Mathematical analysis of the reaction–diffusion of water in glass tubes

The diffusion and reaction of water with glass tubes are mathematically analyzed. A general mathematical model is developed that takes into account the absorption of molecular water from the vapour phase on to the glass tube surface, its subsequent diffusion, and both the forward and backward reactions of formation of the silanol groups. The general solutions are obtained numerically while analytical solutions are obtained for special cases of small time or fast reaction. An approximate integral solution is obtained for the latter and it is shown that the equilibrium model with fast reaction can be cast into a simple yet accurate algebraic form which is easy to implement. The models are applied to few cases of practical importance to optical fiber processing.