So in this porous region your liquid is partially transformed into a solid deposit, and now you want to know to what extent this results in a convective flow of electrolyte through the boundary between the 'free' region and the porous region? I would say you have to impose a flow at the boundary equal to
(1/{density of fluid} - 1/{density of deposit}) * {total mass of fluid reacting to solid per unit time}
If you want to know the convective flow in the complete porous region this would come down to imposing such boundaries throughout the porous region, so if
- x=0 at the free-porous interface
- x=x_el at the porous-charge collector interface
- a=1/{density of fluid} - 1/{density of deposit}
- r(x) mass of fluid reacting to solid per unit time at position x
- phi(x) the vollume flow at position x
you would get
phi(x)=a * integral[x to x_el] r dx
differentiating with respect to x:
d phi/dx = a * r
I hope this addresses your question.
(1/{density of fluid} - 1/{density of deposit}) * {total mass of fluid reacting to solid per unit time}
If you want to know the convective flow in the complete porous region this would come down to imposing such boundaries throughout the porous region, so if
- x=0 at the free-porous interface
- x=x_el at the porous-charge collector interface
- a=1/{density of fluid} - 1/{density of deposit}
- r(x) mass of fluid reacting to solid per unit time at position x
- phi(x) the vollume flow at position x
you would get
phi(x)=a * integral[x to x_el] r dx
differentiating with respect to x:
d phi/dx = a * r
I hope this addresses your question.