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 scale-invariant features. This scale invariance, or self-similarity, appears at eddy sizes that are relatively small. Of special interest in this laboratory is two-dimensional (2D) turbulence, such as one sees in a rapidly flowing soap film, into which a comb (one-dimensional grid) has been inserted. This system owes its two-dimensionality 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 phase-separating systems under external stress.