The invention provides methods and devices for detecting the presence of one or more target analytes in a sample employing a channel having affixed therein one or more binding partners for each target analyte. Assays are carried out by transporting the sample through the channel to each successive binding partner so that target analyte present in said sample binds to the corresponding binding partner. The sample is then transported beyond the binding partner(s), followed by detection of any target analyte bound to each binding partner. In one embodiment, binding efficiency is increased by the use of segmented transport, wherein a first bolus or bubble of a fluid that is immiscible with the sample precedes the sample during transport and a second bolus or bubble of a fluid that is immiscible with the sample follows the sample. Many configurations are possible for the device of the invention. A preferred device includes: a substrate with a channel formed in its surface, and a cover element that overlies and seals the channel. Binding partner(s) are affixed to the surface of the cover element facing the channel lumen.