Does the growing liquid bridge of drops coalescing in a Hele-Shaw cell feel the no-slip wall?*

When drops come into contact with each other, a liquid bridge is formed and grows rapidly during coalescence. When drop coalescence occurs in a narrow confinement such as Hele-Shaw cells filled with a viscous liquid, the temporal growth of the liquid bridge is expected to be affected by the no-slip surface of the cell through the ambient liquid moved by the bridge. To investigate the hypothesis, we captured the liquid bridge growth of corn syrup drops merging in mineral oil confined by the Hele-Shaw cell using high-speed video microscopy, and we measured the width of the liquid bridge using image processing. Then, we determined the bridge width value at which the bridge growth deviated from the scaling law for the initial phase of drop coalescence. It was observed that the determined bridge width values showed a sudden change as the viscosity ratio between the drop and surrounding liquid changed. A simple theoretical model was developed to explain the observed change and to show that the growing neck could feel the no-slip wall of the Hele-Shaw cell depending on the viscosity of the surrounding liquid.