Include section on how to model isotopic exchange reactions at the surface

[jhdark]

Exchange Reactions

Certain isotopic exchange processes can also be approximated, e.g.:

$$\mathrm{T + H_2} \rightleftharpoons \mathrm{H} + \mathrm{HT}$$

If the $\mathrm{H}_2$ concentration is assumed much larger than $\mathrm{HT}$, this reduces to a first-order process in $\mathrm{T}$. Such fluxes can be implemented using festim.ParticleFluxBC with user-defined expressions.

import ufl
from festim import (
    Material,
    ParticleFluxBC,
    Species,
    SurfaceSubdomain,
    VolumeSubdomain,
    k_B,
)

boundary = SurfaceSubdomain(id=1)
my_mat = Material(D_0=1, E_D=0.1)
volume = VolumeSubdomain(id=1, material=my_mat)
tritium = Species("tritium")
Kr_0 = 1.0
E_Kr = 0.1


def my_custom_recombination_flux(c, T):
    Kr_0_custom = 1.0
    E_Kr_custom = 0.5  # eV
    h2_conc = 1e25  # assumed constant H2 concentration in

    recombination_flux = (
        -(Kr_0 * ufl.exp(-E_Kr / (k_B * T))) * c**2
        - (Kr_0_custom * ufl.exp(-E_Kr_custom / (k_B * T))) * h2_conc * c
    )
    return recombination_flux


my_custom_flux = ParticleFluxBC(
    value=my_custom_recombination_flux,
    subdomain=boundary,
    species_dependent_value={"c": tritium},
    species=tritium,
)