(444a) The Shape Evolution of Pendant Droplets 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 experimental 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 experimental work to include the shape evolution of
pendant drops existing in a miscible environment. By examining pendant drops,
the need to account for surface energies arising from a solid-fluid interface,
as in the case of a sessile drop, is eliminated. We have complemented these
experimental studies with a theoretical scaling analysis as well as numerical
simulation.

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 these
droplets in miscible environments that gravitational forces dominate the shape
evolution process. The presence of diffusion sets up a fluid flow of free
convection in the case of a pendant drop in a miscible environment.

A series of liquid pairs (corn
syrup-water, silicone oil-silicone oil) and volumes of droplets have been
studied in the experimental study for pendant droplets. Solving the
convection-diffusion and Stokes equations numerically and in tandem has been
used to simulate these systems, which quantitatively match observations of the
experiments. This talk will present our pendant drop analyses, spanning the
experimental, theoretical, and numerical work.

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.

Figure 2: Numerical simulation of a pendant drop in a miscible environment
evolving in time.

Figure 3: Volume of pendant
drops of corn syrup in water. Volume scaled by maximum volume; time scaled by
radius of pendant drop at maximum volume squared divided by diffusion
coefficient. Symbols are experimental results. Solid lines are numerical
results.