Discussion Forum

I am trying to model the crossover of species across the membrane of a fuel cell. It has multispecies flowing across either side of the membrane to the cathodes and anodes. The membrane has some fixed charge due the initial fixed H+ ions. The nernst equation is to be applied taking account of all three diffusion, convection and migration. The velocity is to be calculated using an alternative form of schlogl equation which is :
v= - (kp/mu)*{delta}p - (kpi/mu)*Cf*F*[ {delta}phi(l,m)+{delta}phi(diff,m) ]
where, kp= hydraulic permeability
mu= viscosity of water
kpi= electrokinetic permeability
Cf= Fixed H+ ion concentration in membrane
F= Faraday's constant
p = pressure
{delta}phi(l,m)= Liquid potential difference across membrane
{delta}phi(diff,m)= effective diffusion potential

The Effective diffusion potential is calculated by-

{delta}phi(diff,m)= F*{summation}[ z(i)*D(i)*{delta}c(i) ] / sigma(eff,m)

where, z(i)= charge on each species
D(i)= Diffusion coefficient of each species in membrane
c(i)= active concentration of each species in membrane
sigma(eff,m)= effective conductivity of membrane,

which is calculated by-

sigma(eff,m)= (F^2/RT)*{summation}[ z(i)^2*D(i)*c(i) ]

where F, R, T has usual meanings
The concentration of one of the species is calculated from the electroneutrality condition
zf*Cf+ {summation}[ z(i)*c(i) ] = 0

where, zf= fixed acid charge
Cf= concentration of fixed H+ ion


Note: The words written in curly brackets are operators ( summation and delta operators)

Here are my queries:

1. Which physics is exactly to be used for the simulation for transport in membrane? I am confused with Transport in diluted species, Tertiary Current Distribution and Nersnt Planck Equation or I have to go for equation based modelling?
2. For the calculation of velocity I am not finding any suitable physics. Do I have to use equation based modelling for this?
3. As the species are crossing from either side (electrodes) of the membrane and going to the opposite side, how I can actually define the boundaries for inflow and outflow?
4. Can one single physics will be able to handle to all the species in the membrane?

The geometry is 2D consisting of three domains cathode, membrane and anode, membrane being sandwiched between the electrode.
The species concentration in the cathode and anode, and the potential in membrane are already modeled. I really need help in this.
Thanks in advance.