Simplified analysis systems that offer the performance of benchtop instruments but the convenience of portability are highly desirable. We have developed novel, miniature devices that feature visual inspection readout of a target's concentration from a ~1 μL volume of solution introduced into a microfluidic channel. Microchannels are constructed within an elastomeric material, and channel surfaces are coated with receptors to the target. When a solution is flowed into the channel, the target cross-links multiple receptors on the surface, resulting in constriction of the first few millimeters of the channel and stopping of flow. Quantitation is performed by measuring the distance traveled by the target solution in the channel before flow stops. A key advantage of our approach is that quantitation is accomplished by simple visual inspection of the channel, without the need for complex detection instrumentation. We have tested these devices using the model system of biotin as a receptor and streptavidin as the target. We have also characterized three factors that influence flow distance: solution viscosity, device thickness, and channel height. We found that solution capillary flow distance scales with the negative logarithm of target concentration and have detected streptavidin concentrations as low as 1 ng/mL. Finally, we have identified and evaluated a plausible mechanism wherein time-dependent channel constriction in the first few millimeters leads to concentration-dependent flow distances. Their simplicity coupled with performance makes these "flow valve" systems especially attractive for a host of analysis applications.