Electroosmotic Switching in a Branched Microchannel (COMSOL) This example investigates the possibility of using electroosmosis as a “switching” mechanism for controlling the flow of liquids in microchannels. Modify Example 12.4 so that it now includes a “vertical” branch of width 5 × 10^−5 m, exten

Question

Electroosmotic Switching

in a Branched Microchannel (COMSOL)

This example investigates the possibility of using electroosmosis as a "switching" mechanism for controlling the flow of liquids in microchannels.

Modify Example 12.4 so that it now includes a "vertical" branch of width [latex]5 imes 10^{-5} \mathrm{~m}[/latex], extending in "height" as far as [latex]y=2.5 imes 10^{-4} \mathrm{~m}[/latex], as shown below. Investigate the streamlines and equipotentials for the two cases of applied voltages shown in Figs. E12.5.1 and E12.5.2. All physical properties are identical with those given in Example 12.4, and the solution procedure is also very similar.

Accepted Answer

Select the Physics

Open COMSOL and select Blank Model. To avoid repeating a lot of preliminary work, use the pull-down File menu to open the file E12.5.mph (or similar) saved in Step 14 of the previous example.
Save the model developed thus far, using a new name.

Define the Parameters and Establish the Geometry

Add two more parameters. L-click Parameter in the Global Definitions node. In the Settings panel, enter the parameters [latex]L 2[/latex] and [latex]\mathrm{rad}[/latex] in the Name column and enter [latex]2.0 \mathrm{e}-4[\mathrm{~m}][/latex] and [latex]0.25 \mathrm{e}-4[\mathrm{~m}][/latex], respectively, in the Expression column.
Add the vertical rectangle to the geometry. R-click Geometry and select Rectangle. Enter the values for Width and Height as [latex]H[/latex] and [latex]L 2[/latex], and change the base for the corner to be located at [latex]((L-H) / 2, H)[/latex]. L-click Build Selected.
R-click Geometry and select Boolean and Partitions and then Union. Add both geometries to the union by L-clicking each rectangle in the Graphics window. Ensure that the Keep interior boundaries option is not selected in the Settings window. L-click Build Selected.
Add the two fillet corners to the new union. R-click Geometry and select Fillet. Enter the parameter rad in the Radius input field in the Settings window. Add the vertices to be "filleted" by hovering and L-clicking the two vertices defined by the intersection of the two rectangles. L-click Build All Objects.

Define the Boundary Conditions

Define a neutral flow condition for the top boundary. R-click Laminar Flow and L-click the Open Boundary leaf. Add the top boundary segment to the Boundary Selection list by hovering in the Graphics window and L-clicking.
Define the potential of the top boundary. R-click the Electric Currents node and select Electric potential. In the Settings window, assign the top boundary segment by hovering and L-clicking that segment in the Graphics window. Also, set the electric potential to [latex]-1[/latex] [V].

Create the Mesh and Solve the Problem

Set the element size. L-click the Mesh node and set the element size to Extra Fine, noting there are 1,957 elements (a finer mesh is needed because of the more complicated geometry than in Example 12.4). Because there is now a flow in the [latex]y[/latex]-direction, there is no longer the need to tackle the scaling problem detailed in Step 13 of the previous example.
R-click the Study node and select Compute. Save the results in a file.
Display the Results for both Case 1 and Case 2
We wish to show 10 streamlines, all starting along the right-hand entrance [latex]\left(x=L=5 imes 10^{-4} ight)[/latex], equally spaced between [latex]y=0[/latex] and [latex]y=H=0.5 imes 10^{-4}[/latex]. Right-click the Results node and select 2D Plot Group. R-click Plot Group 4 and select Streamline. In the Settings window, select the Positioning options, choose Start point controlled, and change the Entry method to Coordinates. To define start points at the right end, set the [latex]x[/latex]-coordinate to a single value, [latex]L[/latex]. For the [latex]y[/latex]-values, L-click the range-build icon to the right of the field. In the panel that opens, change the entry method to Number of values. Enter [latex]0.0[/latex] and [latex]H[/latex] as the Start and Stop values, with 10 as the Number of values. L-click Replace. Note that this process simply builds entries for the range function, and users could directly enter the range function as an option. Change Color to Black. L-click Plot.
To show the equipotentials, R-click the 2D Plot Group 4 and select Contour. In the Expression field, enter the variable representing the potential, [latex]V[/latex]. In the Settings defaults, choose 25 black equipotentials and L-click Plot.
Modify the potentials for the second set of conditions. In the Electric Currents physics node, modify the three Electric Potential boundary definitions to be [latex]-1[\mathrm{~V}], 1[\mathrm{~V}][/latex], and [latex]0[\mathrm{~V}][/latex], which correspond to the left, right, and top boundary segments.
R-click the Study node and select Compute.
Inspect the change in the streamlines and potential by L-clicking the Streamline 1 Group

Discussion of Results

Figs. E12.5.1 and E12.5.2 show that the direction of liquid flow can be controlled by suitable adjustment of the applied voltages. Observe that in both cases the entrance to the system that has no flow has an electric potential (of zero) that is midway between those of the entrances between which there [latex]i s[/latex] a flow. Note also that the streamlines are everywhere orthogonal to the electric equipotentials.

By a similar adjustment of electric potentials, liquid flows can be controlled in a much more complex arrangement of microchannels.

Question 12.5: Electroosmotic Switching in a Branched Microchannel (COMSOL)...

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