(518j) The Shape Evolution of 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 in a recent manuscript accepted at JFM 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; in the case
of a sessile drop in a miscible environment, free convection occurs in tandem
with spreading along the solid substrate.

A series of liquid pairs (corn
syrup-water, glycerol-water, glycerol-ethanol, tricresyl
phosphate-ethanol, silicone oil-silicone oil) and volumes of droplets have been
studied. In addition to experiments, numerical simulations
have been performed by solving the convection-diffusion and Stokes equations in
tandem, which quantitatively match observations of the experiments. This
presentation will convey the sessile and pendant drop work together, spanning
the experimental, theoretical, and numerical work. We have also conducted
preliminary experiments using rising droplets in miscible environments to
understand the dominant physical mechanisms at play.

Figure 1: (a) Bottom view and
(b) side view of a miscible sessile drop of corn syrup immersed in water,
spreading on a glass surface. Arrows indicate leading
edge radius (black) and contact line (white). (c) Particle tracking velocimetry image of a sessile drop of corn syrup
containing 6um particles immersed in water. Arrows indicate particle motion.
(d) Confocal microscopy image of a frustum of a sessile drop of corn syrup, at
its base, spreading on glass while immersed in water. Particles are in the corn
syrup phase that fluoresce and demonstrate the elevated quality of the leading
edge as it spreads radially outward.

Figure 2: Image sequence taken
in time of a corn syrup pendant drop immersed in water, as (a) physical experiment
and (b) numerical simulation. A strand emanates from the apex of the drop and
continues to flow as the entire drop descends and elongates.