electrostaticDeposition

Description

The electrostaticDeposition is a boundary condition to calculate electric potential (V) on a given boundary based on film thickness (h) and film resistance (R) fields which are updated based on a given patch-normal current density field (jn), Coulombic efficiency and film resistivity.

The governing equations are as follows:

$$j_n = - \sigma \nabla^\perp_p V = - \sigma (\vec{n}\cdot(\nabla V)_p)$$ $$\frac{dh}{dt} = C_{eff} (j_n - j_{min})$$ $$\frac{dR}{dt} = \rho \frac{dh}{dt} = \rho C_{eff} (j_n - j_{min})$$ $$V_{film}^n = V_{film}^o + j_n R_\Delta$$ $$V_{body} = j_n R_{body}$$ $$V_p^n = V_i + V_{body} + V_{film}^n$$

where:

Property	Description
$j_n$	Patch-normal current density [A/m^2]
$V_p^n$	Electric potential on film-fluid interface [volt = kg m^2/(A s^3)]
$V_p^o$	Previous time-step electric potential on the interface [volt]
$V_{film}$	Electric potential due to film resistance [volt]
$V_{body}$	Electric potential due to body resistance [volt]
$V_i$	Initial electric potential [volt]
$R_\Delta$	Film resistance (finite increment) [ohm m^2 = kg m^4/(A^2 s^3)]
$R_{body}$	Body resistance [ohm m^2 = kg m^4/(A^2 s^3)]
$\rho$	Isotropic film resistivity [ohm m = kg m^3/(A^2 s^3)]
$h$	Film thickness [m]
$C_{eff}$	Volumetric Coulombic efficiency [m^3/(A s)]
$j_{min}$	Minimum current density for deposition onset [A/m^2]
$\sigma$	Isotropic conductivity of mixture [S/m = A^2 s^3/(kg m^3)]
$\vec{n}$	Patch-normal unit vector [-]

Usage

The condition requires entries in both the boundary and field files.

Boundary file

<patchName>
{
    type            patch;
    ...
}

Field file

<patchName>
{
    // Mandatory entries
    type                    electrostaticDeposition;
    h                       <scalarField>;
    CoulombicEfficiency     <PatchFunction1>;
    resistivity             <PatchFunction1>;

    // Conditional mandatory entries

        // Option-1: single-phase
        sigma       <scalar>;

        // Option-2: multiphase
        phases
        {
            alpha.air
            {
                sigma       <scalar>;
            }
            alpha.water
            {
                sigma       <scalar>;
            }
            alpha.mercury
            {
                sigma       <scalar>;
            }
            ...
        }

    // Optional entries
    jMin                    <scalar>;
    qMin                    <scalar>;
    Rbody                   <scalar>;
    Vi                      <scalar>;
    Vanode                  <scalar>;
    qCumulative             <scalarField>;

    // Inherited entries
    ...
}

where:

Property	Description	Type	Required	Default
type	Type name: electrostaticDeposition	word	yes	-
h	Film thickness	scalarField	yes	-
CoulombicEfficiency	Coulombic efficiency	PatchFunction1<scalar>	yes	-
resistivity	Isotropic film resistivity	PatchFunction1<scalar>	yes	-
sigma	Isotropic electrical conductivity of phase	scalar	yes	-
jMin	Minimum current density for deposition onset	scalar	no	0
qMin	Minimum accumulative specific charge for deposition onset	scalar	no	0
Rbody	Resistance due to main body and/or pretreatment layers	scalar	no	0
Vi	Initial electric potential	scalar	no	0
Vanode	Anode electric potential	scalar	no	GREAT
qCumulative	Accumulative specific charge [A s/m^2]	scalarField	no	0

The inherited entries are elaborated in:

• Foam::fixedValueFvPatchField
• Foam::PatchFunction1

• Depletion or abrasion of material due to negative current is not allowed.
• When accumulative specific charge (qCumulative) is less than minimum accumulative specific charge (qMin), no deposition occurs.
• Boundary-condition updates are not allowed during outer corrections to prevent spurious accumulation of film thickness.
• resistivity, jMin, qMin and Rbody are always non-negative.

Further information

Tutorial:

• electrostaticDeposition

Source code:

• electrostaticDeposition

API:

• Foam::electrostaticDepositionFvPatchScalarField

History: Introduced in version v2112