asl::FDBVKinetics Class Reference

Numerical method which computes electrode reactions. More...

#include <aslFDElChemKinetics.h>

Inheritance diagram for asl::FDBVKinetics:

Collaboration diagram for asl::FDBVKinetics:

Public Types
typedef SPDataWithGhostNodesACLData	Data
typedef SPAbstractDataWithGhostNodes	Field
typedef acl::VectorOfElements	Param
Public Types inherited from asl::SingleKernelMapNM
typedef SPAbstractDataWithGhostNodes	Field

Public Member Functions
	FDBVKinetics (Data a0, double n0, Data aI, double nI, Data phiS, Field phi, const Param &j0, const Param &beta, double n)
void	setElectricFieldSource (Field phi)
Field	getElectricFieldSource () const
Data &	getAI (unsigned int i=0)
void	addAI (Data ai, double ni)
void	executeJ ()
Public Member Functions inherited from asl::SingleKernelMapNM
void	setMap (Field map)
	~SingleKernelMapNM ()
Public Member Functions inherited from asl::SingleKernelNM
virtual void	execute ()
	Executes the numerical procedure. More...
virtual void	init ()
	Builds the necesery internal data and kernels. More...
virtual	~SingleKernelNM ()
Public Member Functions inherited from asl::NumMethod
virtual	~NumMethod ()

Additional Inherited Members
Protected Member Functions inherited from asl::SingleKernelMapNM
	SingleKernelMapNM (const acl::KernelConfiguration &kernelCongig)
	SingleKernelMapNM (Field map, const acl::KernelConfiguration &kernelCongig)
void	initMapInfrastructure (acl::ExpressionContainer &k)
Protected Member Functions inherited from asl::SingleKernelNM
virtual void	preProcessing ()
	the function executed before kernel->compute() More...
virtual void	postProcessing ()
	the function executed after kernel->compute() More...
	SingleKernelNM (const acl::KernelConfiguration &kernelCongig)
Protected Attributes inherited from asl::SingleKernelNM
acl::SPKernel	kernel

Detailed Description

Numerical method which computes electrode reactions.

!!!!!!!!!!!!need corrections

Description of an electrochemical kinetic reaction on an electrode:

\[ \ce{A <-> A^{n+} + n e-} \]

The reaction kinetics is described by the Butler-Volmer equation:

\[ j = j_0 c_A \cdot \left( e^{\frac { \alpha_a nF \eta} {RT}} - e^{ - { \frac { \alpha_c nF \eta} {RT}} } \right), \]

where

• \( j_0 \) is an exchange current density, \( A/m^2 \), note the algorithm assumes \( mol/m^2/s \)
• \( T \) is absolute temperature, \(K\)
• \( n \) is number of electrons involved in the electrode reaction
• \( F \) is the Faraday constant, \( 9.64853399 \cdot 10^4 C mol^{-1} \)
• \( R \) is universal gas constant, \( 8.3144621 J K^{-1} mol^{-1} \)
• \(\alpha_c\) is so-called cathodic charge transfer coefficient
• \(\alpha_a\) is so-called anodic charge transfer coefficient, dimensionless
• \(\eta\) is activation overpotential defined as: \(\eta = \phi - \phi_{eq}\)
• \(E\) is electrode potential, \( V \)
• \(E_{eq}\) equilibrium potential, \( V \)
• \(c_A\) concentration of the component \(\ce{A}\)

The equation describes chemical reaction namely it can be used together with an appropriate transport equations and equation for the elecrostatic potential:

\[ c_A^R = c_A - j \]

\[ c_{A^{n+}}^R = c_{A^{n+}} + j \]

\[ \vec\nabla \kappa \vec\nabla\phi + S_\phi = 0 \]

class parameters are related to the quation ones as follows

Parameters

a0	molar concentration of the component before reaction
aI	molar concentration of the ionized component
efSPhi	source term in the equation for electrostatic potential
phi	electrostatic potential, \( \phi \)
j0	corresponds to \( j_0 \), note it should have the same units as concentrations
phi0	corresponds to \( \phi_{eq} \)
alphaA	corresponds to \( \frac { \alpha_a F} {RT} \)
alphaC	corresponds to \( \frac { \alpha_c F} {RT} \)
n	corresponds to \( n \)

Definition at line 88 of file aslFDElChemKinetics.h.

Member Typedef Documentation

typedef SPDataWithGhostNodesACLData asl::FDBVKinetics::Data

Definition at line 91 of file aslFDElChemKinetics.h.

typedef SPAbstractDataWithGhostNodes asl::FDBVKinetics::Field

Definition at line 92 of file aslFDElChemKinetics.h.

typedef acl::VectorOfElements asl::FDBVKinetics::Param

Definition at line 93 of file aslFDElChemKinetics.h.

Constructor & Destructor Documentation

asl::FDBVKinetics::FDBVKinetics	(	Data	a0,
		double	n0,
		Data	aI,
		double	nI,
		Data	phiS,
		Field	phi,
		const Param &	j0,
		const Param &	beta,
		double	n
	)

Member Function Documentation

void asl::FDBVKinetics::addAI	(	Data	ai,
		double	ni
	)

void asl::FDBVKinetics::executeJ

(

)

FDBVKinetics::Data & asl::FDBVKinetics::getAI ( unsigned int  i = 0 )

inline

Definition at line 141 of file aslFDElChemKinetics.h.

Field asl::FDBVKinetics::getElectricFieldSource

(

)

const

void asl::FDBVKinetics::setElectricFieldSource

(

Field

phi

)

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The documentation for this class was generated from the following file:

• /builddir/build/BUILD/ASL-0.1.7/src/num/aslFDElChemKinetics.h