Wednesday, May 27, 2015

The First Harvest: How Rocks Are Like Bubbles.

[May 27, 2015]

It is said, where rocks are common, that the first crop of the farmer’s new year is the rock harvest. Stones, over the winter, have forced themselves to the surface, where they make plowing impossible. Why do they move at all? 

Rocks are like bubbles, in that they rise in the medium in which they are submerged, because, in both cases, there is more pressure from beneath than from above. The surprise is that rocks are more dense than the medium of their submergence, while bubbles are obviously less dense, so why do rocks rise instead of sink?

Large rocks, like large bubbles, experience a greater difference of forces from top to bottom than do small rocks or bubbles. The vertical span of a large rock or large bubble subtracts more from the vertical column above than that of a small rock or bubble, hence the column above, upon which the downward pressure is largely dependent, is proportionally shorter and less weighty, and therefore the upward forces on a rock or bubble are greater for a large one than for a small one, and we expect large rocks, like bubbles, to rise more quickly than small ones. 

I have seen exhibits in which large and small bubbles were released into fluids differing in their viscosities, and whether the fluid is thick or thin, whether the average speed of the bubbles was quick or slow, the largest of the bubbles rose fastest, and the smallest bubbles rose slowest. This remains true until the bubble achieves a size at which it tends to break up. 

This may seem counter-intuitive: ought not a small object make its way through its field of obstacles more readily? But actually we are familiar with other versions of this thought experiment: Drop a stone from shoulder height and it falls straight away. Drop a fistful of finely pulverized soil, and much of it will float down or just blow away. But put a fistful of dirt in a screen and the smallest particles will get through, while not the large ones. The passage of rocks and bubbles through the medium in which they are submerged is not a screening process, it is one dependent on the behavior of fluids. And the soil which surrounds a rock, like the liquid which surrounds a bubble, behaves like a fluid in some ways, and a fluid will flow around the bubble easily enough, but more quickly where the pressure differences are larger, such as for a larger bubble, and we expect that soil will allow a large rock to rise through it from below more quickly than it will allow small stones to rise. 

But there remains a puzzle. How is it that a rock, which should be more dense than its surrounding medium, should rise through that medium? Ice, which is a water-rock, floats in water because it is less dense than liquid water, which means that the water it displaces weighs more than the water that is bound up in the ice. Perhaps it is too obvious to point out that a rock will sink in water, but what if we made the ice block just a bit heavier, and not much heavier, than the water it displaces, by putting a modestly sized rock in it before we freeze it? This block of ice would most certainly sink. 

In the same way, why doesn’t a rock sink in the soil in which it rests? Indeed why do I think the rock is more dense than the soil? 

Soils are generally made up of the pulverized bits of the bedrock on which they lay, plus some organic matter, water and air. Some soils (clays) are also made from hydrated versions of the bedrock (feldspar). Since organic matter, water and air are all automatically less dense than the rock, we only need to prove that the soil particles born from the original bedrock are themselves less dense than the rock. 

We do this by imagining the hypothetical situation in which  a rock is fractured into the thousands or millions of small, soil-particle size fragments which make up the soil, but are held together in their original positions, so there is no space between them. This mass of rock particles may be as dense as the intact rock only for as long as it is undisturbed. As soon as the rock particles begin to lose this most improbable of all arrangements, other, lighter substances are introduced into the spaces between the particles, the likes of air, water and organic matter. So no arrangement of the particles can be more dense or equally dense, as the original intact rock, which must be more dense than the medium in which it is found. This would be true except, for example, in the atypical case that a rock made of a lighter material, such as limestone, is imported to a field (by glaciation, for example) where the soil lays on a heavier bedrock and by rights could be more dense than the rock in question. However this rock does not present a mystery, as we would expect a rock which is lighter than it’s medium to rise. Still, we want to understand how the heavier rock, nevertheless, would rise in the bed of soil, until it emerges and becomes a nuisance to the farmer. 

In the language of fluid behavior, where bubbles live, the object which is more dense than the fluid will sink, and the object which is less dense will rise. So in the language of fluid behavior, the dense rock rising is anomalous. But of course soil is not a fluid. Some of its behavior is fluid like, and indeed rocks do rise over time through soil. There is “flow” of the substrate around the rock, leaving the zone above the rock and filling in beneath the rock.  The answer to our riddle, I believe, is here, in the difference between the behavior of solids and of fluids. 

The argument is made that frost is responsible. In this scenario, water beneath a stone freezes, and as it does it forms crystals which exert thrust. The thrust will most likely be directed downward, since sideways thrust will be resisted by the ice forming in lateral zones. Hence the rock above might be lifted. 

But let’s consider the possibilities. Because freezing begins at the surface of the ground, the zone above the stone always freezes before the zone below the stone. Only the stone which has already crested will be completely free to rise when the thrust is exerted. The stone which is below the surface must lift entirely the mass of frozen earth above. If the stone is deep enough in the ground, the zone beneath the stone may never freeze, even if the freeze does reach the top. If freezing were the only mechanism, rocks would never lift away from the bedrock from which they are cleaved. 

The freeze-thaw cycle and the thrust forces it induces may indeed play a role in the migration of rocks to the surface of the soil in which they are. But then, why wouldn’t the rock simply fall back to where it had been before the freezing started? Another process is operating. Herein we observe the difference between fluid and solid behavior. 

Whether wet or dry, freezing and thawing or just unfrozen, soil is made up of particles. When they are loose and not locked by friction into a rigid formation, they will move. Reasons to move include freezing, being washed, pressure from one side not balanced at the other, and vibration, with influence from gravity. Generally at depth soils will be packed, but they can still respond to these influences. 

First there is the rock at depth, below the frost line. For this rock, movement depends entirely on vibration. A vibration passing through the soil momentarily and microscopically lifts the rock, and soil particles fall into the space left open, in the manner of fluid particles. But when the vibration forces the rock down upon the soil particles beneath it, the force does not cause the particle to move away from its position beneath the rock; its behavior has become that of a solid. Hence over time and many cycles of vibration, soil migrates under the stone. The solid does not need to be more dense than the object it supports to support it. Once the soil particles are forced beneath the rock, they will stay there, gradually exerting upward force which is not resisted by any equal down ward force. As the rock gradually migrates up through the soil, the soil above remains less packed, may even grow looser, as the pressures from below cause the soil to crown. As the soils below fill in beneath the rock, the particles on the side fall down to fill in behind the soil particles going under the stone, and the particles from above fill in around the stone. Thus the behavior of the soil particles, when the vibration lifts the stone, is fluid-like, but the behavior of the soil particles when the vibration packs down on them is solid-like. The solid-like behavior prevents the rock from moving down, while the fluid-like behavior allows it to move up. Hence they take a one-way journey from below to above the surface. 

From here the action of frost is to accelerate the process of emergence. When ice crystals do form, and melt, they create spaces for particles to fall into. If the process of crystal formation moves the stone, this will leave additional space for soil particles to migrate into. 

Washing of particles may in fact undermine a rock and cause it to subside. Washing is likely to participate in the lifting of a rock on the scale of an individual particle, if just enough water is present to lubricate the passage of the particle, or impel it more expeditiously, to occupy the spaces created by crystals and vibrations. 

The effect of pressure from one side is like the effect of the rock rising through the soil. It has only one direction in which to go. A soil particle poised beside a cavity beneath a rock will, when the some random vibration passes through the soil, fall in the direction of the cavity, and not the other way. That is the one thing it can do. 

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