Pendant Drops and Liquid Jets in Miscible Environments

The spreading of liquids is a classical problem in interfacial fluid mechanics and, historically, the examination has been limited to immiscible systems. We have reported previously on our studies and observations of the spreading of sessile drops in miscible environments, which have distinctly different shape evolution and power law dynamics from sessile drops that spread in immiscible environments. We have extended this work to include the shape evolution of pendant drops and liquid jets existing in a miscible environment. By examining pendant drops and liquid jets, the need to account for surface energies arising from a solid-fluid interface, as in the sessile drop problem, is eliminated.

As time evolves, diffusion across the miscible liquid-liquid boundary proceeds due to the chemical potential difference between the two initially distinct, homogeneous phases. Diffusion, in turn, imparts a time-dependence to the properties of the liquids in the diffusive region – notably the density, viscosity, and interfacial tension – that influence the shape evolution. It was found for sessile drops in a miscible environment that gravitational forces dominate the spreading process, and is expected for pendant drops and liquid jets as well.

A series of liquid pairs have been studied (corn syrup-water, glycerol-water, glycerol-ethanol, tricresyl phosphate-ethanol). Various volumes of droplets, and diameters and flow rates of liquid jets have been considered.

Figure 1: Image sequence taken in time of a corn syrup pendant drop immersed in water. A strand emanates from the apex of the drop and continues to flow as the entire drop descends and elongates.

Particle tracking velocimetry has been performed to identify the internal flow pattern of the pendant drops and liquid jets.

Figure 2: Image from a particle tracking velocimetry experiment of a corn syrup pendant drop immersed in water. The corn syrup contains 6 μm microspheres at a concentration of 10-3 g/ml, which scatter incident light. The arrows indicate velocity vectors obtained from particle movement. Motion was largely restricted to the corn syrup-water interface. Particles within the pendant drop and away from the liquid-liquid interface move with the drop as it descends and elongates; within the reference frame of the drop, these interior particles do not move significantly.