COMSOL 6.4 - Electrocoating of a Car Door

Electrocoating (also known as E-coating) is an electrophoretical method for depositing paint onto electrically conducting objects. The method is widely used in various industries (for instance, in the automotive industry), where electrocoating is broadly used to apply the first priming paint layer on car bodies. A salient feature of the electrocoating process is that the deposited paint layer is highly resistive. Due to this feature, it is possible to achieve fairly uniform paint layers, even for complex body shapes, since the local deposition rate decreases with increasing paint thickness.

This example models electrocoating of a car door where the electrolyte is a dispersion of colloidal paint particles and the paint particles are deposited on the cathode surface.

Model Definition

Figure 1 shows the model geometry. The geometry consists of one single electrolyte domain, with the electrodes being represented as boundaries. The quarter and semi-cylinder surfaces represent the anodes. The car door cathode is completely immersed in the electrolyte.

Figure 1: Model geometry. Car door (cathode) and three cylindrical anodes.

The car door geometry used in the model is a surface geometry (that is, a geometry with zero though-plane thickness), and the car door electrode surface is modeled using the Thin Electrode Surface node (see below).

Electrolyte charge transport

Ohm’s law is used in the electrolyte domain:

where ϕl (V) is the electrolyte potential, il is the electrolyte current density vector (A/m2) and σl (S/m) is the electrolyte conductivity. A uniform composition of the electrolyte is assumed, with an electrolyte conductivity of 0.28 S/m.

Electrode reactions

The applied cell voltage results in water electrolysis. Oxygen is evolved on the anodes according to

The equilibrium potential, Eeq,O2 (V), for this reaction is 1.23 V versus SHE.

On the cathodes, hydrogen is evolved according to

The equilibrium voltage for this reaction is Eeq,H2 = 0 V versus SHE.

Activation overpotentials are assumed to be negligible at both electrodes. The electrode kinetics expression of type Primary condition (thermodynamic equilibrium) is used in the model, to implement that assumption.

Film thickness and resistance

The consumption of protons at the cathode results in a locally increased pH. This in turn results in reduced solubility and deposition rate of the colloidal paint particles on the electrode. This model assumes a linear relation between the paint film formation rate and the local current density:

where s (m) is the thickness of the film, Ccap (kg/C) is the coulombic efficiency of the paint process and ρ (kg/m3) the density of the film. The index i represents the upside and downside of the cathode surface. Ccap is a lumped empirical parameter that needs to be measured for each processing bath. In the present model, a value of 60 g/C is used.

The depositing film results in a lowered electrolyte conductivity at the cathode. This is incorporated in the model by adding a potential drop at the cathode according to:

where Rfilm (Ω·m) is the film resistivity, set to 5 MΩ·m in this model.

Electrode Boundary Conditions

The cathode is grounded in the model. The following condition is used for the electrolyte potential at the car door cathode boundary

For the anodes the electrolyte voltage is set to

where Ecell (250 V) is the cell potential. The potential drop due to the ion-exchange membrane that covers the membrane-electrode anode cells is not included in the model.

The local current density of the charge transfer reactions, iloc (A/m2), which is used in the film thickness and resistance equations, is evaluated such that the above electrolyte potential conditions are satisfied at the cathode and anode boundaries, respectively.

All other surfaces use insulating boundary conditions.

Regarding the Usage of the Thin Electrode Surface node

The Thin Electrode Surface node is used to model the car door cathode surface in this tutorial. The Thin Electrode Surface node introduces “slitting” of the electrolyte potential and surface concentration dependent variables on the interior boundary, which means that they have different values on each side of the car door boundary. Alternatively, one could have modeled the car door geometry with a nonzero thickness in the geometry, removed the volume occupied by the car door domain from the physics selection, and used the Electrode Surface node on the resulting car door external boundaries. However, that approach would have resulted in far more mesh elements and a longer computation time.

Results and Discussion

Figure 2 shows the paint thickness at the upside of the door after 120 s. The layer is around 21 μm thick. The thickness variation is less than 5%.

Figure 2: Paint thickness at the upside of the car door after 120 s.

Figure 3 shows the paint thickness after 120 s on the downside of the door. Here the thickness variation is significant. Inside the window frame, the lowest thickness of 6.2 μm is much lower than on the more exposed parts, which have thicknesses close to 21 μm.

Figure 3: Paint thickness at the inside of the car door after 120 s.

Finally, Figure 4 shows a thickness versus time comparison between the upside and downside of the window frame at a particular point.

Figure 4: Paint thickness comparison between the upside and downside of the window frame at a particular point.

A more elaborate model would include a more detailed description of the electrode reaction activation overpotentials. A further modification would be the inclusion of the transport of paint particles in the electrolyte solution and the paint deposition rate dependence on the local chemistry. Including these modifications would yield a Tertiary Current Distribution model.

Reference

1. F. Hess and U. Gonzalez, “Automotive E-Coat Paint Process Simulation Using FEA,” paper presented at the NAFEMS Ninth International Conference in Orlando, Florida, USA. May 29 2003.

Electrodeposition_Module/Tutorials/car_door

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select > > .

Click .

Click

In the tree, select > .

Click

Geometry 1

The geometry sequence for this model takes some time to set up. To skip these steps you can instead import the geometry sequence from the saved model file in the application library.

To skip setting up the geometry sequence manually: Right click the node and choose . Then choose the Electrodeposition_Module -> Tutorials -> car_door.mph file from the application library.

Import 1 (imp1)

If you inserted the whole geometry sequence you can now move on directly to the Global Definitions section below. Otherwise start setting up the geometry by importing the car_door_geom.mphbin CAD file as follows:

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