Most methods for Direct Numerical Simulations of interfacial species transfer across fluid interfaces suffer from poor stability, accuracy and/or the loss of conservativeness or boundedness properties. In the literature this is often attributed to shortcomings in the 'numerics'. This paper presents a single-field model, termed Continuous Species Transfer (CST) model. The resulting numerical method is virtually void of above problems. In detail we shall set out the model's derivation procedure which is based on the Conditional Volume-Averaging technique and thus guides our consistent Finite Volume discretisation practice. The CST method enables the simulation of species transfer in two-phase flows in a realistic range of Henry coefficients and diffusivity ratios in the context of algebraic Volume-Of-Fluid (VOF) interface capturing techniques, given a sufficient resolution of the concentration boundary layer with at least four to five computational cells. Beside setting out the mathematical and numerical foundation of the CST method, we present a sound validation study. The CST method is then applied to the case of interfacial species transfer from single rising bubbles in quiescent liquids. Our method development and numerical simulations have been based on OpenFOAM (R), in particular its algebraic VOF solver family interFoam. (C) 2015 Elsevier Ltd. All rights reserved.