Transport limited heterogeneous reactions with asymmetric transport rates in the non-reacting phase can exhibit an interesting switch in the concentrations of the reactants in the reacting phase from one limiting reactant to the other. This switch, called "cross-over" [Mchedlov-Petrossyan P.O., Khomenko G., Zimmerman W.B., 2003a. Nearly irreversible, fast heterogeneous reactions in premixed flow. Chemical Engineering Science 58, 3005-3023; Mchedlov-Petrossyan P.O., Zimmerman W.B., Khomenko G.A., 2003b. Fast binary reactions in a heterogeneous catalytic batch reactor. Chemical Engineering Science 58, 2691-2703], relates to the optimum design of the tubular reactor as all the reactants in the reacting phase are completely consumed at cross-over. The cross-over phenomenon, which has been studied by a number of researchers using phenomenological modelling, is investigated here by developing a distributed model using level-set simulations, in order to explore the possibility of the existence of cross-over in the frame of reference of a moving droplet. Cross-over occurs for a droplet moving due to buoyancy with asymmetric transfer rates of the reactants in the non-reacting phase and an instantaneous reaction occurring inside the droplet (reacting phase). The cross-over length obtained using the level-set simulation is found to be within 0.7-8% of that obtained using the phenomenological model. Computational experiments are performed by varying the ratios of the initial concentrations of the reactants and the transfer rates of the reactants, in order to obtain the parametric region for the existence of cross-over which is also compared with the theoretical prediction. (c) 2006 Elsevier Ltd. All rights reserved.