Ring formation in nanoliter cups: Quantitative measurements of flow in micromachined wells

Drying of DNA spots on microarrays and spilled coffee yields ringlike stains, because the outward flow transports dissolved particles to the border. Contact line pinning and diffusion limited evaporation of a liquid sample are the two necessary conditions to induce an outward directed liquid flow during evaporation. In this paper we present quantitative measurements of this flow field visualized by microspheres which are injected into a liquid sample in circular wells with a radius of $100–150\mu \mathrm{m}$ and a depth of $6\mu \mathrm{m}.$ The motion, including Brownian motion, of these microspheres with a radius of $0.25\mu \mathrm{m}$ is recorded using digital fluorescence microscopy. Our analysis, using optic flow, does not require object identification, nor tracking of the individual objects. The spatiotemporal measurement space is sparsely filled at only those space/time positions where a microsphere is present. A confidence measure is computed indicating the presence of microspheres in this measurement space. The circular well shape allows us to transform the sparse measurement space into a denser, averaged radial velocity field. In this transformation we “interpolate” the radial velocity between values with a high confidence, which results in quantitative measurements of this outward flow field during the complete time interval of the evaporation process and at all radial positions in the circular wells. This allows for a quantitative validation of the elegant theory of ring formation.