In this article, a numerical method for detailed studies of two-phase mass transfer is introduced that is based on a three-dimensional finite volume Arbitrary Lagrangian-Eulerian method. The implementation of the two-phase species equation employs the Dirichlet-Neumann algorithm, following the domain coupling technique of the underlying hydrodynamical solver by Tukovic and Jasak (2012). The coupling is found to be dependent on the discontinuities of the concentration and its first derivative, as well as on which side of the interface Dirichlet or Neumann conditions are specified. Relaxation parameters are introduced to stabilize the algorithm and optimal coefficients are calculated explicitly. The numerical method is thoroughly validated by a three dimensional advection-diffusion test case, proving the accuracy of the local Sherwood numbers for Peclet numbers up to 100000, which is ten times higher than the currently reported maximum. Additionally, a limit model for instantaneous reactions is implemented and validated, allowing the computation of product concentrations and of local and global enhancement factors. (C) 2016 Elsevier Ltd. All rights reserved.