(234p) Shape Evolution and Spreading of Liquid 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; 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. 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 poster will present the sessile and
pendant drop work together, spanning the experimental, theoretical, and
numerical work.

Figure 1: Side view of a
miscible sessile drop of corn syrup immersed in water.

Figure 2: 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 3: Numerical simulation of a pendant drop in a miscible environment
evolving in time.