Specify the initial concentration of the intercalating species (that is, the initial charge level of the electrode) either as a
Initial species concentration cs,init (SI unit: mol/m
3) or an
Initial electrode potential.
The Initial electrode potential Einit (SI unit: V) is used as argument to the
Equilibrium concentration function, which may be specified either
From material or
User defined.
Note that if the SOC and Initial Charge Distribution is active in the model, only the
Equilibrium concentration setting is active, and
Einit is defined internally based on the settings in the
SOC and Initial Charge Distribution node.
The Maximum species concentration cs,max (SI unit: mol/m
3) defines the maximum possible concentration of the intercalated concentration. The value is used by
Porous Electrode Reaction when the
Kinetic expression type has been set to
Lithium Insertion. If the
SOC and Initial Charge Distribution is active in the model this concentration is also used to compute the electrode host capacity.
The Species concentration transport model specifies the diffusion model for the intercalating species in the electrode particles.
Fick’s law and
Baker-Verbrugge both add an extra dimension, defined on the porous electrode domain, within which a diffusion equation is applied in order to solve for the concentration distribution along the depth within a single particle of the electrode. The transport in the extra dimension is defined by the
Intercalation diffusivity Ds (SI unit: m
2/s). The
From material option of
Ds does not support concentration varying diffusion coefficients. The
User defined option of
Ds can be used to set up concentration varying diffusion coefficients, by specifying the diffusivity as a function of the solid lithium concentration in the electrode particles,
cs. Refer to
Dependent Variables and Extra Dimensions in
The Lithium-Ion Battery Interface (or
Dependent Variables and Extra Dimensions in
The Battery with Binary Electrolyte Interface) for a discussion on the variable name to be used for the
cs dependent variable.
Fick’s law defines the molecular flux of the intercalated species as the product of the diffusion coefficient and the concentration gradient. The
Baker-Verbrugge models adds a correction to the diffusion coefficient based on the
Equilibrium potential,
Eeq, of the intercalation reaction. This potential is defined in the
Equilibrium Potential section below. Generally, the Baker–Verbrugge model is better at capturing state-of-charge dependent transport rates and staging phenomena, whereas Fick’s law may be numerically more stable. Note that the parameter values of the diffusivity from the material library generally have been estimated assuming Fick’s law and may have to be reduced when switching to Baker–Verbrugge.
Use No spatial gradients to assume a constant concentration along the depth of the particle.
No spatial gradients significantly reduces the computational load of the model.
Set Maximum and the
Minimum operational potential,
Emax and
Emin, to specify the potential window of the electrode. These values are used together with the
SOC and Initial Charge Distribution node to define and compute dynamic global cell variables.
Use these settings to control the Distribution of the mesh and the
Element order of the extra particle dimension.
The predefined distributions Square or
Cubic root sequence create mesh distributions with a denser mesh toward the particle surface.
The Use fast assembly in particle dimension option enables an alternative method for assembling of the diffusion equation in the particle dimension that may decrease computation time when the number of mesh elements in the battery cell dimension is of the same order of magnitude as the number of elements in the particle dimension (this is typically the case for 1D problems). When the fast assembly option is enabled, it is not possible to postprocess the solid particle concentration along the particle dimension, and the diffusion coefficient in the particle cannot vary along the particle depth. The same equations are solved for regardless of assembly method.
The fast assembly option is not available if Baker-Verbrugge species concentration transport model is enabled.
Include heat of mixing defines a heat source defined as the gradient of the molar enthalpy times the molar flux of the intercalating species, integrates it over the particle, and adds it to the total heat source variable in the domain. The molar enthalpy is based on the
Equilibrium potential of the insertion reaction, defined below.
This section defines the Equilibrium potential of the intercalation reaction, Eeq (SI unit: V), used by the
Particle Transport Properties and
Heat of Mixing sections, when applicable.
When modeling diffusion in the particle you may enable the Calculate stress and strain checkbox to compute a number stress and strain related variables in the particle. The variables are based on the Young’s modulus and Poisson’s ratio values and the relative volume change of the particle. The relative volume change is typically dependent on the concentration in the particle.
