OpenFOAM Solver for mass transfer in steady-state: Validation with stagnant medium and equimolar counter-diffusion in mass-flux variables

This work presents three OpenFOAM v2012 solvers (BDF, EDF, FTF) for steady-state binary mass transfer derived from the species continuity equation: stagnant-gas diffusion, equimolar counter-diffusion, and a unified flux-based equation, respectively. Simulations were conducted on a 1D domain (0 ≤ z ≤ 1 m) with w_A,0 = 0.95, w_A,L = 0 (stagnant-B) or 0.05 (equimolar). Validation against analytical solutions and scalarTransportFoam produced mean relative errors below 10^-4 (BDF, FTF) and 10^-6 (EDF), confirming the unified formulation recovers both limiting cases.