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.

A Review on the Coalescence of Confined Drops with a Focus on Scaling Laws for the Growth of the Liquid Bridge

“…It needs to be pointed out that in the studies summarized in this section, drops did not make a direct contact with the wall of Hele-Shaw cells. Instead, a thin layer of the outer liquid existed between the drop and the wall [8]. Thus, these studies belong to the two-phase coalescence with two confining surfaces category and involved neither contact line dynamics nor surface wettability.…”

“…Drop coalescence is captured using high-speed videography due to the extremely fast occurrence of the event, and then d is measured from the captured images [1]. For example, the inset of Figure 1 shows two corn syrup drops coalescing in mineral oil confined in a Hele-Shaw cell with a depth of D = 1 mm [6][7][8]. The coalescence process was imaged at a frame rate of 49,000 fps (∆t ≈ 0.02 ms).…”

“…Micromachines 2023, 14, 2046 2 of 22 confined in a Hele-Shaw cell with a depth of D = 1 mm [6][7][8]. The coalescence process was imaged at a frame rate of 49,000 fps (Δt ≈ 0.02 ms).…”

“…In addition, the existence and motion of a three-phase contact line can complicate the coalescence phenomenon [19]. [6][7][8]. This case belongs to the two-phase drop coalescence with two confining surfaces category shown in Figure 2.…”

“…In contrast to the first subcategory, the Hele-Shaw cell provides an advantage that drops and their liquid bridge are symmetrical with respect to the midplane of the cell. When a Hele-Shaw cell is filled with a liquid and drops of an immiscible liquid are formed and coalesce in the outer liquid, drops do not make direct contact with the confining surface due to the existence of a thin layer of the outer liquid between the drop and the surface [8,23]. Thus, drop coalescence involves only two phases despite the solids surface (i.e., two-phase coalescence), and the surface wettability of the surface does not matter.…”