In this report a physical model is developed which considers unsteady state mass transfer through the interface of bubbles in liquids as well as accompanying deformation turbulence. The basis of this model is the hypothesis of deformation turbulence developed by H. Brauer. The mathematical functions for turbulent terms were introduced into the differential equations for the momentum and mass transfer and solved numerically. The comparison of theoretical values with experimental results shows that the model of deformation turbulence describes adequately the unsteady mass transfer process not only on single bubbles but also on bubble swarms.