The invention provides a passive fluidics circuit for directing different fluids to a common volume, such as a reaction chamber or flow cell, without intermixing or cross contamination. The direction and rate of flow through junctions, nodes and passages of the fluidics circuit are controlled by the states of upstream valves (e.g. opened or closed), differential fluid pressures at circuit inlets or upstream reservoirs, flow path resistances, and the like. Free diffusion or leakage of fluids from unselected inlets into the common outlet or other inlets at junctions or nodes is prevented by the flow of the selected inlet fluid, a portion of which sweeps by the inlets of unselected fluids and exits the fluidics circuit by waste ports, thereby creating a barrier against undesired intermixing with the outlet flow through leakage or diffusion. The invention is particularly advantageous in apparatus for performing sensitive multistep reactions, such as pH-based DNA sequencing reactions.