
Dr. Walter Goldburg
Professor Emeritus
University of Pittsburgh
Pittsburgh, PA
Fluid Mechanics in Two and Three Dimensions
For over a hundred years, scientists have struggled to
understand turbulence in fluids. The physicist's goal is to identify
its scaleinvariant features. This scale invariance, or
selfsimilarity, appears at eddy sizes that are relatively small. Of
special interest in this laboratory is twodimensional (2D) turbulence,
such as one sees in a rapidly flowing soap film, into
which a comb (onedimensional grid) has been inserted.
This system owes its twodimensionality to the fact that it
is only a few microns thick.
The turbulence produces thickness variations, which are observable
in monochromatic light as seen in the figure to the right. The film is
flowing downward at a mean speed of several m/sec. To the left is a von
Karman vortex street generated by a cylinder of small diameter that
replaces the comb. Even in this
laminar case, the interaction of these vortices pose a problem which
cannot be solved analytically.
Many tools are brought to bear to probe the velocity
fluctuations in our films, including laser Doppler velocimetery,
dynamic light scattering, particle imaging velocimetry, and other
schemes devised in this laboratory. Our emphasis is on finding new ways
of probing turbulence in both 2D and 3D, and in asking questions of the
turbulence that are often not asked by the engineering community. By
studying flow in both soap films and liquid crystal films, we can also
study the nature of diffusion in two dimensions and the anomalous
viscous properties that these films exhibit. Thus the research
encompasses both fluid dynamics and condensed matter physics.
Dynamics of Phase Separation
Though equilibrium critical phonomena are now quite well
understood, the dynamics of phase separation is still an active area of
research. Our most recent work has centered on the influence of shear
on a fluid mixture near the threshold of nucleation. Shear will rupture
all droplets exceeding a certain size, and this maximum size diminishes
with increasing shear strength. In a supercooled fluid or mixture, no
droplets can exist with a radius less than a certain size. This
phenomenon invites the question, ``What happens when the shear is so
large that the largest possible droplet has a radius just equal to the
critical radius?'' Will all droplets abruptly disappear if the shear is
increased just beyond this point? Or is the phenomenon more complicated
than this? Light scattering experiments in this laboratory have been
aimed at asking questions of this type about phaseseparating systems
under external stress.
