Hi,

I am currently working on gas diffusion through membranes and I am having issues finding a coefficient for the ODE's solution, based on the method presented here.

My problem concerns the coefficient lambda, appearing after developping Fick's law, given by eq.16 :

tan(λ_{n}) = (k*S_{R}− δ_{R}λ_{n}(λ_{n}+ S_{R}β_{n})) / (S_{R}δ_{R}λ_{n}+ β_{n}(k*S_{R}− δ_{R}λ_{n}^{2})

where k = 1,

S_{R}remains a symbolic variable,

δ_{R }is a known constant,

β_{n }is a function of λ_{n},δ_{R},S_{R }and k

To perform a curve fit with my experimental data, I need to find an explicit formulation of λ_{n. }In practice, I can consider only the first term of the summation (λ_{1}) for sufficient accuracy.

How can I express explicitly λ_{1}? The tan() function is giving me a headache

Thank you,

edit : I would like to do something similar to the transformation in eqs 11-12 in this paper