electrochemical polishing sbs

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Example—Electrochemical PolishingSOLVED WITH COMSOL MULTIPHYSICS 3.5a

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electrochemical_polishing_sbs.book Thursday, December 4, 2008 1:41 PM

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Examp l e—El e c t r o c h em i c a l Po l i s h i n g

Introduction

This example illustrates the principle of electrochemical polishing. The simplified 2D model geometry consists of two electrodes and an intermediate electrolyte domain The positive electrode has a protrusion, representing a surface defect. The purpose of the model is to examine how this protrusion and the surrounding electrode material are depleted over a period of time.

Model Definition

The potential drop over the electrodes is 30 V, and the electrolyte has a conductivity of 10 S/m.

Modeling the depletion of the positive electrode requires a moving boundary because the geometry changes and the current density distribution with it. A simple model for the depletion is based on the assumption that the depletion rate is proportional to the normal current density at the electrode surface. The velocity, U, normal to the mesh at the electrode surface then becomes

where K is the coefficient of proportionality, and Jn is the normal current density. In this model, K = 10−11 m3/As.

Electrode Material

Electrode Material

30 V

Ground (0 V)

Electrolyte

U KJn–=

E X A M P L E — E L E C T R O C H E M I C A L P O L I S H I N G | 1


The part of the electrode and electrolyte that the model includes is about 3 mm wide and the distance between the electrodes is 0.4 mm.

Modeling in COMSOL Multiphysics

This model uses the Conductive Media DC and transient Moving Mesh (ALE) application modes. The variable for the normal current density defines the mesh velocity. The dynamics of the model is quasi-static in nature, and the time dependence only enters in the depletion (removal of material) of the electrode.

Results

After 10 s, the protrusion is somewhat smoothed out, and a significant portion of the positive electrode has been depleted:

Model Library path: COMSOL_Multiphysics/Electromagnetics/electrochemical_polishing



Modeling Using the Graphical User Interface

M O D E L N A V I G A T O R

1 Select 2D in the Space dimension list. (This model can easily be generalized to 3D.)

2 In the application mode list, open COMSOL Multiphysics>Deformed Mesh and then Moving Mesh (ALE)>Transient analysis.

3 Click the Multiphysics button and then the Add button.

4 In the application mode list, open COMSOL Multiphysics>Electromagnetics>Conductive Media DC.

5 Click the Add button. This adds the Conductive Media DC application mode to the moving mesh frame.

6 Click OK to close the Model Navigator.

O P T I O N S

1 From the Options menu, open the Constants dialog box.

2 Enter a constant with the name K, the expression 1e-11[m^3/(A*s)], and the description Coefficient of proportionality (the description is optional).

3 Click OK to close the Constants dialog box.

G E O M E T R Y M O D E L I N G

1 Click the Rectangle/Square button on the Draw toolbar, and draw a rectangle with corners at x = −1.4, y = 0 and x = +1.4, y = 0.4.

2 Shift-click the Ellipse/Circle (Centered) button.

3 In the Circle dialog box, type 0.3 in the Radius edit field and set the center coordinates to (0, 0.6) by typing 0 in the X edit field and 0.6 in the Y edit field.

4 Click OK.

5 Select both objects by using the keyboard shortcut Ctrl+A. Both objects are now highlighted in red.

6 Click the Difference button on the Draw toolbar to remove the circle object from the rectangle. This creates the protruding part of the electrode.

7 The model needs to be the order of mm and not m. Click to select the object and then click the Scale button on the Draw toolbar.

8 Enter a scale factor of 10−3 by typing 1e-3 in both the X and Y edit fields in the Scale factor area. Click OK.

9 Click the Zoom Extents button on the Main toolbar.



The geometry is now ready.

P H Y S I C S S E T T I N G S

Subdomain Settings—Conductive Media DC1 From the Multiphysics menu, select the Conductive Media DC application mode.

2 From the Physics menu, select Subdomain Settings.

3 In the Subdomain Settings dialog box, select Subdomain 1 (the only one) and type 10 in the Electric conductivity edit field.

4 Click OK to close the Subdomain Settings dialog box.

Boundary Settings—Conductive Media DC1 From the Physics menu, select Boundary Settings.

2 For Boundaries 3, 4, 6, and 7, select the Electric potential in the Boundary condition list and type 30 in the Electric potential edit field.

3 For Boundaries 1 and 5, select Electric insulation in the Boundary condition list. Electric insulation is a good approximation if you want to simulate that the electrodes are extended indefinitely in both directions.

4 For Boundary 2, select Ground as the boundary condition.

5 Click OK to close the Boundary Settings dialog box.

Boundary Settings—Moving Mesh (ALE)1 From the Multiphysics menu, select the Moving Mesh (ALE) application mode.

2 From the Physics menu, select Boundary Settings.

3 In the Boundary Settings dialog box, for boundary 2, click the Mesh displacement button and set the mesh displacement in both directions to 0 by selecting the dx and dy check boxes.

4 For Boundaries 1 and 5, click the Mesh velocity button and set the mesh velocity, in the x direction to 0 by selecting the vx check box.

5 Select Boundaries 3, 4, 6, and 7, and select Tangent and normal coord. sys. in

deformed mesh in the Coordinate system list. Click the Mesh velocity button. Then select the vn check box and type -K*nJ_dc in the Mesh velocity, n direction edit field. This makes the normal mesh velocity equal to −K Jn (nJ_dc is the variable for the current density outflow from the Conductive Media DC application mode).

6 Click OK.



M E S H G E N E R A T I O N

1 Click the Initialize Mesh button on the Main toolbar.

2 Click the Refine Mesh button on the Main toolbar once.

C O M P U T I N G T H E S O L U T I O N

1 From the Solve menu, select Solver Parameters.

2 In the Time stepping area, type range(0,10) for Times. This defines a simulation that runs from 0 to 10 s in steps of 1 s.

3 Click OK to close the Solver Parameters dialog box.

4 Click the Solve button (equal sign) on the Main toolbar to solve the model (or choose Solve Problem from the Solve menu).

PO S T P R O C E S S I N G A N D V I S U A L I Z A T I O N

The default plot shows the x-displacement for the moving mesh. Change the visualization settings to plot the current density distribution:

1 From the Postprocessing menu, select Plot Parameters.

2 On the Surface page, select Conductive Media DC (dc)>Total current density, norm

from the Predefined quantities list.



3 Click OK to plot.

The maximum current density appears to be of the order of 106 A/m2. To see the magnitude of the depletion in the y direction more easily, plot the ALE-displacement variable dy:

1 From the Postprocessing menu, select Plot Parameters.

2 On the Surface page, type dy_ale in the Expression edit field.

3 Click OK to plot.



The maximum value for the y-displacement is approximately 10−4 m (or 0.1 mm).

You can now compare this with an approximate formula for the total depletion increment, d:

This shows that the approximate formula (which does not take effects from the curved boundary into account) is in fact very accurate.

d U Δt K Jn Δt 10 11– m3

As-------⎝ ⎠

⎛ ⎞ 106 Am-----⎝ ⎠

⎛ ⎞ 101s( )⋅ ⋅ 10 4– m= = = =


electrochemical polishing sbs

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