides spatially resolved component concentrations at different axial locations during the mixing process. This work documents real-time mixing of highly viscous fluids via distributive mixing with an application to personal care products.

Magnetic resonance imaging (MRI) provides a powerful tool to evaluate the effectiveness of process equipment during operation. We discuss the use of MRI to visualize mixing in a static mixer. The application is relevant to personal care products, but can be applied to a broad range of food, chemical, biomass and biological fluids.

Mixing is a unit operation that combines two or more components into a homogeneous mixture.  This work involves mixing two viscous liquid streams using an ...

Biology

Surface Dye Flow Visualization: A Qualitative Method to Observe Streakline Patterns in Supersonic Flow

Flow visualization around or on a body is an important tool in aerodynamics research. It provides a method to qualitatively and quantitatively study flow structure, and it also helps researchers theorize and verify fluid flow behavior. Flow visualization can be divided into two categories: off-the-surface visualization and surface flow visualization. Off-the-surface flow visualization techniques involve determining the flow characteristics around the body of interest. They include but are not restricted to particle image velocimetry (PIV), Schlieren imaging, and smoke flow visualization. These techniques can provide qualitative as well as quantitative data on the flow around a body. However, these techniques are generally expensive and difficult to set-up. Surface flow visualization techniques, on the other hand, involve coating the body of interest with a dye to study flow on the surface. These techniques, which are more invasive in practice, include dye flow visualization and, more recently, use pressure-sensitive paint, which gives a detailed image of the flow on the body&#39;s surface. This allows researchers to visualize different flow features, including laminar bubbles, boundary layer transitions, and flow separation. Dye flow visualization, the technique of interest in the current experiment, provides a qualitative picture of the surface flow and is one of the simplest and most cost-effective surface flow visualization methods, specifically for visualizing gaseous flows on a body.
In this experiment, the surface flow behavior on six bodies are studied in supersonic flow. The streakline patterns are obtained using the dye flow visualization technique, and the flow paths, degree of flow attachment and separation, and location and type of shocks are identified and studied from the flow images.

Surface Dye Flow: Streakline Patterns in Supersonic Flow

Flow visualization around or on a body is an important tool in aerodynamics research. It provides a method to qualitatively and quantitatively study flow ...

The Diffusion of Passive Tracers in Laminar Shear Flow

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Confocal Imaging of Confined Quiescent and Flowing Colloid-polymer Mixtures

Parallel-plate Flow Chamber and Continuous Flow Circuit to Evaluate Endothelial Progenitor Cells under Laminar Flow Shear Stress

In Situ Monitoring of Diffusion of Guest Molecules in Porous Media Using Electron Paramagnetic Resonance Imaging

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

A Permanent Window for Investigating Cancer Metastasis to the Lung

Analyzing Mixing Inhomogeneity in a Microfluidic Device by Microscale Schlieren Technique

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Controlling Flow Speeds of Microtubule-Based 3D Active Fluids Using Temperature

Quantifying Mixing using Magnetic Resonance Imaging

Surface Dye Flow Visualization: A Qualitative Method to Observe Streakline Patterns in Supersonic Flow