DiffusionLimitedReaction

Source: models/chemical_reactions/DiffusionLimitedReaction.py

Diffusion-limited reaction rate for a shrinking-core product phase.

Given the dimensionless inner radius \(r_i\) and outer radius \(r_o\) of the product phase, the liquid and solid reactivities \(R_l\) and \(R_s\) (both in \([0, 1]\)), the characteristic diffusion coefficient \(D\) of the rate-limiting species, and the molar volume \(\omega\) of that species, the volumetric reaction rate is

\[ \dot{\alpha} = \frac{2 D R_l R_s}{\omega} \cdot \frac{r_o}{r_o - r_i + \delta} \]

where \(\delta\) is a small “dummy thickness” added to the product thickness \(r_o - r_i\) to keep the rate finite at the start of the reaction.

Inputs

product_inner_radius — input · Scalar · required

Inner radius of the product phase

solid_inner_radius — input · Scalar · required

Inner radius of the solid phase

liquid_reactivity — input · Scalar · required

Reactivity of the liquid phase, between 0 and 1

solid_reactivity — input · Scalar · required

Reactivity of the solid phase, between 0 and 1

Outputs

reaction_rate — output · Scalar · required

Product phase substance volumetric rate of change

Parameters

diffusion_coefficient — parameter · Scalar · required

Diffusion coefficient of the rate-limiting species in the product phase

Other options

product_dummy_thickness — float · default 0.01

Minimum product thickness to avoid division by 0

molar_volume — float · required

Molar volume of the rate-limiting (liquid) species