The Dark Annulus of a Drop in a Hele-Shaw Cell Is Caused by the Refraction of Light through Its Meniscus

Abstract

Knowing the meniscus shape of confined drops is important for understanding how they make first contact and then coalesce. When imaged from the top view by brightfield microscopy, a liquid drop (e.g., corn syrup) confined in a Hele-Shaw cell, surrounded by immiscible liquid (e.g., mineral oil), had a dark annulus, and the width of the annulus decreased with increasing concentration of corn syrup. Since the difference in the annulus width was presumed to be related to the meniscus shape of the drops, three-dimensional images of the drops with different concentrations were obtained using confocal fluorescence microscopy, and their cross-sectional meniscus profile was determined by image processing. The meniscus of the drops remained circular despite varying concentration. Since the refractive index of corn syrup increased with concentration, while the surface tension coefficient between corn syrup and mineral oil remained unchanged, the observed change in the annulus width was then attributed to the refraction of light passing through the drop’s meniscus. As such, a ray optics model was developed, which predicted that the annulus width of the drop would decrease as the refractive index of the drop approached that of the surrounding liquid. Therefore, the dark annulus of the drops in the Hele-Shaw cell was caused by the refraction of light passing through the circular meniscus of the drop.