Name: Adapting Taylor Dispersion to Measure the Dispersion Coefficient of Electrolyte Solutions via an Accessible Microfluidic Setup (Video) | JoVE Journal
Uploaded: 2025-10-07T13:00:00.000+00:00
Duration: 9 min 56 s
Description: Learn to adapt Taylor dispersion for measuring electrolyte diffusion coefficients using an accessible microfluidic setup with low-cost fabrication. This method enables rapid visualization of multispecies ion interactions.

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Bernardi and Teague wish to acknowledge the support of the Lab for Education &#38; Application Prototypes (LEAP) at Worcester Polytechnic Institute, as well as funding from the Simons Foundation through a&#160;Travel Support for Mathematicians (award number 963534). Bernardi and Teague also thank Geneva Isaacson, Justin Shen, and Tom Kohen for early work on the experimental setup, Remy Kaplinsky and Academic &#38; Research Computing at Worcester Polytechnic Institute for 3D-printing support, as well as Daniel M. Harris, Eli Silver, and other members of the Harris Lab at Brown University for their insight and helpful advice when setting up the first experiments at Worcester Polytechnic Institute.

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<li>Stroock, A. D., Dertinger, S. K. W., Ajdari, A., Mezic, I., Stone, H. A., Whitesides, G. M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/pubmed?term=((Chaotic+mixer+for+microchannels%5BTitle%5D)+AND+%22Science%22%5BJournal%5D)">Chaotic mixer for microchannels.</a> Science. 295 (5555), 647-651 (2002).</li>
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</ol>

The authors have nothing to disclose.

In this report, we presented a repeatable and accessible experimental setup and protocol to adapt the Taylor dispersion experiment to the microfluidic scale. We leverage an existing xurography technique5 to manufacture our microchannels in-house at low cost using 3D-printing and a desktop craft cutter. The current industry standard for microchannel manufacturing involves the creation of master molds in which channels can be cast. Compared to the technique discussed in this manuscript, these methods can have significantly better channel resolution and feature size (some as small as 0.1 µm), but have the drawback of much higher overhead costs, up to tens of thousands of USD14. In addition to the initial overhead cost, any change to channel design features requires both the creation of a new master mold and the curing of new channels, increasing downtime. In contrast, the starter cost of the channel manufacturing equipment used in this report is approximately 300 USD; this is comparable to the least expensive way of producing a master mold, (such as using polydimethylsiloxane (PDMS)-based techniques, but has the advantage that changes in channel design and the printing of new channels take significantly less time while maintaining surface roughness comparable to the leading manufacturing techniques for 200 µm wide channels5. We are able to cut a microfluidic chip in less than 5 minutes and for less than 1 USD.
In this protocol, data is recorded at a fixed capture point downstream from the tracer inlet through brightfield imaging using a D-SLR camera mounted with a macro lens. While the protocol was developed using a solution of fluorescein sodium salt in deionized water (DI), this imaging method is applicable to other types of dye, such as food coloring, as long as there is a linear relation between the tracer's intensity and concentration. The potential range of chemicals to use can be further expanded by considering their absorption spectrum and background lighting. However, we note that some food dyes are derived from plant materials and may contain more than one chemical species; caution should be employed when selecting the food coloring to be used to avoid conflicting outcomes.
The validity of this setup and protocol was verified by computing the experimental dispersion factor, f, for varying channel aspect ratio and experimental flow rate, and comparing it to its theoretical values for microchannels of rectangular cross-sections, as shown in Figure 7. We also computed the diffusion coefficient, κ, for single-species passive tracers under these varying experimental conditions. Table 1 reports the molecular diffusion coefficient of fluorescein sodium salt obtained from this experimental investigation. Specifically, the tabulated κ-values were computed from equation (3) by using experimental fits for the enhanced dispersion coefficient, K, and theoretical values for the dispersion factor, f. We report average values for four experiments on microchannels with varying aspect ratios (λ = 0.1, 0.25, and 0.5) and flow rates (0.05, 0.1, and 0.2 cm/s). For each, we also include the relative error with respect to the theoretical value10,11, κ = 5.70 x 10-6 cm2/s, demonstrating the accuracy of our method. Finally, for each set of experimental parameters we report the Péclet number and the nondimensional time range defined by dividing the dimensional time t when the experimental intensity curve deviates from the baseline, by diffusion time td = h2/(4κ). We include the nondimensionalized experimental time range to demonstrate that our system has entered the Taylor dispersion regime and therefore can be well-approximated by a Gaussian profile15. In fact, the observation times reported in the last two columns of Table 1, are approximately 2–5 (or more) times the diffusion time td. 
Next, we extended the protocol to investigate multispecies ion interaction and separation. We report below our results from applying the Taylor dispersion experiment to a multispecies electrolyte solution made by mixing fluorescein sodium salt and blue food coloring in DI water. Figure 8 shows the time evolution of the inverted blue channel intensity curves at the camera capture point for three solutes: blue food coloring solution in DI water (–), fluorescein sodium salt solution in DI water (...), and mixed blue food coloring and fluorescein sodium salt solution in DI water (----). Each curve is the average of five experimental trials with one standard deviation in each direction (shading). The curves show the experiments with blue food coloring alone (–) reaching a minimum first, compared to the timescale of the maximum for the fluorescein sodium salt experiments (...). This is consistent with the fact that fluorescein sodium salt has a molecular diffusion coefficient one order of magnitude smaller than that of blue 1, the dye ingredient for the blue food coloring used16. The mixed solution experiments (----) highlight this timescale difference and the consequent ion separation visible through a concavity change in the intensity profile; the curve dips below the baseline first before turning upward and peaking above the baseline. In Figure 9 we plot the same mixed solution inverted blue channel intensity curve (----) overlaid with a curve obtained by summing the individual contributions of the blue food coloring experiments and the fluorescein sodium salt experiments (+++). The difference between the two curves underlines the effect that the ion-ion interaction has on the mixed solution intensity curve. When simply adding the two individual solute contributions, the (+++) curve presents a deeper minimum driven by the strong below-baseline contribution of the blue dye solution (shown as – in Figure 8), before the concavity changes on a longer timescale compared to the mixed solution curve (----). Finally, the sum curve shows again a higher peak above the baseline compared to the mixed curve, due to the fluorescein sodium salt solution behavior (shown as ... in Figure 8). The softer peaking along with the timescale shortening is an indication of the interaction between the blue food coloring and fluorescein sodium salt ions.
The intensity profiles in Figure 6, Figure 8, and Figure 9 exhibit skewness; this may be due to a few differences between classic Taylor dispersion theory2,5,9 and the quantity measured in the experiments. The concentration profile predicted by equation (2) is symmetric in space, but in our experimental setup the measurement is taken at a fixed capture point downstream from the tracer injection site as a function of time. When viewed as a function of time, the resulting profile is inherently skewed. This temporal asymmetry is consistent with observations reported in previous studies, including Taylor and Harris (2019)5. Another possible cause of skewness is the influence of the finite area of the experimental image capture window. A possible alternative to the Gaussian fit described in equation (1), involves fitting the experimental data to the integral of the Gaussian expression in equation (2) over the finite image capture region (in x), as done in Bharadwaj, Santiago, and Mohammadi (2002)17. This contribution to skewness becomes particularly relevant when the size of the capture box is comparable to the standard deviation of the Gaussian curve; here, the length of our capture window is always at least one order of magnitude smaller than the Gaussian’s standard deviation.
This low-cost experimental method provides an accessible approach to the Taylor dispersion experiment at the microscale. The most delicate step in the protocol is the manufacturing and removal of the microchannel negative. During the manufacturing process, extra care must be taken to ensure the channel is secure before cutting to prevent miscuts. When removing the negative, ensure no material is left behind and avoid any contact with the channel sidewalls, which need to be smooth, parallel, and straight to ensure reliable experimental outcomes. A limitation of this method is the inherent xurography resolution limit. In this manuscript, the most difficult channels to produce are those with width w = 200 μm (and aspect ratio λ = 0.5), which pushed against the limit of the craft cutter resolution5. The primary cause of error is the stepper motor employed by the craft cutter, which moves the blades in defined step increments based on mechanical gears. When designs require cuts to be in between the defined step increment, greater error is introduced. In-depth work identifying the resolution limits of this xurography method is available in the literature5.
This experimental procedure provides a simple way to compute the enhanced dispersion factor, K, and molecular diffusion coefficient, κ, of single-species passive tracers. Additionally, the protocol offers a straightforward way of visualizing the interaction and separation dynamics between ion species. Given the accessibility and versatility of the platform, this method is suitable for analyzing the dynamics between ion species and further understanding the complex interplay of transport phenomena and it can be readily employed in applications such as a micromixer.
<table border="1" fo:keep-together.within-page="1" fo:keep-with-next.within-page="always">
	<tbody>
		<tr>
			<td></td>
			<td></td>
			<td></td>
			<td></td>
			<td></td>
			<td colspan="2">Nondimensional time</td>
		</tr>
		<tr>
			<td>Aspect ratio, λ</td>
			<td>Flow rate (cm/s)</td>
			<td>Experimental κ (cm2/s)</td>
			<td>Relative error</td>
			<td>Péclet number (Pe)</td>
			<td>tmin/td</td>
			<td>tmax/td</td>
		</tr>
		<tr>
			<td>0.1</td>
			<td>0.02</td>
			<td>5.813 x 10-6   ±   3.797 x 10-7</td>
			<td>1.982 x 10-2</td>
			<td>~ 18</td>
			<td>~ 30</td>
			<td>~ 52</td>
		</tr>
		<tr>
			<td>0.25</td>
			<td>0.05</td>
			<td>5.333 x 10-6   ±   4.179 x 10-7</td>
			<td>6.443 x 10-2</td>
			<td>~ 44</td>
			<td>~ 11</td>
			<td>~ 27</td>
		</tr>
		<tr>
			<td>0.25</td>
			<td>0.1</td>
			<td>5.655 x 10-6   ±   2.822 x 10-7</td>
			<td>7.838 x 10-3</td>
			<td>~ 88</td>
			<td>~ 6</td>
			<td>~ 16</td>
		</tr>
		<tr>
			<td>0.25</td>
			<td>0.2</td>
			<td>5.978 x 10-6   ±   1.724 x 10-7</td>
			<td>4.884 x 10-2</td>
			<td>~ 175</td>
			<td>~ 2</td>
			<td>~ 10</td>
		</tr>
		<tr>
			<td>0.5</td>
			<td>0.1</td>
			<td>5.444 x 10-6   ±   4.790 x 10-7</td>
			<td>4.496 x 10-2</td>
			<td>~ 88</td>
			<td>~ 6</td>
			<td>~ 16</td>
		</tr>
	</tbody>
</table>
Table 1: Experimental molecular diffusion coefficient (κ) for fluorescein sodium salt. Results are computed from equation (3) by using experimental fits for the enhanced dispersion coefficient, K, and theoretical values for the dispersion factor, f. Each row reports the average κ-value (and related standard deviation) for four experiments on microchannels with a specified aspect ratio (λ = 0.1, 0.25, or 0.5) and flow rate (0.05, 0.1, or 0.2 cm/s). For each, we include the relative error with respect to the theoretical value10,11, κ = 5.70 x 10-6 cm2/s, to demonstrate the accuracy of our method. Additionally, for each row we list the experimental Péclet number and the nondimensional time range defined by dividing the dimensional time t when the experimental intensity curve deviates from the baseline, by diffusion time td = h2/(4κ).
<img alt="Transient absorption graph; intensity vs. time for blue, fluorescein dye mixing experiment." class="xfigimg" src="/files/ftp_upload/69040/69040fig8.jpg" data-altupdatedat="1762509930000" data-alt="Figure 8"> 
Figure 8: Time evolution of averaged inverted blue channel tracer intensity at the camera capture point for three tracers. Time evolution of averaged inverted blue channel tracer intensity at the camera capture point for three tracers: solution of blue food coloring in DI water (at concentration ratio food coloring:DI = 1:20 mL, –), solution of fluorescein sodium salt in DI water (at concentration 0.6 g/L, ...), and a mixed solution containing both blue food coloring and fluorescein sodium salt with the same concentrations as in their individual tracer experiments (----), i.e. blue food coloring:DI = 1:20 mL and 0.6 g/L of fluorescein. Each curve is the average of five experimental trials with one standard deviation in each direction (shading). <a href="https://www.jove.com/files/ftp_upload/69040/69040fig8large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Transient absorption graph, intensity vs. time for dye and fluorescein solutions, spectral analysis." class="xfigimg" src="/files/ftp_upload/69040/69040fig9.jpg" data-altupdatedat="1762509930000" data-alt="Figure 9"> 
Figure 9: Time evolution of averaged inverted blue channel tracer intensity at the camera capture point for mixed solution. Time evolution of averaged inverted blue channel tracer intensity at camera capture point for mixed solution containing blue food coloring and fluorescein sodium salt (----) with blue food coloring:DI = 1:20 mL and 0.6 g/L of fluorescein, and a sum curve (+++) combining the intensity of the blue food coloring solution experiments (solid curve in Figure 8, –) and fluorescein sodium salt solution experiments (dotted curve in Figure 8, ...). The mixed curve is the average of five experimental trials with one standard deviation in each direction (shading). The standard deviation of the sum curve is calculated by taking the square root of the sum of the standard deviations squared from the experiments with each individual tracer solution. <a href="https://www.jove.com/files/ftp_upload/69040/69040fig9large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>

In recent years, significant research efforts have been focused on investigating and developing cost-effective microfluidic devices that offer precise control over flow, particles, and solute transport. Multispecies electrolyte solutions play a critical role in a wide range of applications, from energy storage and biomedical diagnostics to environmental monitoring and water purification. Understanding how different ion species diffuse and interact in these systems is essential for optimizing performance and stability in electrochemical and transport-driven processes.
When an electrolyte solution contains ions with different diffusion coefficients, their unequal migration induces an internal electric field, even in the absence of an externally applied voltage. Faster-diffusing ions tend to separate from slower ones, momentarily creating a charge imbalance. To preserve electroneutrality, the system generates a diffusion-induced electric potential. This field slows the faster ions and accelerates the slower ones. The resulting electric potential depends on the relative ion mobilities and concentration gradients and is well described by the Nernst-Planck equations under electroneutrality constraints. Classical electrochemical models, such as the Henderson and Nernst equations, quantify this phenomenon by relating it to ion transport numbers and concentration differences1.
Taylor dispersion analysis has long been a powerful technique to measure molecular diffusivity by observing how a solute spreads in a pressure-driven laminar flow through a straight channel2,3. It accounts for the interplay between advection and diffusion and enables accurate inference of molecular diffusion coefficients from effective dispersion rates. This method is particularly attractive because it combines precision, minimal sample requirements, and fast data acquisition. Traditionally used for single-species tracers, recent theoretical extensions now enable its application to multispecies systems, allowing researchers to theoretically infer individual ion diffusivities based on the coupled transport behavior4.
However, the high cost and technical complexity of conventional microfluidic setups&#8211;often based on cleanroom-dependent photolithography&#8211;pose significant barriers to the broader adoption of this method. In this work, we present a low-cost, accessible, and reproducible adaptation of the Taylor dispersion technique, which employs microchannels fabricated via xurography with a desktop craft cutter. This approach, with a startup cost of approximately 300 USD, allows for rapid prototyping and consistent channel fabrication without the need for costly specialized facilities5. Using brightfield imaging via a D-SLR camera and macro lens, the protocol builds a time series of the tracer concentration evolution at a fixed capture point downstream from the injection site6. We demonstrate that this platform can accurately measure diffusion coefficients for single-species passive tracers and extend the method to analyze multispecies electrolyte systems. Results reveal clear signatures of diffusivity variations arising from ion-ion coupling effects. This accessible and cost-effective method offers a practical tool for investigating ionic transport phenomena in complex electrolyte mixtures. For example, the proposed experimental setup can be readily adapted to be used as a micromixer to evaluate the mixing efficiency of multispecies solutes7, or to design desired polymer molecular weight distributions through a computer-controlled tubular flow reactor8.

<table><tbody><tr><td>Adjustable volume pipette, 0.5&amp;ndash;10 &amp;mu;L</td><td>MUHWA&amp;nbsp;</td><td>B08TBPMKZL</td><td>Turned into table</td></tr><tr><td>Cameo Cutting Mat, 12 x 12 in</td><td>Silhouette America</td><td>8.19177E+11</td><td>used aphabetize function in table</td></tr><tr><td>Camera plug-in battery</td><td>NEEWER</td><td>B0B5WY8T96</td><td>removed 3D printed ports</td></tr><tr><td>Camera tripod&amp;nbsp;</td><td>Vanguard</td><td>B00CCA1Y3S</td><td>added Form 2 3D printer&lt;br/&gt; &lt;br/&gt; added Form 2 3D printer</td></tr><tr><td>Clear Resin V5</td><td>Formlabs</td><td>&lt;a href=&quot;https://formlabs.com/store/materials/clear-resin/&quot;&gt;https://formlabs.com/store/materials/clear-resin/&lt;/a&gt;</td><td>3D-printing resin</td></tr><tr><td>Cyanoacrylate (CA) glue accelerator</td><td>Starbond</td><td>B00BUVAZ5S</td><td>added a resin as well</td></tr><tr><td>D-SLR camera</td><td>Nikon</td><td>D500</td><td>added printer software</td></tr><tr><td>Dashboard software</td><td>Formlabs</td><td>&lt;a href=&quot;https://formlabs.com/software/dashboard/&quot;&gt;https://formlabs.com/software/dashboard/&lt;/a&gt;</td><td>3D-printing software&lt;br/&gt; &lt;br/&gt; added CAD solidworks</td></tr><tr><td>DeIonized water</td><td>N/A</td><td>N/A</td><td>added matlab</td></tr><tr><td>Dimmable LED ligth panel</td><td>Kaiser Fototechnik</td><td>202455</td><td>Slimlite Plano 5000K 19.6 x 13.8 in&lt;br/&gt; &lt;br/&gt; changed the FSS lot to catalog num</td></tr><tr><td>Double-sided polyimide tape, 1 in x 36 yd roll</td><td>Bertech</td><td>B00HFN6E0K</td><td></td></tr><tr><td>Flourescein sodium salt dye - 100 g</td><td>Sigma-Aldrich</td><td>5184A17</td><td></td></tr><tr><td>Form 2 3D Printer</td><td>Formlabs</td><td>&lt;a href=&quot;https://formlabs.com/3d-printers/form-2/&quot;&gt;https://formlabs.com/3d-printers/form-2/&lt;/a&gt;</td><td></td></tr><tr><td>Glass syringe with Luer tip, 500 &amp;micro;L</td><td>Hamilton Company</td><td>PN: 80801</td><td></td></tr><tr><td>High-precision tweezers, 0.004 in wide x 0.002 in thick</td><td>McMaster Carr</td><td>ECCN: EAR99</td><td>Standard pointed tip</td></tr><tr><td>KimWipes</td><td>Kimtech</td><td>B0013HT2QW</td><td>4.4 x 8.4 in</td></tr><tr><td>Liquid pipette pipettor tips, 1000 pcs/bag</td><td>MUHWA&amp;nbsp;</td><td>B07S1WJCHP</td><td>1 needed per experimental trial</td></tr><tr><td>Macro lens 20 mm f/2</td><td>Mitakon Zhongyi</td><td>B075JRGWW1</td><td></td></tr><tr><td>Masking tape, 0.70 in x 54.6 yd</td><td>Scotch Brand</td><td>B00347A8E4</td><td></td></tr><tr><td>MATLAB software, edition 2023b</td><td>Mathworks</td><td>&lt;a href=&quot;https://www.mathworks.com/products/matlab.html&quot;&gt;https://www.mathworks.com/products/matlab.html&lt;/a&gt;</td><td></td></tr><tr><td>Medium CA Glue, 2 oz.&amp;nbsp;</td><td>Starbond</td><td>126150047</td><td>Premium Cyanoacrylate Super Glue</td></tr><tr><td>Memory Card, 64 GB</td><td>San Disk</td><td>&amp;lrm;B09X7C7NCZ</td><td></td></tr><tr><td>Neon assorted food colors &amp;amp; egg dye, 1.5 fl oz</td><td>McCormick &amp;amp; Company, Inc.</td><td>B09PFV6275</td><td>Pink, green, and blue. Only 1 vial of blue food coloring needed. Blue food coloring ingredients: water, propylene glycol, FD&amp;amp;C blue 1, propylparaben (preservative).</td></tr><tr><td>Precision balance</td><td>Sartorius Lab Instruments</td><td>BCE224 - 1S</td><td>Entris&amp;reg; II Essential Line. Used to weigh fluorescein sodium salt powder for tracer mixing.</td></tr><tr><td>PTFE microtubing, 0.012&quot; ID x 0.030&quot; OD</td><td>Cole Parer</td><td>mp-00060882</td><td>Microbore transfer tubing. Minimum needed: 50 cm.</td></tr><tr><td>Remote programmable trigger</td><td>Pixel Pro</td><td>TW-283DC0/DC2</td><td></td></tr><tr><td>Scissors</td><td>Amazon</td><td>B01BRGUAT6</td><td></td></tr><tr><td>Scotch tape</td><td>Scotch Brand</td><td>B01C5IHGJW</td><td></td></tr><tr><td>Silhouette Cameo 4 Craft Cutter</td><td>Silhouette America</td><td>8.19177E+11</td><td></td></tr><tr><td>Silhouette Cameo AutoBlade (Type B)</td><td>Silhouette America</td><td>8.19177E+11</td><td>2 needed</td></tr><tr><td>Silhouette Studio Basic Edition software version 4.5</td><td>Silhouette America</td><td>&lt;a href=&quot;https://www.silhouetteamerica.com/silhouette-studio&quot;&gt;https://www.silhouetteamerica.com/silhouette-studio&lt;/a&gt;</td><td>If importing the .DXF template files provided as part of the Supplementary Files in this software version, first set the software import settings to read the file size &#039;as is&#039; by clicking: Edit &gt; Preferences &gt; Import &gt; DXF &gt; Open &gt; As-is.</td></tr><tr><td>Soft rubber brayer, 4.75 x 1.75 x 6.62 in</td><td>Speedball</td><td>B003IFY622</td><td></td></tr><tr><td>SOLIDWORKS software, Education Edition</td><td>SOLIDWORKS</td><td>&lt;a href=&quot;https://www.solidworks.com/solution/job-functions/educators&quot;&gt;https://www.solidworks.com/solution/job-functions/educators&lt;/a&gt;</td><td></td></tr><tr><td>Standard infuse/withdraw 11 elite syringe pump</td><td>Harvard Apparatus</td><td>70-4504</td><td></td></tr><tr><td>Syringe tip with Luer lock, tip size: 0.5 in, 27 Gauge, Clear</td><td>Metcal&amp;nbsp;</td><td>B00F4B9W40</td><td>2 needed</td></tr><tr><td>Ultra clear polyester sheets, 12 x 12 x 0.007 in</td><td>Grafix</td><td>B001K7Q6Z0</td><td></td></tr></tbody></table>

adapting taylor dispersion to measure the dispersion coefficient of electrolyte solutions via an accessible microfluidic setup

Adapting Taylor Dispersion to Measure the Dispersion Coefficient of Electrolyte Solutions via an Accessible Microfluidic Setup

The field of microfluidics has become increasingly prominent as it allows for rapid and precise control of fluids and particles, making it easier to synthesize compounds and separate mixtures. We perfected an accessible, repeatable microscale adaptation of the Taylor Dispersion experiment using microchannels fabricated in-house with a desktop craft cutter. The starter cost of this fast and accessible microfluidics xurography technique is approximately 300 USD, orders of magnitude lower than typical photolithography methods. Pressure-driven laminar flow from a programmable syringe pump transports an injected tracer solution downstream in the microchannel, where a digital single-lens reflex (D-SLR) camera with a macro lens captures the tracer concentration evolution over time at a fixed location. Using this experimental platform, we can compute the diffusion coefficients for single-species passive tracers under varying experimental conditions. We then extended the protocol to electrolyte mixtures, observing preliminary evidence of diffusivity changes arising from nontrivial ion-ion coupling effects. This accessible experimental method provides a practical tool for probing multispecies transport and offers insights into the complex interactions governing ionic mobility.

The microfluidic chip fabrication steps are shown in Figure 1. We include in Figure 2 the suggested steps to connect PTFE tubing to the syringe tip used to inject the background flow of deionized water (DI) in the microfluidic chip through the programmable syringe pump. Figure 3 includes a labeled photo of the complete experimental setup. Figure 4 includes not to scale top view (Figure 4A) and side view (Figure 4B) diagrams of the experimental setup highlighting relative microfluidic chip and camera positioning. Figure 5 reports the sequence of operations applied to the experimental images during the data processing phase of the protocol. In Figure 5A we showcase how the code aligns the microchannel horizontally (if needed), then Figure 5B shows the cropping of the square region of interest centered around the capture point and with side length set by the microchannel width, w. Figure 5C isolates the blue channel from the full RGB image in the cropped region of interest, and then finally Figure 5D shows the inverted intensity value for the blue channel of the cropped region obtained by subtracting it from 255 (the maximum intensity for each color-channel).
Figure 6 overlays the results from one experimental run (dashed) with the corresponding extrapolated fit (solid). Here, each experimental data point is the averaged inverted blue channel intensity value computed through the data processing steps shown in Figure 5. At the fixed capture point downstream from the tracer inlet, Taylor dispersion theory2,5,9 predicts that the tracer concentration evolution over time is described by:
<img alt="Heat diffusion equation C(t)=C₀/√(4πKt) e^(-(x-Ut)²/4Kt) symbol." src="/files/ftp_upload/69040/69040eq2v5.jpg" data-altupdatedat="1762509930000" data-alt="Equation 1">  (2)
where C(t) is the cross-sectionally averaged tracer concentration (g/L), which has been verified to be linearly related to the tracer's measured intensity; C0 is the initial tracer concentration (g/L), U is the flow rate (cm/s), t is time (s), and x (cm) is the axial coordinate in the channel with respect to the tracer injection location. K is the tracer's enhanced dispersion coefficient (cm2/s) due to the interplay of advection and molecular diffusion. We input the experimental parameters and use the code's nonlinear curve-fitting application (curveFitter) to find the best fit value for K. Three experimental frames for time t = 140 s, 150 s, and 200 s are shown alongside the experimental (dashed) and fitted (solid) curves produced for one experimental run at flow rate U = 0.1 cm/s in a microchannel of length 18.77 cm and aspect ratio λ = 1/4; this corresponds to Péclet number Pe <img alt="Symbol representing static equilibrium in diagram; ΣFx=0 indicates balance of forces." src="/files/ftp_upload/69040/69040eq10.jpg" style="opacity: 0.9; margin: 0px;" data-altupdatedat="1762509930000" data-alt="Equation 10"> 88. Here, the tracer consists of 0.6 g/L of fluorescein sodium salt diluted in DI water with molecular diffusion coefficient reported in the literature10,11 as κ = 5.70 x 10-6 cm2/s. All experiments reported in this manuscript were run at a room temperature of 22 °C.
The experimental enhanced dispersion coefficient, K, can be used to benchmark the validity of our experimental setup and protocol by computing a related quantity–the dispersion factor2,5,9,12, f. This parameter depends on the geometry of the channel and is calculated as5,12,13:
<img alt="Fluid dynamics equations; stability analysis; mathematical formula; understanding flow behavior." src="/files/ftp_upload/69040/69040eq3v5.jpg" data-altupdatedat="1762509930000" data-alt="Equation 1">  (3)
where κ is the tracer's molecular diffusion coefficient (cm2/s) and h/2 is the chosen characteristic length. The Péclet number is a nondimensional parameter quantifying the ratio of advective to diffusive effects, Pe = Uh/(2κ). Figure 7 shows good agreement between dispersion factor results from experimental runs in microchannels with rectangular cross-sections of three different aspect ratios and flow rates, and the theoretical dispersion factor behavior5,12,13.
<img alt="Static equilibrium diagram; bar dimensions, hole placements, layered structure details; engineering analysis." class="xfigimg" src="/files/ftp_upload/69040/69040fig1.jpg" data-altupdatedat="1762509930000" data-alt="Figure 1"> 
Figure 1: Microfluidic chip fabrication. (A) Design for the top polyester sheet of a 21 x 5 cm chip. Three holes are cut by the desktop craft cutter, left to right, to serve as flow inlet, tracer inlet, and flow outlet, respectively. (B) Design for an 18.77 cm polyimide microchannel with capture point 15 cm downstream from the tracer inlet. (C) Exploded view of microfluidic chip assembly, bottom to top: bottom polyester layer, polyimide microchannel layer, top polyester layer with polyimide gasket and 3D-printed port. <a href="https://www.jove.com/files/ftp_upload/69040/69040fig1large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Capillary action diagram; liquid rise in tubes showing surface tension, adhesion, cohesion concepts." class="xfigimg" src="/files/ftp_upload/69040/69040fig2.jpg" data-altupdatedat="1762509930000" data-alt="Figure 2"> 
Figure 2: Diagram showing how to connect PTFE tubing to a syringe tip. The tubing ID is 0.3048 mm, and the 27-G syringe tip OD is 0.4064 mm, so making a small cut of approximately 1 mm (left) can be helpful in providing a wider opening area to guide the syringe tip (center). Use tweezers to insert the tubing over the syringe tip and pull down (right). <a href="https://www.jove.com/files/ftp_upload/69040/69040fig2large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Microfluidic setup with syringe pump, glass syringe, micropipette, camera, light panel, PTFE tubing." class="xfigimg" src="/files/ftp_upload/69040/69040fig3.jpg" data-altupdatedat="1762509930000" data-alt="Figure 3"> 
Figure 3: Labeled photo of the experimental setup. Left to right: A D-SLR camera with a 20 mm f/2 macro lens is mounted facing down on a tripod to capture the microchannel taped to the illuminated light panel. A 0.5 mL glass syringe connected to the microchannel through PTFE tubing is set on the programmable syringe pump. The remote trigger is used to activate the camera during the experimental runs. The micropipette is used to generate the tracer initial condition, as described in step 3.2 of the protocol. <a href="https://www.jove.com/files/ftp_upload/69040/69040fig3large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Optical imaging setup for droplet measurement; syringe, camera, scale; fluid dynamics experiment." class="xfigimg" src="/files/ftp_upload/69040/69040fig4.jpg" data-altupdatedat="1762509930000" data-alt="Figure 4"> 
Figure 4: Diagrams of the experimental setup (not to scale). (A) Top view, left to right: programmable syringe pump mounted with a 0.5 mL glass syringe; PTFE tubing connecting syringe pump to microfluidic chip; microfluidic chip taped on a light panel 1 cm away from the edge; micropipette used to inject tracer solution through tracer inlet hole; D-SLR camera with macro lens mounted on tripod face down to frame the capture point. (B) Side view, left to right: PTFE tubing connecting syringe pump to microfluidic chip; syringe tip and 3D-printed port on microfluidic chip; micropipette used to inject tracer solution through tracer inlet hole; D-SLR camera with macro lens mounted face down 1 cm above the capture point. <a href="https://www.jove.com/files/ftp_upload/69040/69040fig4large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Microscope image of microchannel structure for fluid flow analysis, featuring 1000 μm scale bar." class="xfigimg" src="/files/ftp_upload/69040/69040fig5.jpg" data-altupdatedat="1762509930000" data-alt="Figure 5"> 
Figure 5: Image processing steps in the provided code (see Supplementary File 5). (A) Rotated experimental image so that the microchannel is horizontal. Scale bar: 1000 µm. (B) Square selection for the region of interest (ROI) to be cropped with side length matching the distance between microchannel walls; here, 400 µm. (C) Cropped ROI where the blue channel is selected out of the full red, green, and blue (RGB)  image. Scale bar: 200 µm. (D) Inverted blue channel for the cropped ROI. <a href="https://www.jove.com/files/ftp_upload/69040/69040fig5large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Graph of intensity vs time with experimental data and MATLAB fit; microscopy images included." class="xfigimg" src="/files/ftp_upload/69040/69040fig6.jpg" data-altupdatedat="1762509930000" data-alt="Figure 6"> 
Figure 6: Cross-sectionally averaged tracer intensity vs. time at camera capture point for fluorescein tracer (dashed) overlaid with the extrapolated curve fit (solid). This trial was run with a 0.6 g/L of fluorescein sodium salt in DI water tracer, on a microchannel with length 18.77 cm and aspect ratio λ = 1/4, at flow rate 0.1 cm/s and Pe <img alt="Symbol representing static equilibrium in diagram; ΣFx=0 indicates balance of forces." src="/files/ftp_upload/69040/69040eq10.jpg" style="opacity: 0.9; margin: 0px;" data-altupdatedat="1762509930000" data-alt="Equation 10"> 88. The inverted blue channel intensity for three experimental frames at times 140 s (blue), 150 s (orange), and 200 s (green) is shown above the plot with brightness doubled for clarity. <a href="https://www.jove.com/files/ftp_upload/69040/69040fig6large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Dispersion factor vs. aspect ratio graph; theoretical curve, experimental data points with error bars." class="xfigimg" src="/files/ftp_upload/69040/69040fig7.jpg" data-altupdatedat="1762509930000" data-alt="Figure 7"> 
Figure 7: Dispersion factor vs. microchannel aspect ratio. Comparison of theoretical (blue curve) and experimental values (black data points) for the dispersion factor, f. The theoretical curve is obtained using the built-in finite element method partial differential equations solver in Wolfram Mathematica (NDSolve)12. We show average and standard deviation of experimental data for: four trials with λ = 0.1 and flow rate 0.02 cm/s; twelve trials with λ = 0.25 and flow rates 0.05 cm/s (four), 0.1 cm/s (four), and 0.2 cm/s (four); four trials with λ = 0.5 and flow rate 0.1 cm/s. All experiments were conducted on microchannels of length 6.07 cm (with capture point 3 cm downstream from the tracer inlet); results were then benchmarked on 18.77 cm microchannels. <a href="https://www.jove.com/files/ftp_upload/69040/69040fig7large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
Supplementary File 1: .sdlprt file for the port  <a href="https://www.jove.com/files/ftp_upload/69040/3DPort_revised" target="_blank">Please click here to download this file.</a>
Supplementary File 2: .DXF template file of the chip top layer. <a href="https://www.jove.com/files/ftp_upload/69040/Chip_top.dxf" target="_blank">Please click here to download this file.</a>
Supplementary File 3: .DXF template file of the chip gaskets. <a href="https://www.jove.com/files/ftp_upload/69040/Chip_gaskets.dxf" target="_blank">Please click here to download this file.</a>
Supplementary File 4: .DXF template file of the chip microchannel. <a href="https://www.jove.com/files/ftp_upload/69040/Chip_microchannel.dxf" target="_blank">Please click here to download this file.</a>
Supplementary File 5: MATLAB code files used for data processing. <a href="https://www.jove.com/files/ftp_upload/69040/MATLAB%20files%20documentation.pdf" target="_blank">Please click here to download this file.</a>

Here, we present a protocol to adapt the Taylor dispersion experiment to the microscale using microchannels fabricated in-house with a desktop craft cutter. The experimental platform can be used to compute the diffusion coefficient of single-species passive tracers and to visualize multispecies ion interaction and separation.

The field of microfluidics has become increasingly prominent as it allows for rapid and precise control of fluids and particles, making it easier to ...

The scope of our work is to design and implement an accessible microfluidics experimental platform suitable to answer a broad range of fundamental fluids questions. The biggest challenge is to develop a reproducible and yet flexible manufacturing process for microchannels with sufficient precision utilizing low-cost equipment. Our research seeks to address the current lack of easily accessible and accurate experimental setups and protocols to measure the enhanced diffusivity of an electrolyte species.Our platform also allows for visualization of multi-species ion interactions. Our experimental setup and protocol are inexpensive, easily accessible, and accurate. The low-cost microchannel manufacturing technique employed allows for the production of custom design chips in minutes.To begin, launch the craft cutter design software on the connected computer. Design the microchannel top directly in the software, or import a compatible design from external software. Then attach a 21 centimeter by five centimeter polyester rectangle to the sticky side of the cutting mat.Using masking tape, tape all four perimeter edges to secure the rectangle. Next, load the cutting mat into the craft cutter by aligning the marked edges with the arrow indicators on the device. Insert the blade in the first carriage slot of the craft cutter.Click on Send located at the top right of the design page on the monitor to proceed to the review screen. Then set the blade depth to nine, force to 33, passes to one, and speed to one. Now click on Send to submit the job to the craft cutter and initiate the cutting process.After removing the cutting mat from the cutter, use tweezers to remove the negative polyester material from the cut sheet. Next, design donut-shaped polyamide gaskets using the craft cutter design software or import the gasket design from compatible software. Attach a 21 centimeter long piece of polyamide tape with the sticky side facing up onto the cutting mat and secure it with masking tape along all four edges.Enter the cut settings for the polyamide tape with a blade depth of nine, force of one, passes of one and speed of one. Click on Send to submit the gasket cutting job to the craft cutter. Then place the cut polyester sheet on a clean, flat surface with the protrusions facing upward.Using tweezers, peel off one gasket from the cut polyamide tape and place it onto the flat underside of a 3D printed port. Align the port with the flow inlet hole, and using the gasket, attach it to the flat-laid polyester sheet. Now in a fume hood, apply a small amount of super glue along the perimeter of the port while pressing it downward to create a watertight seal.For the fabrication of the polyamide microchannel body, design the microchannel body using the craft cutter design software or by importing a compatible external design. Attach the 21 centimeter long strip of polyamide tape with the sticky side up onto the cutting mat. Then, load the cutting mat into the craft cutter by aligning the marked edges with the arrow indicators on the device.Click on Send at the top right of the design page to review the material and cut settings. Use the same cutting parameters as used for the gaskets. Click Send to submit the cutting job to the craft cutter.Then remove the cutting mat from the cutter and using tweezers, remove the negative polyamide material from the channel design. Now place the polyamide tape with the sticky side facing upward on a flat, clean surface. Carefully position the polyester rectangle onto the exposed polyamide tape, centering the polyamide strip across the width of the polyester.Using a roller, apply even downward pressure to eliminate large air bubbles and visually inspect for any debris or warping. Afterward, flip the polyamide tape assembly and remove the protective cover from the adhesive side. Align the top polyester sheet mounted with the 3D printed port to the inlet and outlet of the polyamide tape, then carefully lay the polyester sheet over the polyamide layer.For the syringe pump setup, fill a 0.5 milliliter glass syringe with deionized water. Mount the syringe onto a programmable syringe pump and press the fast forward button until water begins to emerge from the syringe tip. Then, cut a 50 centimeter long piece of polytetrafluoroethylene tubing.Using tweezers, connect the two ends of the tubing to 27 gauge syringe tips by inserting the tubing over the tips and pulling it downward. Fill the connected syringe tip and tubing with deionized water until a convex meniscus forms at the tip opening. Attach the tip to the prem mounted glass syringe on the pump, ensuring there are no air bubbles present in either the syringe or the tip.Set the syringe pump to infuse mode only. Input the syringe type and size as 0.5 milliliters into the pump's interface. Using 2.54 centimeter wide masking tape, tape the fully assembled microfluidic tip to the light panel.Next, mount a 20 millimeter F2 macro lens onto the camera and connect it to a remote trigger. Set up a tripod and mount the camera above the light panel, angled downward to face the experiment. Center the view on the capture point cut in the polyamide tape.Program the camera via the remote trigger to take images every one second. Apply a layer of transparent tape over the tracer inlet hole to prevent liquid from escaping, ensuring one edge of the tape is folded over to form a small tab for easy removal. Connect and run the programmable syringe pump to gently flood the microchannel with deionized water at a very low flow rate.Then fill a 0.5 microliter micro pipette tip with a prepared tracer solution. Using the folded tab, peel back the tape covering the tracer inlet hole. Using the corner of a low lint wipe, lightly wick away any excess deionized water from the inlet hole and wait 30 seconds for the waterfronts to stabilize.After 30 seconds, dispense the tracer solution into the inlet hole using the pipette. Immediately smooth the tape back over the hole using minimal pressure and a continuous motion to reseal the inlet. After ensuring that the syringe pump is programmed to the target volumetric flow rate, start the syringe pump and trigger the remote camera simultaneously to begin imaging.If the horizontal edges of the rectangle overlay are not aligned with the microchannel walls, hover the cursor over a rectangle corner, click and rotate the image until the horizontal walls align parallel to the channel walls. Press any key to proceed. The image popup will close and reopen with the corrected orientation.Click and drag to select a square region with sides equal to the channel width, centered at the capture point. Press any key to continue and the image popup will close. Then extract the blue channel intensity at each pixel within the selected crop region from the RGB image.Invert the values by subtracting each from 255, the maximum blue channel value. Compute the mean intensity value of the inverted blue channel across all pixels in the cropped region. Save each computed value to generate a time series of average inverted blue channel intensity at the capture point.Use the nonlinear curve fitter toolbox in the code to input the full-time series of average inverted blue channel intensities. The averaged inverted blue channel intensities over time were plotted and showed close agreement between experimental data and the theoretical tailor dispersion fit, with time points at 140 seconds, 150 seconds and 200 seconds clearly shown. Dispersion factor results from experiments at three different aspect ratios showed good agreement with theoretical predictions.

adapting-taylor-dispersion-to-measure-dispersion-coefficient

Research

JoVE Journal

Engineering

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Generation of Dynamical Environmental Conditions using a High-Throughput Microfluidic Device

This protocol details the design and fabrication of a microfluidic device suitable for investigating microtubule polymer mechanics. The synthesis of microfabrication, automated flow control, and computational modeling techniques enables a flexible system ideally suited for probing the cellular cytoskeleton in vitro.

Development of a Microfluidics-Based Approach for Investigating Microtubule Polymer Mechanics

Learn to adapt Taylor dispersion for measuring electrolyte diffusion coefficients using an accessible microfluidic setup with low-cost fabrication. This method enables rapid visualization of multispecies ion interactions.

Adapting Taylor Dispersion to Measure the Dispersion Coefficient of Electrolyte Solutions via an Accessible Microfluidic Setup

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