Multilayer Nano-Particle Image Velocimetry in Microscale Poiseuille Flows

Nano-particle image velocimetry (nPIV) uses evanescent waves generated by total internal reflection at a glass-water interface to illuminate fluorescent colloidal tracers and measure the two velocity components parallel to the wall. For blue light at 488 nm, the exponential decay in the intensity of the illumination with distance normal to the wall z ensures that only about the first 300 nm next to the wall are imaged. The exponential decay also suggests that illuminated tracers in nPIV that are closer to the wall have images that are brighter than those farther from the wall. This variation in tracer intensity is exploited in the “multilayer nPIV” technique, which determines a velocity “profile” at a few different z-locations within the region illuminated by the evanescent wave—and hence velocity gradients within several hundred nanometers of the wall. The feasibility of this technique has already been demonstrated using artificial images of plane Couette flow [1]. We describe here the application of multilayer nPIV to experimental images of incompressible Poiseuille flow through rectangular microchannels with cross-sectional dimensions of 40 μm × 312 μm. In all cases, the flow Reynolds number is O(1) or less, and the velocity profile over the first 400 nm next to the wall is essentially linear. Calibration experiments that incorporate the effects of tracer polydispersity are used to determine the intensity of the tracers at a given distance from the wall. These calibration data are then used to classify and divide the tracers in a given nPIV image into three different layers. The results show that velocities are overestimated in the layer nearest the wall, most likely because of the asymmetry of the Brownian diffusion in this region. The results also show that velocities are underestimated in the layer farthest from the wall because of the nonuniform illumination inherent to evanescent wave-based velocimetry. The extent of this effect is estimated using artificial images. This estimate is then used to correct the experimental result. The mnPIV results in the two layers farther away from the wall are in good agreement with the classic analytical solution for two-dimensional fully-developed laminar Poiseuille flow after this correction, giving a velocity gradient within 7% of the expected value.