Dimensional crossover in the coalescence dynamics of viscous drops confined in between two plates

Abstract

Coalescence of liquid drops is a daily phenomenon familiar to everybody and is related to many fields from biology to astronomy and also related to a variety of practical problems in industry. However, the detailed physical understanding of the dynamics has been revealed only recently with the aid of high-speed camera, high-performance computer, and scaling analysis. In this study, coalescence of a viscous drop to a bath of the same liquid is studied in a confined space. This is because dealing with a small amount of liquid drops becomes increasingly important (e.g., in industrial and biological applications). Here, the aqueous drop and bath are surrounded by low-viscosity oil and sandwiched by two parallel plates of the cell. We quantify experimentally the width of a neck that bridges the drop and the bath during coalescence. As a result, we find that the neck width increases linearly with time at short times, but the dynamics slows down significantly at longer times. Thanks to simple and original scaling arguments, we clearly show that this transition of the dynamics with time in a single coalescence event is brought about by a crossover from a three-dimensional viscous dynamics for a spherical drop to a quasi two-dimensional one for a disk drop. In addition, we report an unusual type of coalescence that is possibly caused by naturally accumulated electric charge in the confined geometry and whose dynamics seems self-similar.