A mathematical model has been developed for a differential wetted sphere contactor in which a gas-liquid reaction occurs. The mathematical model given by the parabolic non-linear partial differential equation was solved numerically by the moving finite element method (MFEM) using the Lagrange polynomial approximations of arbitrary degree in each of the finite elements, which the interior nodes optimised as in the orthogonal collocation method. A new approach attaining the local physical mass transfer coefficient near the gas-liquid interface has been demonstrated. The novelty of that approach is that the spherical liquid film exerts a bounding influence on the rate of absorption. The validity of the concept as well as the quantitative predictability of the theoretical analysis is demonstrated by experimentation on the carbon dioxide-water system. Direct comparisons of the local physical mass transfer coefficient obtained with the MFEM and the asymptotic analytical solutions from the literature are presented here. (c) 2005 Elsevier Ltd. All rights reserved.