Domain Equations for Primary and Secondary Current Distributions
Assuming electroneutrality (which cancels out the convection term) and negligible concentration gradients of the current-carrying ion (which cancels out the diffusion term), the following expression is left for the current density vector in an electrolyte:
.
Further, assuming approximately constant composition of charge carriers, we can define a constant electrolyte conductivity as:
the current density in the electrolyte can be written as
This equation takes the same form as Ohm’s law; in an electrolyte, charge transport is ohmic, subject to the above assumptions.
Conservation of charge yields the domain equation usually used for the electrolyte in the Primary and Secondary Current Distribution interfaces:
In a pore electrolyte, the homogenization used in porous electrode theory introduces a source or sink term in the pore electrolyte current balances due to the charge transfer reactions at the electrode-electrolyte interface within the porous material. In such cases, a source term,
Q
l
, is introduced on the right-hand side of the equation above.
The Primary and Secondary Current Distribution interfaces define two dependent variables: one for the potential in the electrolyte and one for the electric potential in the electrode. The conduction of current in the electrolyte is assumed to take place through transport of ions as described above, while electrons conduct the current in the electrode.
Since Ohm’s law is also used for current conduction in the solid electrode phase, the general equation in these interfaces is according to the following:
with
where
Q
k
denotes a general source term,
k
denotes an index that is
l
for the
electrolyte
or
s
for the
electrode
,
σ
k
denotes the conductivity (SI unit: S/m) and
k
the potential (SI unit: V).
.
k the potential (SI unit: V).