Subgrid Particle Intercalation

In batteries, such as Li-ion batteries, ions are transported across a separator and then intercalate into the crystalline lattice of the active electrode material, such as graphite. In Simcenter STAR-CCM+, this intercalation process is modeled by the Subgrid Particle Intercalation model.

The Subgrid Particle Intercalation model assumes that the active electrode material is composed of spherical particles. As a result, the particle concentration only changes in the radial direction. A diffusion transport equation is solved in spherical coordinates for the transport of ions into the active electrode phase:

图 1. EQUATION_DISPLAY
∂ ∂ t ⁡ ∫ V c ⁢   d V = ∮ A ⁢ D ( c , T ) ∇ c ⋅ d A
(4147)
where:
  • c is the concentration within the active electrode solid porous phase [kmol/m3] .
  • D ( c , T ) is the concentration and temperature dependent molecular diffusivity [m2/s] .
  • r is the radial distance in the particle [m] .

For t > 0 the boundary conditions are defined as:

图 2. EQUATION_DISPLAY
∂ c ∂ r | r = 0 = 0 ∂ c ∂ r | r =   R s = − Φ ( t ) D ( c , T )
(4148)

and the flux is defined as:

图 3. EQUATION_DISPLAY
Φ ( t ) = N ( t ) R s 3 ( 1 − χ ) η S
(4149)
where:
  • N is the bulk substance electrochemical reaction flux of the electrode material [kmol/m3s].
  • R s is the radius at the surface [m].
  • χ is non-unity porosity.
  • η S is the available volume fraction of the electrode material.