The current response for ion transfer across a polarised liquid-liquid interface under hydrodynamic conditions is presented via numerical solution of the relevant coupled two-phase transport equations. The liquid-liquid case can allow for asymmetric flow in either phase: a channel geometry is assumed and numerical solution achieved using implicit finite-difference methods. The response is simulated for chronoamperometry and cyclic voltammetry. The computed waveshapes for reversible, irreversible and quasi-reversible ion transfer are presented. The variation of the steady state current and half-wave potential with relative flow rates are explored and are compared with analytical theory where applicable. (c) 2007 Elsevier B.V. All rights reserved.