Struct DiffusionInElectrode 

pub struct DiffusionInElectrode {
    pub diffusivity: f64,
    pub particle_radius: f64,
    pub c_surface: f64,
    pub c_bulk: f64,
    pub c_max: f64,
}

Solid-state Li diffusion inside a spherical electrode particle.

Models concentration profiles and C-rate limitations using Fick’s second law in spherical coordinates.

Fields

diffusivity: f64

Solid-state diffusivity of Li⁺ [m²/s].

particle_radius: f64

Particle radius [m].

c_surface: f64

Surface concentration [mol/m³].

c_bulk: f64

Bulk (centre) concentration [mol/m³].

c_max: f64

Maximum Li concentration [mol/m³].

Implementations

impl DiffusionInElectrode

pub fn new( diffusivity: f64, particle_radius: f64, c_surface: f64, c_bulk: f64, ) -> Self

Construct a new DiffusionInElectrode with default c_max = 30_000.0.

pub fn with_c_max( diffusivity: f64, particle_radius: f64, c_surface: f64, c_bulk: f64, c_max: f64, ) -> Self

Construct with explicit maximum concentration.

pub fn concentration_profile(&self, r: f64) -> f64

Approximate radial concentration profile [mol/m³] at fractional radius r ∈ [0, 1].

Uses a parabolic (pseudo-steady-state) profile: c(r) = c_bulk + (c_surface − c_bulk) × r²

pub fn diffusion_length(&self) -> f64

Characteristic diffusion length [m].

L_d = sqrt(D × t_ref) where t_ref = R² / D (time to diffuse across particle).

pub fn diffusion_time_scale(&self) -> f64

Diffusion time scale [s]: τ = R² / D.

pub fn max_c_rate(&self) -> f64

Maximum C-rate [1/h] at which the particle can be fully discharged.

Defined as C_max = 1 / τ_diff [h⁻¹] where τ_diff = R² / (π² D). Higher diffusivity or smaller particle → higher accessible C-rate.

pub fn surface_concentration_gradient(&self) -> f64

Surface concentration gradient [mol/m⁴] approximation (linear).

dc/dr|_R ≈ (c_surface − c_bulk) / R

pub fn soc_from_concentration(&self) -> f64

State of charge estimated from average concentration: SOC = c_avg / c_max.

Average concentration for parabolic profile: c_avg = c_bulk + 3/5 (c_surf - c_bulk).

pub fn surface_flux(&self) -> f64

Flux at the surface [mol/(m²·s)] using Fick’s law.

J = −D × dc/dr|_R

Trait Implementations

impl Clone for DiffusionInElectrode

fn clone(&self) -> DiffusionInElectrode

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for DiffusionInElectrode

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.