Finite Element Modeling of Galvanic Corrosion of Metals · dissolution due to the chemical properties of the metals and the environment. Galvanic corrosion is particularly prevalent

Finite Element Modeling of Galvanic Corrosion of Metals

by

Megan Elizabeth Turner

An Engineering Project Submitted to the Graduate

Faculty of Rensselaer Polytechnic Institute

in Partial Fulfillment of the

Requirements for the degree of

MASTER OF ENGINEERING IN MECHANICAL ENGINEERING

Approved:

_________________________________________

Ernesto Gutierrez-Miravete, Project Adviser

Rensselaer Polytechnic Institute

Hartford, CT

December 2012

ii

© Copyright 2012

by

Megan Turner

All Rights Reserved

iii

CONTENTS

LIST OF TABLES ............................................................................................................. v

LIST OF FIGURES .......................................................................................................... vi

LIST OF SYMBOLS ...................................................................................................... viii

GLOSSARY...................................................................................................................... ix

LIST OF KEYWORDS ..................................................................................................... x

ACKNOWLEDGMENT ................................................................................................... xi

ABSTRACT ..................................................................................................................... xii

1. Introduction .................................................................................................................. 1

1.1 Background ........................................................................................................ 1

1.2 Problem Description ........................................................................................... 1

1.3 Prior Work .......................................................................................................... 2

2. Methodology ................................................................................................................ 4

2.1 Theory ................................................................................................................ 4

2.2 Geometry and Boundary Conditions .................................................................. 4

2.3 Corrosion Rate .................................................................................................... 8

3. Results and Discussion................................................................................................. 9

3.1 Model Validation ................................................................................................ 9

3.1.1 Using the Butler-Volmer Relationship for Current Density-Potential ... 9

3.1.2 Using a Basic Geometry Subjected to Polarization .............................. 11

3.2 Results for Different Electrode Geometries ..................................................... 13

3.2.1 Electrode Geometry with a 90 Degree Step ......................................... 13

3.2.2 Electrode Geometry with an Elliptical Step ......................................... 15

3.2.3 Axisymmetric Electrode Geometry ...................................................... 17

3.3 Results for Different Electrolyte Thicknesses Using a Copper-Zinc Galvanic

Couple .............................................................................................................. 19

4. Conclusion ................................................................................................................. 24

iv

5. References .................................................................................................................. 26

6. Appendix A ................................................................................................................ 27

7. Appendix B ................................................................................................................ 29

v

LIST OF TABLES

Table 1: Input Data Used for Model Validation [3] .......................................................... 9

Table 2: Summary of Data for the Different Geometries ............................................... 18

Table 3: Input Data Used for Copper-Zinc Galvanic Couple [3] ................................... 20

Table 4: Properties of Zinc .............................................................................................. 19

Table 5: Summary of Results for the Copper-Zinc Galvanic Couple with an Electrolyte

2mm and 20mm Thick ..................................................................................................... 23

Table 6: Input Data Used for Copper-Zinc Galvanic Couple [3] ................................... 29

Table 7: Summary of Results for the Copper-Zinc Galvanic Couple with an Electrolyte

2mm and 20mm Thick ..................................................................................................... 32

vi

LIST OF FIGURES

Figure 1: Coplanar Model Used for Initial Model Validation [3] ..................................... 2

Figure 2: Marine Propulsion Unit Analyzed in Reference [6] .......................................... 3

Figure 3: 2D Cartesian Geometry ..................................................................................... 5

Figure 4: COMSOL Results for B-V Current Density Distribution on the Electrode

Surfaces (Surface Plot)..................................................................................................... 10

Figure 5: COMSOL Results for B-V Current Density Distribution and from Reference

[3] ..................................................................................................................................... 10

Figure 6: Current Density and Reaction Rate for the Basic Geometry ........................... 11

Figure 7: COMSOL Results for the System Subjected to Polarization (Surface Plot) ... 12

Figure 8: COMSOL Results for the System Subjected to Polarization and from

Reference [3] .................................................................................................................... 12

Figure 9: Current Density and Reaction Rate for the System Subjected to Polarization 13

Figure 10: COMSOL Results for the Electrode Geometry with a 90 Degree Step

(Surface Plot) ................................................................................................................... 14

Figure 11: COMSOL Results for the Electrode Geometry with a 90 Degree Step ........ 14

Figure 12: Current Density and Reaction Rate for the Electrode Geometry with a 90

Degree Step ...................................................................................................................... 15

Figure 13: COMSOL Results for the Electrode Geometry with an Elliptical Step

(Surface Plot) ................................................................................................................... 16

Figure 14: COMSOL Results for the Electrode Geometry with an Elliptical Step ........ 16

Figure 15: Current Density and Reaction Rate for the Electrode Geometry with an

Elliptical Step ................................................................................................................... 17

Figure 16: COMSOL Results for the Axisymmetric Electrode Geometry (Surface Plot)

.......................................................................................................................................... 17

Figure 17: COMSOL Results for the Axisymmetric Electrode Geometry ..................... 18

Figure 18: Current Density and Reaction Rate of the Axisymmetric Electrode Geometry

.......................................................................................................................................... 18

Figure 19: Copper-Zinc Galvanic Couple in a Hydrochloric Acid Solution [3] ............ 19

Figure 20: COMSOL Results for the Copper-Zinc Couple with 2mm and 20mm Thick

Electrolyte (Surface Plot) ................................................................................................ 21

vii

Figure 21: COMSOL Results for the Copper-Zinc Couple with 2mm Thick Electrolyte

.......................................................................................................................................... 21


.......................................................................................................................................... 22

Figure 23: Current Density and Corrosion Rate for Copper-Zinc Couple with 2mm

Thick Electrolyte .............................................................................................................. 22

Figure 24: Current Density and Corrosion Rate for Copper-Zinc Couple with 20mm

Thick Electrolyte .............................................................................................................. 23

Figure 25: COMSOL Results for Linear Current Density Distribution on the Electrode

Surfaces (Surface Plot)..................................................................................................... 27

Figure 26: COMSOL Results for Linear Current Density Distribution on the Electrode

Surfaces ............................................................................................................................ 28

Figure 27: COMSOL Results for the Copper-Zinc Couple with 2mm and 20mm Thick

Electrolyte (Surface Plot) ................................................................................................ 30


.......................................................................................................................................... 30


.......................................................................................................................................... 31

Figure 30: Current Density and Corrosion Rate along the Anode Surface of the Copper-

Zinc Couple with 2mm Thick Electrolyte........................................................................ 31

Figure 31: Current Density and Corrosion Rate along the Anode Surface of the Copper-

Zinc Couple with 20mm Thick Electrolyte...................................................................... 32

viii

LIST OF SYMBOLS

current density (A m-2

)

charge density (C m-3

)

t time (s)

E electric field intensity (N C-1

)

corrosion potential (V)

σ conductivity (Ω-1

m-1

)

free current density (A m-2

)

free corrosion potential (V)

z number of electrons transferred (unitless)

F Faraday’s constant (96487 C mol-1

)

reaction rate (mol m-2

s -1

)

CR corrosion rate (mm year-1

)

Mw molecular weight (kg mol-1

)

ρ density (kg m-3

)

electron

aa anodic transfer coefficient (V)

ac cathodic transfer coefficient (V)

α anodic Tafel parameter (V)

β cathodic Tafel parameter (V)

ix

GLOSSARY

Anode –

The portion of a galvanic couple which sees a decrease in potential along the

electrode surface

Cathode –

The portion of a galvanic couple which sees an increase in potential along the

electrode surface

Electrolyte –

A solution capable of carrying/transferring charge

(Electrochemical) Potential –

Measure of the voltage in a system

Galvanic Corrosion –

“…the corrosion that occurs as a result of one metal being in contact with

another in a conducting environment” [2]

Overpotential –

The difference between the actual potential and the free potential

x

LIST OF KEYWORDS

COMSOL

Galvanic Corrosion

Electrochemical Potential

Current Density

Corrosion Rate

xi

ACKNOWLEDGMENT

I would like to thank the Rensselaer faculty and staff for their commitment to educating

their students. I would especially like to thank Professor Gutierrez-Miravete for the

guidance he provided throughout this project.

xii

ABSTRACT

Corrosion is an ever-present problem in all different environments, particularly in

marine applications. The goal of this project is to develop a finite element model that

can be used with experimental data to characterize the corrosion of a galvanic couple in

an electrolyte. This project first addresses a simple system with coplanar electrodes.

The finite element model is developed using COMSOL Multiphysics Math Module

through derivation of equations describing corrosion thermodynamics and

electrochemical kinetics. The model is validated through replication of previously

determined experimental results and then applied to the study of some system

configurations relevant to marine applications.

1

1. Introduction

1.1 Background

Corrosion is the breakdown of materials, namely metals, through electrochemical

reactions within their environment. Corrosion is a consideration in virtually all

engineering applications. Each year, industries invest time and money into trying to

curtail the effects of corrosion. Many different corrosive environments have been

studied and monitored to develop corrosion control methods [1].

There are different types of corrosion, including galvanic corrosion. Galvanic corrosion

is an electrochemical process that occurs when at least two dissimilar metals are in

electrical contact with one another, and are in a conducting environment known as an

electrolyte [2]. Of these dissimilar metals, one acts as the anode and the other acts as the

cathode. The anode is the portion of the galvanic couple that undergoes material

dissolution due to the chemical properties of the metals and the environment. Galvanic

corrosion is particularly prevalent in marine applications because seawater acts as a

naturally free flowing electrolyte.

1.2 Problem Description

The amount and rate of corrosion can be correlated to the electrochemical potential

distribution within a system. The goal of this project is to develop a finite element

model that can be used in conjunction with experimental data to characterize the

corrosion of a galvanic couple in an electrolyte. There are a number of factors that can

contribute to the amount of corrosion within a system from material factors (e.g.

geometry) to environmental factors (e.g. type of electrolyte present) [1]. To limit the

effects of these factors, this project first utilized a simple model of coplanar electrodes as

shown in Figure 1 [3].

2

Figure 1: Coplanar Model Used for Initial Model Validation [3]

Utilizing a simple geometry allowed the initial focus to be on development of the

boundary conditions rather than generation of geometry representing a specific system.

Reference [3] data was used for finite element model validation. Following

development and validation of the finite element model, additional galvanic couple

geometries were evaluated. This project is limited to galvanic couples of one anode and

one cathode. Distributions of electrochemical potential within the electrolyte were

generated to describe the behavior of the system. Current densities and corrosion rates

along the anode surface were generated to quantify to amount of corrosion.

1.3 Prior Work

There is a lot of past precedence of scientists taking an interest in galvanic corrosion,

looking to understand what causes it and what limits or accelerates the process.

Numerous studies have been conducted; some take a more global outlook as in

Reference [4], whereas some take a more focused approach as in Reference [5].

The study conducted in Reference [4] looked at many different galvanic couples

commonly used in seawater applications. The study focused on developing reasonable

models for systems experiencing varying periods of exposure to the corrosive

environment. The studies were also conducted under potentiostatic and potentiodynamic

scenarios. The potentiostatic experiment allowed for analysis of the corrosion under the

natural potentials of the system. While the potentiodynamic experiment introduced

3

potential to the electrodes to analyze the impacts of changing the electrode potential on

the corrosion.

Other studies seek to analyze corrosion for a specific system geometry and environment.

Generally these investigations look to develop methods to prevent or minimize corrosion

of that specific system. This is most commonly achieved through a process known as

cathodic protection. This process involves introducing an additional part, known as a

sacrificial anode, to the system. The sacrificial anode is generally another piece of metal

that is introduced into a system so that it will corrode prior to other elements. Reference

[5] looked at developing a method to model cathodic protection of a carbon steel pipe in

seawater using one or two aluminum sacrificial anodes. Reference [6] looked at

utilizing a sacrificial zinc anode to cathodically protect the marine propulsion unit shown

in Figure 2.

Figure 2: Marine Propulsion Unit Analyzed in Reference [6]

4

2. Methodology

2.1 Theory

The potential distribution within the electrolyte of a galvanic system is fundamentally

based on the continuity equation for conservation of charge [2] in the electrolyte.

−∇. = [1]

In a steady state system, = 0 and ∇. = 0

The relationship between the electric field intensity and the electric potential is

= −∇ [2]

and Ohm’s Law is

= [3]

where σ is the conductivity of the electrolyte.

From the above, the continuity equation becomes

∇∇ = 0 [4]

and for constant, isotropic conductivity this yields

∇ = 0 [5]

which is Laplace’s Equation for the potential distribution within the electrolyte.

2.2 Geometry and Boundary Conditions

The model geometry must be representative of the system being analyzed and must be

subjected to appropriate boundary conditions. There are generally three types of

boundary conditions that are considered at the electrode surfaces: linear, exponential

(Tafel) and Butler-Volmer.

This project utilized the finite element program COMSOL Multiphysics to solve

Equation [5] for selected systems. Geometry was developed to represent the electrolyte

of the system being modeled. During initial model and boundary condition

development, a simple 2D geometry as shown in Figure 1 was used. This initial

5

coplanar model was created using a 2D Cartesian geometry as shown in Figure 3.

Additional geometries were also created and evaluated as discussed in Sections 3.2 and

3.3.

Figure 3: 2D Cartesian Geometry

The main assumption for this system is that there is no current flow normal to the

insulating boundaries [3]. This assumption is in accordance with Equation [1] at a

steady state, because the charge within the system cannot change. This allows for a Zero

Flux boundary condition to be applied to edges 1-2, 2-3, and 3-4, of Figure 3

Edges 1-5 (Electrode A) and 5-4 (Electrode B) are the electrode surfaces. For this

system, Electrode A is the cathode and Electrode B is the anode. The electrode

boundary conditions were assigned by using a Flux/Source boundary condition to

represent the Butler-Volmer relationship

2 3

1 A 5 B 4

6

Note: This model is just a generic case to illustrate the methodology, and does not

represent specific materials’ reduction and oxidation reactions. For instance, the

cathodic reaction could be oxygen reduction (O2 + e

- → O2

-) or hydrogen evolution (2H

+

+ 2e- → H2) [2] and the parameters for those reactions could be inputs to the model for

specific cases.

The Butler-Volmer relationship for current density is based on the identifying the anodic

and cathodic reactions that are taking place on each electrode. In any environment, a

metal is undergoing both an anodic and a cathodic reaction. This characteristic is what

requires the net current density to account for both reactions on each metal, regardless of

if the metal is acting as the anode or the cathode in a galvanic couple. At the equilibrium

potential (zero overpotential) the anodic and cathodic currents are equal; this point is

known as the exchange current. However, when the overpotential is not equal to zero,

the anodic and cathodic currents are different.

Therefore, for a given electrode, the anodic current density is

= expa !""#$%& ' [6]

while the cathodic current density is

( = −exp−a( !""#$%& ' [7]

so that net current density is

) = + ( =

= expa !""#$%& ' − exp−a( !""#$%& '[8]

This is known as the Butler-Volmer equation.

Hence, for Electrode A, which acts as the cathode, the total current density is

+ = ,!+$ -exp ./0,1 2""#,!1$3%& 4 − exp ./5,1 2""#,!1$3%& 46 [9]

for Electrode B, which acts as the anode, the total current density is

7

7 = ,!7$ -exp ./0,8 2""#,!8$3%& 4 − exp ./5,8 2""#,!8$3%& 46 [10]

At low overpotentials, ! − $ < 0.01;, the Butler-Volmer equation reduces to the

following linear relationships for current density-potential

Cathodic + = #,!1$ 2""#,!1$3%& [11]

Anodic 7 = #,!8$ 2""#,!8$3%& [12]

On the other hand, at large overpotentials an exponential (Tafel) relationship results.

For anodic polarization ! − $ > 0.01;, the Butler-Volmer equation reduces to

) = expa !""#$%& ' [13]

such that the expression for the overpotential is

! − $ = = logA BCD# [14]

This is known as the anodic Tafel equation.

For cathodic polarization ! − $ < −0.01;, the Butler-Volmer equation reduces to

) = −exp−a( !""#$%& ' [15]

such that the expression for the overpotential is

! − $ = E logA BCD# [16]

This is known as the cathodic Tafel equation.

It should be noted that the input data in Table 1 that was used for model validation refers

to anodic and cathodic Tafel parameters (slopes). Based on Equations [14] and [16], the

relationships that were used to determine the appropriate transfer coefficients are

a = %& F [17]

a( = %& G [18]

8

Regardless of the relationship used for the current density, the Flux Source boundary

condition reflects the relationship in Equation [19] for the surfaces of Electrode A and

Electrode B respectively

" =

"H =

1IJ8K [19]

where y is the distance from the electrode surface. For the system in Figure 1, the

derivative normal to the surface is the same as the derivative with respect to y.

2.3 Corrosion Rate

Based on the current density as derived from Equation [19]

" = [20]

and Faraday’s Law

= LM [21]

the reaction rate is

= K N

"O [22]

Corrosion rate is then defined as

PQ = RS/U [23]

Reaction and corrosion rates are only developed for the anodic surface of each system,

because only the anode corrodes.

9

3. Results and Discussion

3.1 Model Validation

The geometry that is used in the model reflects the configuration shown in Figure 1. The

input data used is shown in Table 1.

Table 1: Input Data Used for Model Validation [3]

Property Value Units

Tafel Parameters:

αA anodic reaction of metal A 0.05 V

αB anodic reaction of metal B 0.05 V

βA cathodic reaction of metal A 0.05 V

βB cathodic reaction of metal B 0.05 V

σ conductivity of the electrolyte 10 Ω-1

m-1

,!+$ free current density of metal A 1 Am-2

,!7$ free current density of metal B 1 Am-2

a surface length of metal A 0.01 m

b surface length of metal B 0.01 m

w thickness of the electrolyte 0.01 m

,!+$ free corrosion potential of metal A 0.5 V

,!7$ free corrosion potential of metal B -0.5 V

3.1.1 Using the Butler-Volmer Relationship for Current Density-Potential

Using Butler-Volmer (B-V) relationships for the current densities at the electrode

surfaces, in accordance with Equations [9] and [10], produced the potential distribution

in the electrolyte shown in Figure 4.

10

Figure 4: COMSOL Results for B-V Current Density Distribution on the Electrode Surfaces

(Surface Plot)

Figure 5 describes the COMSOL results for potential in the electrolyte along the

electrode surfaces and the top of the electrolyte respectively as compared to the

calculations in Reference [3].

Figure 5: COMSOL Results for B-V Current Density Distribution and from Reference [3]

11

The COMSOL results correlate qualitatively and quantitatively well to the results from

Reference [3]. The potential varies from -0.2293V to 0.2293V along the surface of the

electrode, and varies from approximately -0.11V to 0.11V along the top of the

electrolyte, both of which agree with the calculated data in Reference [3]. The good

correlation suggests that the finite element model produced reliable results.

Figure 6 shows the current density along the entire electrode surface, and the associated

reaction rate along the anodic surface. The maximum current density is approximately

4500A/m2 and the approximate maximum reaction rate is 0.024mol/m

2s.

Figure 6: Current Density and Reaction Rate for the Basic Geometry

The reaction rate is being reported for this system because this is a generic case and

there are no specific values for molecular weight (Mw) or density (ρ).

Appendix A describes the initial attempt at model validation using the linear current

density-potential expressions. However, the results obtained using the linear expressions

did not correlate quantitatively well with the experimental results because this system

has a large overpotential, for which the linear approximation is not valid.

3.1.2 Using a Basic Geometry Subjected to Polarization

In addition to the input data provided in Table 1, further model validation was completed

using the same system with an applied polarization of 4.5V. The resulting potential

distribution in the electrolyte is shown in Figure 7. Figure 8 describes the potential in

the electrolyte along the electrode surfaces. The same B-V boundary conditions were

12

utilized on the electrode surfaces as in Section 3.1.1. In order to apply the polarization,

the Zero Flux condition on edge 2-3 of Figure 3 was replaced with a Dirichlet Boundary

Condition. The Dirichlet Boundary Condition allowed the edge to be held at a constant

value, in this case 4.5V. The potential along the top of the electrolyte is not shown for

this case, because it will always be equal to 4.5V due to the polarization of the system.

Figure 7: COMSOL Results for the System Subjected to Polarization (Surface Plot)

The COMSOL results and the calculated results from Reference [3] correlate

qualitatively and quantitatively well as shown in Figure 8. The potential along the

electrode surface varies from -0.0772V to approximately 0.9V, which agrees with the

experimental data.

Figure 8: COMSOL Results for the System Subjected to Polarization and from Reference [3]

13

The good correlation further validates that the finite element model appropriately

characterizes the system.




2s. These values

are much higher than those for the un-polarized system. By polarizing the system, the

change in potential normal to the surface is greater for this system, thereby increasing

both the current density and reaction rate.

Figure 9: Current Density and Reaction Rate for the System Subjected to Polarization

3.2 Results for Different Electrode Geometries

Following validation of the finite element model, additional cases were evaluated using

the same boundary conditions used in Section 3.1.1 and the input data from Table 1, but

for different electrode geometries. The following geometries were developed to explore

the impacts of variations in geometry of a galvanic couple on potential distribution

within the electrolyte, as well as current density along the entire electrode surface and

reaction rate along the anodic surface. Current density and associated reaction rate were

developed in accordance with Equations [21] and [23] respectively.

3.2.1 Electrode Geometry with a 90 Degree Step

The following geometry depicts two non-coplanar electrodes. Electrode A extends

further into the electrolyte at a 90 degree angle to the surface of Electrode B. This

14

geometry could be representative of an area where two plates are not flush to one

another.

Figure 10 shows the potential distribution in the electrolyte that was produced. Figure

11 describes the potential in the electrolyte along the electrode surfaces and the top of

the electrolyte respectively. The potential varies from -0.2082V to 0.2782V. This

system shows an increase in the range of the potential within the electrolyte, and a shift

to more positive potentials.

Figure 10: COMSOL Results for the Electrode Geometry with a 90 Degree Step (Surface Plot)

Figure 11: COMSOL Results for the Electrode Geometry with a 90 Degree Step

15



8500A/m2 and the approximate reaction rate is 0.045mol/m

2s. These values are higher

than those for the coplanar electrode geometry. By increasing the electrode surface area,

more charge can be transferred to the electrolyte, which creates a larger gradient along

the electrode surfaces. Per Equations [21] and [22], current density and reaction rate are

directly related to the potential gradient normal to the electrode surface.

Figure 12: Current Density and Reaction Rate for the Electrode Geometry with a 90 Degree Step

3.2.2 Electrode Geometry with an Elliptical Step

The following geometry depicts two non-coplanar electrodes. Electrode A extends

further into the electrolyte elliptically from the surface of Electrode B. This geometry

could be representative of an area where one plate has been machined to meet its

abutting plate.



the electrolyte respectively. The potential varies from -0.2164V to 0.2533V. This

system produces results similar to the electrode geometry with a 90 degree step.

16

Figure 13: COMSOL Results for the Electrode Geometry with an Elliptical Step (Surface Plot)

Figure 14: COMSOL Results for the Electrode Geometry with an Elliptical Step


corrosion rate along the anodic surface. The maximum current density is approximately


2s. The surface

area of the electrode with the elliptical step is slightly less than the surface area of the 90

degree step, which is why the values are slightly less.

17

Figure 15: Current Density and Reaction Rate for the Electrode Geometry with an Elliptical Step

3.2.3 Axisymmetric Electrode Geometry

The next case assumed a 2D axisymmetric geometry. This geometry could be

representative of a pipe made of two different metals.



the electrolyte respectively. The potential distribution for this electrode geometry is the

same as with the coplanar geometry.

Figure 16: COMSOL Results for the Axisymmetric Electrode Geometry (Surface Plot)

18

Figure 17: COMSOL Results for the Axisymmetric Electrode Geometry

Figure 18 shows the current density along the entire electode surface, and the associated

reaction rate on the anodic surface. Since this system had the same potential distribution

as the coplanar geometry, it follows that the current density and the reaction rate would

be the same as well.

Figure 18: Current Density and Reaction Rate of the Axisymmetric Electrode Geometry

Table 2 provides a summary of the data discussed above.

Table 2: Summary of Data for the Different Geometries

Coplanar Polarization 90 Degree Step Elliptical Step Axisymmetric

Max. Potential (V) 0.2293 4.5 0.2782 0.2533 0.2293

Min. Potential (V) -0.2293 -0.0772 -0.2082 -0.2164 -0.2293

Range (V) 0.4586 4.5772 0.4864 0.4697 0.4586

Max. Current

Density (A/m2)*

4500 17500 8500 8500 4500

Max. Reaction

Rate (mol/m2 s)*

0.024 0.09 0.045 0.045 0.024

*Maximum current densities and corrosion rates are approximate

19

3.3 Results for Different Electrolyte Thicknesses Using a Copper-Zinc

Galvanic Couple

In this section computed results are shown for the copper-zinc galvanic couple in Figure

19 [3]. The inputs used for this system are included in Table 4. This case is included

because it is a real situation with experimental data, rather than a generic system.

Figure 19: Copper-Zinc Galvanic Couple in a Hydrochloric Acid Solution [3]

For this system, the anodic reaction is:

VW X VWY + Z [24]

Table 3 provides data needed to support calculation of the corrosion rate of a zinc anode.

Table 3: Properties of Zinc


z number of electrons transferred 2 --

Mw molecular weight 65.409 x 10-3

kg mol-1

ρ density 5610 kg m-3

20

Table 4: Input Data Used for Copper-Zinc Galvanic Couple [3]


aa,Cu anodic transfer coefficient of Copper* 0.025 V

aa,Zn anodic transfer coefficient of Zinc* 0.025 V

ac,Cu cathodic transfer coefficient of Copper* 0.025 V

ac,Zn cathodic transfer coefficient of Zinc* 0.025 V

σ conductivity of HCl solution 0.42 Ω-1

m-1

![\$ free current density of Copper 1 Am-2

!]$ free current density of Zinc 1 Am-2

a surface length of Copper 0.0075 m

b surface length of Zinc 0.02 m

w thickness of the HCl solution 0.002 and 0.02 m

[\ free corrosion potential of Copper -0.845 V

] free corrosion potential of Zinc -0.985 V

*Note: These values are not from Reference [3], they have been chosen based on

standard values rather than the experimental data

Figure 20 shows the potential distribution produced in the 2mm and 20mm thick

electrolyte. Figure 28 describes the potential in the electrolyte along the electrode

surfaces and along the top of the electrolyte respectively for the system with a 2mm

thick electrolyte, while Figure 29 provides the same information for the 20mm thick

electrolyte.

21

Figure 20: COMSOL Results for the Copper-Zinc Couple with 2mm and 20mm Thick Electrolyte

(Surface Plot)

Both systems have approximately the same range of potentials -0.9615V to -0.9249V for

a 2mm electrolyte and -0.9506V to -0.9383V for a 20mm electrolyte. However, the

distributions shown in Figure 21 and Figure 22 indicate that even though the range of

potentials is approximately the same for both of the electrolyte thicknesses, the

distribution of the potential within the electrolyte is very different. As expected, there

are more significant differences in the potentials at the top of the electrolyte for each

thickness. For the 2mm thick electrolyte, the potentials at the top surface of the

electrolyte vary from approximately -0.968V to -0.926V, whereas for the 20mm thick

electrolyte, they vary from approximately -0.948V to -0.946V


22


Figure 23 shows the current density along the anode surface, and the associated

corrosion rate for the 2mm thick electrolyte, while Figure 24 provides the same

information for the 20mm thick electrolyte. For the 2mm thick electrolyte, the

approximate maximum current density is 0.2A/m2 and the approximate maximum

corrosion rate is 0.4mm/year. Similarly, for the 20mm thick electrolyte, the approximate

maximum current density is 0.18A/m2 and the approximate maximum corrosion rate is

0.345mm/year

Figure 23: Current Density and Corrosion Rate for Copper-Zinc Couple with 2mm Thick

Electrolyte

23

Figure 24: Current Density and Corrosion Rate for Copper-Zinc Couple with 20mm Thick

Electrolyte

Table 5: Summary of Results for the Copper-Zinc Galvanic Couple with an Electrolyte 2mm and

20mm Thick

2mm Thick Electrolyte 20mm Thick Electrolyte

Max. Potential (V) -0.9249 -0.9398

Min. Potential (V) -0.9615 -0.9506

Range (V) 0.0366 0.0108

Max. Current Density (A/m2)* 0.2 0.18

Max. Corrosion Rate (mm/year)* 0.4 0.345


Appendix B describes this system using linear expressions for the current density. Due

to the relatively small overpotential in this system, linear conditions were a reasonable

system to review prior to implementing the Butler-Volmer conditions.

24

4. Conclusion

Each of the geometries that were investigated in Section 3.2 utilized the same system

inputs. In doing so, the results that were generated could be evaluated with respect to

the different geometries. Each of the geometries demonstrates the same qualitative trend

of potential in the electrolyte along the electrode surfaces, while the same overall

magnitude of potential and zero potential at the intersection of the two electrodes are

also seen. Table 2 summarizes the maximum and minimum potentials that were seen in

the electrolyte for each of the systems in Section 3.2.

The geometry with the 90 degree step saw the greatest range of potentials in the

electrolyte, followed by the geometry with the elliptical step. These ranges were also

shifted more positive than for the coplanar electrode geometry. This increase in range of

potential is due to the greater electrode surface area, which allows for more transfer of

charge from the electrode to the electrolyte. The shift to more positive potentials is

because the increase in surface area was only made to the cathode. The axisymmetric

model yielded the same results as the coplanar 2D Cartestian model developed during

finite element model validation. As expected, when all else is equal, the greater the

electrode surface area, the greater the potential change in the electrolyte.

Table 2 also summarizes the approximate maximum current density along the entire

electrode surface, and maximum reaction rate along the anode surface for each of the

systems in Section 3.2. The impacts of electrode geometry can also been seen with

current densities and reaction rates. As with the potential distributions, the coplanar

systems (Cartesian and axisymmetic) exhibit the same results for current density and for

reaction rate. The same correlation is seen for the systems with the 90 degree step and

the elliptical step. These results were expected since both current density and reaction

rate are based on potential distribution at the electrode surface.

Table 5 summarizes the maximum and minimum potentials that were seen in the

electrolyte for the copper-zinc galvanic couple for both a 2mm and 20mm thick

25

electrolyte. Table 5 also summarizes the approximate maximum current densities and

maximum corrosion rates along the anode surface.

The data in Table 5 would indicate that the thickness of the electrolyte did not have a

significant impact on the potential distribution within the electrolyte. However, Figure

20 demonstrates that even if the range of potentials is approximately the same for both of

the electrolyte thicknesses, the distribution of the potential within the electrolyte is very

different. There is a lot less variation of the potential at the top of the electrolyte in the

system with the thicker electrolyte. This result is in keeping with physical principles.

The same trend can be seen with processes such as heat transfer and diffusion; the

greater the distance from an input, the less impact is seen from the input. This same

rationale also explains the similar results for potential distribution 1mm from the

electrode surfaces.

The similarities in the maximum current densities and maximum corrosion rates were

also expected. These values are dependent on the behavior of potential at and near the

electrode surface and as such are minimally impacted by changing the thickness of the

electrolyte.

26

5. References

[1] Zhang, X. G. (2011). Galvanic Corrosion. In Uhlig's Corrosion Handbook (Third

ed., pp. 123-143). John Wiley & Sons, Inc.

[2] Oldfield, J. W. (1988). Electrochemical Theory of Galvanic Corrosion. In H. P.

Hack (Ed.), Galvanic Corrosion, ASTM STP 978 (pp. 5-22). Philadelphia, PA:

American Society for Testing and Materials.

[3] Doig, P., & Flewitt, P. E. (1979). A Finite Difference Numerical Analysis of

Galvanic Corrosion for Semi-Infinite Linear Coplanar Electrodes. Journal of The

Electrochemical Society , 126 (12), 2057-2063.

[4] Hack, H. P., & Scully, J. R. (1986). Galvanic Corrosion Prediction Using Long-

and Short-Term Polarization Curves. Corrosion , 42 (2), 79-90.

[5] Yan, J. F., Pakalapati, S. N., Nguyen, T. V., & White, R. E. (1992).

Mathematical Modeling of Cathodic Protection Using the Boundary Element

Method with a Nonlinear Polarization Curve. J. Electromchem. Soc. , 139 (7),

1932-1936.

[6] Astley, D. J. (1988). Use of the Microcomputer for Calculation of the

Distribution of Galvanic Corrosion and Cathodic Protection in Seawater

Systems. In H. P. Hack (Ed.), Galvanic Corrosion, ASTM STP 978 (pp. 53-78).

Philadelphia, PA: American Society of Testing and Materials.

27

6. Appendix A

Using a Basic Geometry with Linear Expressions for Current Density

Using linear relationships for the current densities at the electrode surfaces, in

accordance with Equations [11] and [12], produced the potential distribution in the

electrolyte shown in Figure 25. Figure 26 describes the potential in the electrolyte along

the electrode surfaces and the top of the electrolyte respectively.

Figure 25: COMSOL Results for Linear Current Density Distribution on the Electrode Surfaces

(Surface Plot)

The COMSOL results in Figure 26 correlate qualitatively well to the results from

Reference [3], as shown in Figure 5. However, there are discrepancies in the values for

the potential within the system. This linear relationship is only appropriate when there is

a very small overpotential in the system (generally <0.01V), which is not applicable in

this case. The linear approximation gives conservative results for the potential

distribution. This system is more appropriately represented by Butler-Volmer

relationships for the current density.

28

Figure 26: COMSOL Results for Linear Current Density Distribution on the Electrode Surfaces

29

7. Appendix B

Results for Different Electrolyte Thicknesses Using a Copper-Zinc Galvanic Couple

Using Linear Expressions for Current Density

The copper-zinc galvanic couple that was evaluated is representative of Figure 19, and

the inputs that were used for this system are included in Table 6.

Table 6: Input Data Used for Copper-Zinc Galvanic Couple [3]


σ conductivity of HCl solution 0.42 Ω-1

m-1

![\$ free current density of Copper 1 Am-2

!]$ free current density of Zinc 1 Am-2

a surface length of Copper 0.0075 m

b surface length of Zinc 0.02 m

w thickness of the HCl solution 0.002 and 0.02 m

[\ free corrosion potential of Copper -0.845 V

] free corrosion potential of Zinc -0.985 V

Linear relationships were used for the current density along the electrode surfaces, in

accordance with Equations [11] and [12]. The maximum overpotential for this system is

0.14V, which is greater than 0.01V, but still relatively small making it a reasonable

approximation. Figure 27 shows the potential distribution produced in the 2mm and

20mm thick electrolyte. Figure 28 describes the potential in the electrolyte along the

electrode surfaces and along the top of the electrolyte respectively for the system with a

2mm thick electrolyte, while Figure 29 provides the same information for the 20mm

thick electrolyte.

30

Figure 27: COMSOL Results for the Copper-Zinc Couple with 2mm and 20mm Thick Electrolyte

(Surface Plot)

Both systems have approximately the same range of potentials -0.9846V to -0.8594V for

a 2mm electrolyte and -0.9745V to -0.8864V for a 20mm electrolyte. However, the

distributions shown in Figure 28 and Figure 29 indicate the total range of potential is not

enough information to characterize the whole system. As expected, there are more

significant differences in the potentials at the top of the electrolyte for each thickness.

For the 2mm thick electrolyte, the potentials at the top surface of the electrolyte vary

from approximately -0.985V to -0.873V, whereas for the 20mm thick electrolyte, they

vary from approximately -0.938V to -0.855V


31


Figure 30 shows the current density along the anode surface, and the associated

corrosion rate for the 2mm thick electrolyte, while Figure 31 provides the same

information for the 20mm thick electrolyte. For the 2mm thick electrolyte, the

approximate maximum current density is 5 A/m2 and the approximate maximum

corrosion rate is 10 mm/year. Similarly, for the 20mm thick electrolyte, the approximate

maximum current density is 4.5 A/m2 and the approximate maximum corrosion rate is

8.5 mm/year

Figure 30: Current Density and Corrosion Rate along the Anode Surface of the Copper-Zinc

Couple with 2mm Thick Electrolyte

32

Figure 31: Current Density and Corrosion Rate along the Anode Surface of the Copper-Zinc

Couple with 20mm Thick Electrolyte

Table 7: Summary of Results for the Copper-Zinc Galvanic Couple with an Electrolyte 2mm and

20mm Thick

2mm Thick Electrolyte 20mm Thick Electrolyte

Max. Potential (V) -0.8594 -0.8864

Min. Potential (V) -0.9846 -0.9745

Range (V) 0.1252 0.0881

Max. Current Density (A/m2)* 5 4.5

Max. Corrosion Rate (mm/year)* 10 8.5


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Finite Element Modeling of Galvanic Corrosion of Metals · dissolution due to the chemical properties of the metals and the environment. Galvanic corrosion is particularly prevalent