COMSOL 6.4 - Results

Create a surface dataset to view the pressure on the channel walls.

1

In the Results toolbar, click More Datasets

and choose Surface

2

In the Settings window for Surface, locate the Selection section. Click Paste Selection

3

In the Paste Selection dialog, type 1 3 5 6 7 8 11 12 13 14 15 17 18 19 20 21 22 24 26 27 in the Selection text field.

4

Velocity (Uncoupled Flow)

First plot the velocity of the flow within the channel.

1

In the Results toolbar, click 3D Plot Group

2

In the Settings window for 3D Plot Group, type Velocity (Uncoupled Flow) in the Label text field.

Use a slice plot to view the data on one or more slices through the geometry.

1

In the Model Builder window, right-click Velocity (Uncoupled Flow)

and choose Slice

2

In the Settings window for Slice, locate the Expression section. From the Unit list, choose mm/s.

Add additional slices in different directions.

1

Right-click Velocity (Uncoupled Flow)

and choose Slice

2

In the Settings window for Slice, locate the Expression section. From the Unit list, choose mm/s.

3

Locate the Plane Data section.

-

From the Plane list, choose xy-planes.

-

In the Planes text field, type 1.

The extra slices should use the same scale and colors for the velocity plot as the existing slice.

4

Click to expand the Inherit Style section. From the Plot list choose Slice 1.

To avoid duplicate titles, turn off the title for additional slices.

5

Click to expand the Title section. From the Title type list, choose None.

Add slices in a third plane.

1

Under Velocity (Uncoupled Flow)

, right-click Slice 2

and choose Duplicate

2

In the Settings window for Slice, locate the Plane Data section.

-

From the Plane list, choose zx-planes.

-

In the Planes text field, enter 2.

Use the arrow volume plot to visualize the flow direction.

1

Right-click Velocity (Uncoupled Flow)

and choose Arrow Volume.

2

In the Settings window for Arrow Volume, locate the Arrow Positioning section.

-

Find the x grid points subsection. In the Points text field, type 14.

-

Find the y grid points subsection. In the Points text field, type 21.

-

Find the z grid points subsection. In the Points text field, type 3.

3

Locate the Coloring and Style section. From the Color list, choose Black.

4

In the Velocity (Uncoupled Flow) toolbar, click Plot

Next add a pressure plot, using the dataset created previously.

Pressure (Uncoupled Flow)

1

In the Home toolbar, click Add Plot Group

and choose 3D Plot Group

2

In the Settings window for 3D Plot Group, type Pressure (Uncoupled Flow) in the Label text field.

3

Locate the Data section. From the Dataset list, choose Surface 1.

Add a uniformly colored surface to highlight the channel walls.

1

Right-click Pressure (Uncoupled Flow)

and choose Surface

2

In the Settings window for Surface, locate the Expression section. In the Expression text field, type 1.

3

Locate the Coloring and Style section.

-

From the Coloring list, choose Uniform.

-

From the Color list, choose Gray.

Next use contours to visualize the pressure.

1

Right-click Pressure (Uncoupled Flow)

and choose Contour

2

In the Settings window for Contour, click Replace Expression

in the upper-right corner of the Expression section. From the menu, choose Component 1 (comp1) > Creeping Flow > Velocity and pressure > p – Pressure – Pa.

3

In the Pressure (Uncoupled Flow) toolbar, click Plot

Next create a slice plot to visualize the concentration in the device. Use the existing velocity slice plot as a basis for this plot.

Concentration (Uncoupled Flow)

1

In the Model Builder window, under Results right-click Velocity (Uncoupled Flow)

and choose Duplicate

2

In the Label text field, type Concentration (Uncoupled Flow).

For each of the slice subnodes, change the plotted quantity to concentration.

1

In the Model Builder window, expand the Results > Concentration (Uncoupled Flow) node, then click Slice 1

2

In the Settings window for Slice, click Replace Expression

in the upper-right corner of the Expression section. From the menu, choose Component 1 (comp1) > Transport of Diluted Species > Species c > c – Molar concentration, c – mol/m3.

1

In the Model Builder window, click Slice 2

2

In the Settings window for Slice, click Replace Expression

in the upper-right corner of the Expression section. From the menu, choose c – Molar concentration, c – mol/m3

1

Repeat steps 1 and 2 in Slice 2 for Slice 3

Disable the arrow volume plot.

2

Right-click Arrow Volume 1

and choose Disable

Concentration (Uncoupled Flow)

Look at the plot for each of the three diffusion coefficient levels.

1

Click Concentration (uncoupled flow)

2

In the Settings window for 3D Plot Group locate the Data section. From the Parameter value (D) list, choose each of the values: 1e-11, 5e-11, and 1e-10, clicking the Plot button

after each selection.

The plots on the next page show the results for each of the diffusion coefficients solved for. For the heaviest species, which has the smallest diffusivity, there is limited mixing between streams A and B. For the lightest species, which has the largest diffusion coefficient, the mixing is almost perfect.

Add a global plot to show how the concentration at the output differs with diffusion coefficient.

Output Concentration (Uncoupled Flow)

1

In the Home toolbar, click Add Plot Group

and choose 1D Plot Group

2

In the Settings window for 1D Plot Group, type Output Concentration (Uncoupled Flow) in the Label text field.

3

Right-click Output Concentration (Uncoupled Flow) and choose Global

Use the built in variable to compute the average concentration at the device output.

4

In the Settings window for Global, click Replace Expression

in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 > Transport of Diluted Species > Outflow 2 > tds.out2.c0_avg_c - Average concentration - mol/m3.

5

Locate the x-Axis Data section. From the Parameter list, choose Expression. In the Expression text field, type D.

6

Click to expand the Legends section. Clear the Show legends checkbox (no legend is necessary for this plot, as only one quantity is plotted).

Add a marker in the computed data points.

7

Click to expand the Coloring and Style section. Find the Line markers subsection.

-

From the Marker list, choose Point.

Change the axis titles.

HTML tags and a range of mathematical symbols and Greek letters can be entered in the axes and plot titles. See “Using Special Formats and Symbols in Texts” in the “Results Evaluation and Visualization” chapter of the COMSOL Multiphysics Reference Manual for more information.

8

In the Model Builder window, click Output Concentration (Uncoupled Flow)

9

In the Settings window for 1D Plot Group, click to expand the Title section. From the Title type list, choose None.

10

In the Settings window for 1D Plot Group, locate the Plot Settings section.

-

Select the x-axis label checkbox. In the associated text field, enter Diffusion Coefficient (m<sup>2</sup>/s).

-

Select the y-axis label checkbox. In the associated text field, enter Concentration at Stream B Outlet (mol/m<sup>3</sup>).

Change the axis limits for the plot.

11

Locate the Axis section. Select the Manual axis limits checkbox.

-

In the y minimum text field, enter 0.

-

In the y maximum text field, enter 0.5.

12

This plot shows that the concentration of the species at the output is strongly dependent on the diffusion coefficient of the molecule. Thus the device could be used to separate species with different diffusion coefficients, particularly if multiple stages of the device were arranged in series.

In some cases, particularly if the solution consists of large macromolecules, the dissolved species has a large influence on the liquid’s viscosity. In such situations, the Navier–Stokes and the convection–diffusion equations become coupled, and so they must be solved simultaneously.