A microfluidic device comprises a matrix of rotary flow reactors. The microfluidic matrix device offers a solution to the "world-to-chip" interface problem by accomplishing two important goals simultaneously: an economy of scale in reagent consumption is achieved, while simultaneously minimizing pipetting steps. N.sup.2 independent assays can be performed with only 2N+1 pipetting steps, using a single aliquot of enzyme amortized over all reactors. The chip reduces labor relative to conventional fluid handling techniques by using an order of magnitude less pipetting steps, and reduces cost by consuming two to three orders of magnitude less reagents per reaction. A PCR format has immediate applications in medical diagnosis and gene testing. Beyond PCR, the microfluidic matrix chip provides a universal and flexible platform for biological and chemical assays requiring parsimonious use of precious reagents and highly automated processing.