s] is the solution pressure at the slit entrance and [P.
Based on the quasi-static approximation, the pressure of the gas phase can be related to the local solution pressure using Laplace's Eq 13 where the cells are treated as having a uniform radius, R, P is the solution pressure, and [[Gamma].
By combining Eqs 12, 13, and 15, an expression relating the gas phase pressure and the solution pressure is derived and given by Eq 16.
Calculating the gas phase pressure for a given solution pressure, requires Eq 16 to be solved iteratively, precluding a closed form solution of Eq 7.
Equations 17 and 18 can be solved using the boundary condition that at the slit exit the solution pressure is given by P(x = L) = [P.
Notice that the volumetric flow rate increases parabolically along the slit length, and the solution pressure decreases non-linearly along the slit length.