Scientific and Technical Aerospace Reports Volume 39 April 6, 2001

’axial curvature pressure’. A time-dependent lubrication pressure is set up using a flow external to such an interface. Real-time
feedback control using this pressure, based on video images of the interface shape, suppresses the first mode of instability. In this
way, the subdominant mode is revealed for wavelengths between instability of the dominant (first) and subdominant (second)
modes. A quantitative comparison to weakly nonlinear stability predictions is favorable. Surface tension disconnects a bubble
from a capillary bridge while driving a surrounding inviscid flow. Spatial and temporal behavior is studied just prior to and just
after disconnection, via computation and experiment. They are in agreement both before and after the event but anticipated selfsimilarity
is observed only beforehand. Computation coincides with observation due to modeling that identifies the cascade of
physics probed over decades of length scales. To the extent that unconstrained disconnection or pinchoff of any surface will tend
to be axisymmetric, at least locally near the pinchoff location, constraints on curvature signatures for axisymmetric surfaces frame
the development of singularities in general surfaces. We show, based on differential geometry alone, that is, regardless of the
underlying fluid flow, be it viscous or inviscid, how the spatial distribution of curvatures are constrained as singularities in principal
curvatures develop. This framework is illustrated by a pinchoff via inviscid dynamics. A new approach to the computation
of bifurcation diagrams is illustrated on axisymmetric equilibria of liquid droplets and bridges. The new technique has an architecture
that solves boundary-value problems in parallel and delivers a global bifurcation diagram, capturing isolated branches. In
contrast, conventional techniques deliver solutions in sequence using local path-continuation. A suitable mathematical formulation
for the classical problem of predicting shapes of droplet and bridge equilibria is introduced and it is shown how the new technique
yields global diagrams. Properties of these diagrams allow families of equilibria to be organized in a way that reveals
common structures.
Author (revised)
Capillary Flow; Drops (Liquids); Interfacial Tension; Liquid-Liquid Interfaces; Shapes
20010024973 National Center for Microgravity Research on Fluids and Combusiton, Cleveland, OH USA
Instability of Miscible Interfaces
Balasubramaniam, R., National Center for Microgravity Research on Fluids and Combusiton, USA; Rashidnia, N., National Center
for Microgravity Research on Fluids and Combusiton, USA; Wilson, R. G., National Center for Microgravity Research on
Fluids and Combusiton, USA; Alexander, J. I. D., National Center for Microgravity Research on Fluids and Combusiton, USA;
Maxworthy, T., University of Southern California, USA; Proceedings of the Fifth Microgravity Fluid Physics and Transport Phenomena
Conference; December 2000, pp. 1325-1334; In English; See also 20010024890; No Copyright; Avail: CASI; A02, Hardcopy;
A10, Microfiche
The dynamics of miscible displacements in a cylindrical tube will be studied experimentally and numerically, specifically
when a more viscous fluid displaces a less viscous fluid. In the converse situation where a less viscous fluid displaces a more viscous
fluid, a fingering instability is known to occur, and a flight experiment proposed by Maxworthy and Meiburg to investigate
the interface dynamics in this case is currently being developed by NASA. From the current theory of miscible displacements,
developed for a porous medium satisfying Darcy’s law, it can be shown that in the absence of gravity the interface between the
fluid is displaced by a less viscous one. Therefore, the initial flat interface in the displacement of a less viscous fluid by a more
viscous one ought to be stable. However, numerical simulations by Chen and Meiburg for such displacement in a cylindrical tube
show that for a viscosity ratio equal to e, a finger of the more viscous fluid is indeed formed.These calculations were restricted
to axisymmetric solutions of the Stokes equations that are valid for negligible values of the Reynolds number. Preliminary experiments
that we have performed show that not only can fingering occur when the more viscous fluid displaces a less viscous one
in a cylindrical tube, but also that under certain conditions the advancing finger achieves a sinuous or snake-like spatial pattern.
These experiments were performed using silicone oils in a vertical pipette of small diameter. In the initial configuration, the more
viscous fluid rested on top of the less viscous one, and the interface was nominally flat. The top fluid also had a slightly larger
density than the lower fluid. A dye was added to the upper liquid for ease of observation of the interface between the fluids. The
tube diameter and the density and viscosity of the fluids were such that buoyancy induced flow was not observed. The flow was
initiated by draining the lower fluid from the bottom of the pipette. The draining velocity was in the range 10 to 50 microns per
second.When the viscosity ratio between the fluids is two, an axisymmetric finger of the more viscous fluid was observed to form.
When the viscosity ratio is ten, the steady state shape attained by the interface is not axisymmetric. Rather, the upper liquid has
a sinuous shape as it flows down the pipette. The density difference for this liquid pair is 0.01 g/cc. Since the upper fluid is heavier,
this raises a question whether the instability is due to buoyancy. to explore this, a small amount of carbon tetrachloride was added
to the lower fluid such that the lower fluid is slightly heavier than the upper fluid. The sinuous shape of the interface persists in
this case as well, suggesting that the instability might not be due to buoyancy, but is a shear instability. However, carbon tetrachloride
diffuses across the interface, and the results must be interpreted with caution. We plan to modify our apparatus so that the
more viscous fluid can be injected from either end of the tube. This will not only enable better control of the displacement
compared to the draining technique we have used, but also ascertain the role played by buoyancy forces in the experiments. Thus
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