Comsol 4.2 Tutorial

Example 2 (MASS TRANSFER)

Consider a small drop of water, which is at the bottom of a vertical tunnel diffusing in the air

contained within it. In order to accelerate the diffusion process, air is blown over the top of the

tunnel such that a negligible concentration of water at the top can be assumed. Strictly speaking

this problem is transient; however, we can assume it as steady state to determine the

concentration profile of water along the tunnel. Let us consider a spherical drop of water with a

1 mm radius as in Figure 1. To simplify the analysis, assume a perfectly cylindrical tunnel of 7.5

mm height and 2.5 mm diameter. The diffusion coefficient of water in air is 10-6

m2/s.

The region of interest is limited by the surface of the drop and the tunnel walls as shown in

Figure 2.

Start Up: Double click the Comsol 4.2 icon.

Model Wizard: The model wizard will appear in the interface;

this will guide you through selecting the appropriate geometry,

physics, and study type (stationary or time dependent).

This problem can be described in just 2 dimensions because of

the angular symmetry. Make sure you see why this problem is

2D despite dealing with 3D objects.

1) Select 2D and click the right facing arrow.

2) We now need to select the appropriate physics, in this

case “transport of diluted species” will do the job. This

can be found under the “Chemical species transport” tab.

As seen to the right �

3) Finally we need to choose the study type. Because we are assuming steady

state (even though this problem is inherently transient) the appropriate study

type will be “stationary” To finish click the finish flag.

Geometry:

This geometry consists of both a rectangular region and a circular region. Accordingly we will

need to add both a rectangle and a circle to create this geometry. Since the region we are really

interested in is the region between the water droplet surface and the top of the cylindrical tunnel

where water concentration is zero, we will actually subtract the circular water region from the

rectangular air region using what is a called a Boolean operation. To do this:

1) Right click “geometry” and add a rectangle. Set height =7.5 [mm] and width=5 [mm]. The

center of the rectangle should be at the origin.

2) Right click “geometry to add a circle. Set the radius = 1 [mm] and set the center position to

x=0 y=-2.75 [mm]. After these two steps your geometry should look like the one below.

3) Now for the Boolean subtraction. Do this by right clicking on geometry, below where the

different types input shapes are you will see “Boolean operations”, highlight this to bring up the

menu of different possible Boolean operations. In this case we want to select “difference.

4) Within the Boolean difference

interface there are two boxes where

different shapes can be entered. The

first box is all the objects you wish to

“add” while the second box contains

the objects you wish to “subtract”. We want to add the rectangle, but subtract the circle. To do

this simply click the add box, then either left and right click the shape you wish to add to this box

or left click to highlight then click the + button. Your interface should look like this once you

finished.

5) Once the proper shapes have been selected in the appropriate

boxes click the “build all” button to carry out the subtraction.

You should obtain the following result �

Transport of Diluted Species:

Here we need only do 2 things. Set the diffusivity of water

through air and set the boundary conditions.

1) Under the Transport of Diluted Species tab you will see the “convection and diffusion” tab.

Left click this to open the interface.

2) You will see a “Diffusion” tab within this interface here you can set Dc equal to the

appropriate value of 1x10-6

m2/s. This should look like the graphic below.

3) We now need to input the appropriate boundary conditions to the problem. Since our two

conditions are values of concentration at two surfaces we will need to add two “concentration”

boundary conditions. The concentration boundary condition is found by right clicking the

Transport of Diluted Species tab and left clicking “concentration”, since we have two boundaries

we will need two separate boundary conditions.

4) First let us add the boundary at the surface of the water droplet. This surface will have the

concentration of pure water thus set c=55,556 mol/m3. This condition must be applied to the

appropriate subdomain so in the usual manner, left click to highlight and right click to add the

appropriate surface while in the concentration 1 interface.

5) Now in similar fashion we need to add the negligible concentration of water condition to the

top surface. At this surface we can assume c=0.

For a simple diffusion problem such as this specifying the appropriate boundary conditions and

the appropriate diffusivity (the only physical parameter which comes directly into play in

diffusion) is all we need to do. The problem is now ready to be solved as the meshing by default

will be fine for a problem like this. Right click on study and left click compute in the menu it

brings up.

Results:

Now that we have our solution let us examine it using two important techniques with which you

should be familiar.

2D Cut Line:

1) First we will examine the concentration profile of water 1 mm away from the wall. This is

done by right clicking on “data sets” under the results tab and left clicking on “Cut Line 2D”.

This will add a new data set under the data set tab, however the two points defining this line

segment need to be specified. The points x1=-1.5 [mm] y1=-3.75 [mm] and x2=-1.5 [mm]

y2=3.75 [mm].

2) We now need to add a 1D plot group to display this cut line data. Right click on Results and

left click “1D Plot Group”, this will add the one dimensional plot group where the data can be

displayed. Right click the “1D plot group” tab and select “Line Graph”, finally in the “Line

Graph” interface choose “Cut line 2D” in the data set box and click the paint brush (graph button

at top right of interface).

The second graphical tool we will employ is called a contour plot. This type of plot connects all

points of an equal value with a certain parameter difference between each line. The closer

together the lines the faster the change in whatever parameter is being contoured.

Contour Plot of Concentration:

1) To graph the surface contours of concentration we will need to add another 2D plot group. Do

this the same way as adding a 1D plot group, right click on results and left click 2D plot group.

2) Now that the second 2D plot group is up right click this tab and select “Contour”. This will

bring up the contour plot interface, by default the parameter to be contoured is concentration c

(concentration of water). All that remains to do is to press the plot button (the paint brush button

again at the upper right of the interface).