Monthly Archives: August 2013

High Curvature “Relationship”

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A high curvature relationship occurs at the beginning and the end of our two-fluid experiment.

A tiny bubble has such a high curvature/small radius that it is difficult for random vibrations to deform it.
As the water-based fluid flows into the oil-based fluid, into the crests (fingers) of the unstable waves at the boundary, their tip radii get very small and their curvature very large, thus damping out vibrations there.

In both cases (beginning and end), the curvature at the boundary of the two-fluid system is so large that the boundary cannot be made to deform. In this case, there exists no relationship across the boundary. Therefore, no recognizable existence there.

Four Basic Kinds of Relationship

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In our two-fluid experiment, where a water-based fluid tries to push an oil-based fluid out of the way across a boundary, we can describe four basic relationships. The first three relationships require a certain amount of interfacial tension at the boundary to carry interactive information from one fluid to another. The fourth and last relationship has little or no tension on the boundary. Molecular diffusion occurs and therefore we call it a degraded relationship, where, because of the static at the boundary, little information gets through. [continued]

Primitive Relationships

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The experiments Suresh Advani (University of Delaware) and I performed were classified as two-fluid problems. In such problems there are two thermodynamic systems (fluid 1 and fluid 2) that relate to one another across a boundary between the two fluids.

Thermodynamics (thermo) is a well-organized and descriptive language scientists use to examine what happens when two systems (objects in specified spaces) come together. The language of thermo specifies what is exchanged across boundaries when two or more systems interact or relate.

In our two-fluid experiments, an expanding circular droplet of a less-dense, water-based fluid is pushing a more-dense, viscous oil out of the way. This relationship is considered unstable, because the water flows easier than the sluggish oil. Because the oil cannot move fast enough out of the water’s way, the boundary between the two fluids buckles (adopts a wavy pattern like a sine wave).

At the trough of the wave, the watery fluid sees a concave-upward boundary. The oily substance sees a concave-downward one. So, not only are the fluids flowing against one another, exchanging the momentum of movement at their boundaries, but they see this exchange in starkly different ways. Each with its own perspective or point of view (POV).

For this example, then, we see that primitive relationship does not just involve the energy exchanged across a boundary between relating systems, but, also, the unique perspectives of each.