April 20, 2018 T: Tensile Fields (Since surface tension is mathematically like gravitational tension, what can we learn from that analog?)
A field is a model of our universe (or parts thereof) that tells us something about how energy/matter is distributed in a regular pattern. It tells us something about how equilibrium is maintained in any position (for example: gravitational field lines equidistant from the Earth’s surface tell us something about the speed required to maintain an orbit at any distance from the Earth.)
Put a rubber band between two fingers. Now stretch your fingers apart. Notice there is tension in the rubber band. Stress flows through the rubber between the two fingers. We call the pull on each bit of rubber and the force per length of the rubber, TENSION. The force of the tension between the two fingers can be found by fixing one finger to a given location and pulling outward with the other finger. This is a simple example of a tensile field. Notice that the rubber at the fixed end pulls the rubber towards itself, as does the force of gravity acting from a mass.
In the same way, in our experiment, the crest of a sine wave at the relationship boundary (interface) is forced outward, and it pulls against the sluggist trough. As this happens the curvature of the trough tightens (increases (1/radius-of-trough)) while the expanded crest goes to near zero curvature. As we stated before, seeking the least resistance, the fluid flow from the source does not expand the trough radially outward like it does the crest. The trough, that becomes tightly curved, looks as if it resists the outward flow (and so like the fixed finger in the rubber band, it doesn’t move much). But the crest boundary continues to pull against the trough creating a high tension field whose forces can be predicted using a formula almost the same as that of gravitation (Newton’s Gravitational Equation).
A COMPARISON OF NEWTON’S GRAVITATIONAL EQUATION and THE INTERFACIAL TENSION EQUATION (as they apply in normal space-time):
In the gravitational equation, forces are equal to mass 1 times mass 2, all divided by the distance (between the two masses) squared.
In the interfacial equation, tension is equal to surface tension (in air) of fluid 1 times surface tension (in air) of fluid 2, all divided by the distance (the force due to the tension on the boundary is related to the distance squared (as is the gravitational equation).
Along objects of very small dimensions surface tension balances out or exceeds gravitation (as in our experiment. The thickness of our expanding droplet is 1 mm, therefore the force of gravity over that height is negligible.)
As the troughs narrow on the relationship boundary, their curvature increases (the more curvature the greater the forces resisting information transfer (the pressure across the relationship boundary (F/area) are the curvature times the interfacial tension). But at the crest where the curvature is near zero, random perturbations transfer energy and information across the interface in the form of random perturbations (very small waves that fit on the remaining (nearly flat) interface. With a lowering curvature, the interface is open to information and energy transfer. Eventually, the surface tension goes almost to zero (meaning the two fluids that meet at the boundary can mix) and with a near zero curvature, forces are not enough to prevent molecular diffusion. This may be an analog of what happens in the quantum-controlled behavior of tiny particles in outer space (between large masses).
The differing boundaries at the troughs and crests suggest different characteristics and behaviors for these regions of our expanding droplet’s relationship boundary and out in space. So, not much hope can be held out for TOEs (theories of everything.)