This invention provides a method and apparatus for detecting the presence of analyte particles in a sample fluid also comprising larger particles, particularly blood. It exploits diffusion to provide simultaneous filtering of the larger particles and reaction of the analyte particles. A sample stream and a reagent stream join on the upstream end of a laminar flow reaction channel and flow in adjacent laminar streams. The reagents can be in solution or immobilized on a bead. The analyte particles diffuse from the sample stream into the reagent stream, leaving behind the larger particles in the residual sample stream. In the reagent stream the analyte particles react with reagent particles and form product particles, thereby creating a product stream. At the downstream end of the reaction channel, the residual sample stream and the product stream are divided. The product particles are then detected, preferably optically, in the product stream. Prior to detection, the product stream can undergo further filtering or separation, or can join a second reagent stream to form secondary product particles. This apparatus and method can be used to implement competitive immunoassays or sandwich immunoassays using enzymatically or fluorescently labeled immunoreagents. The apparatus and method can also be used to synthesize products, in which case two reagent streams join in the laminar flow reaction channel.