The computational modelling of multiphysics mass transfer in a microchannel is a challenging endeavour. This article has proposed and validated a Lagrangian methodology for modelling coupled physics using near optimal computational efforts. This new development has been verified and compared with a reference Eulerian finite difference model. A heuristic theory for computational mass transfer phenomena has been studied. At high Peclet numbers when the reference Eulerian model fails, the Lagrangian model resolves electro-osmotic mass transfer, showing a good quantitative agreement with theoretical analysis. The Lagrangian model also helps to estimate necessary parameters so that an optimal electro-osmotic pumping can be designed in a microchannel. The computational efficiency of the Lagrangian model has been examined, showing that an increase of the Peclet number by a factor of 32 increases the global computational complexity by about a factor of 10(4) if the reference Eulerian model were used. This verifies the optimal performance of the Lagrangian model. (C) 2012 Elsevier Ltd. All rights reserved.