How much of a finite sample can a microchannel surface sensor capture? Optimal flow rate, universal capture map and closed-form design rules

Surface-capture immunoassays and biosensors in microchannels are usually analysed as if the sample never runs out. A diagnostic sample does: a few microlitres must be processed within a fixed assay time, and the detection limit is set by how many analyte molecules reach the capture surface. I modelled a capture patch on the floor of a rectangular channel through which a finite sample is pumped, using a steady marching solver and an independent two-dimensional transient solver with Langmuir kinetics. Both were validated against the Lévêque, Graetz and reaction-limited solutions and against each other to within 0.5%. The flow rate that maximises capture is the one that delivers the whole sample in exactly the available time, Q* = V/T, and transient simulations confirmed this in every case tested, including near saturation. At that flow rate the captured fraction depends on only two dimensionless groups and is bounded by a transport ceiling and a kinetic ceiling. The kinetic group contains neither channel height nor diffusivity. A closed-form combination of the two ceilings reproduces the numerical solution to within − 2.2% to + 1.4% over the whole design space. Recirculation helps only up to the kinetic ceiling. For a nominal point-of-care design, pumping ten times faster than Q* cut the captured fraction from 8.5% to 1.2% and raised the detection limit from 3.9 fM to 27.6 fM. Simple design rules follow, and the code is provided.