Science from An Old Bucket of Water

Trees’s growth  ignore the slope. Picture Source:

If you climb a hill, you will notice that the trees are not perpendicular to the slope. With some variations due to wind, tree trunks generally meet the horizon at a right angle. Similarly, if you are collecting rain water with an old bucket on a slanted driveway, you will notice that the water level is not parallel to the asphalt. More water leans against the walls of the bucket facing downslope.


If you wait for more rain to fall into the bucket it will look like the second illustration. Wait longer and liquid water will not reach point C.  Instead it will overflow at point A. The bucket never fills with liquid.

All this is a reminder that gravity neither acts from the surface just below trees, nor from the surface below the driveway. It acts from the center of the Earth. We know from geometry that any radius is perpendicular to a line tangent to the circle. The horizon is equivalent to a tangent line, hence the reason for the alignment of trees and for the fact that points A and B in the bucket are at the same height above the horizon. (see green arrows in the diagram) It’s at those positions that they have the same potential energy, the product of weight and distance from the plane’s center.

If you leave the bucket out in late autumn, you will be in for a more pleasant surprise. After I knocked the bucket down, here’s what slid out along with the water that had not yet frozen.

Two views of the same hollow cylinder of ice from a bucket. My keys are at the base for a sense of scale.

The ice is in the form of a hollow cylinder, one that eventually would have filled the whole bucket. The sight is a little deceiving. Unfrozen water is not the only thing missing from the picture. On its way out, the unfrozen water broke through a thin layer of surface-ice, which formed first because it’s the only part of the water that was directly in contact with the cold air. But why was the core of the liquid left unfrozen? The inner plastic walls not only cooled off faster than the subsurface water due to the lower specific heat of plastic, but the impurities and imperfections on its surface also provided nucleation sites for ice crystals to form. Even at the very beginning, one observes a crescent of thin ice on the colder surface, not coincidentally resting on the side of the bucket with more plastic exposed.

If we had waited long enough, why would the entire bucket have been filled with ice, something liquid water is incapable of doing when the bucket is sitting on a slope? On average, in liquid water, each molecule is hydrogen-bonded to about 3.4 neighboring molecules that constantly break and reform. But in ice each each molecule is hydrogen-bonded to 4 other molecules in a more stable fashion. This spreads out the H2O molecules in the ice structure, lowering its density. It’s the reason ice expands as it freezes into a hexagonal network, one that’s 3 kJ/mole stronger than that of a non-supercooled liquid network. It’s also the reason ice can’t flow like liquid water.

Text and image modified from a combo of AP Biology and diagrams.

So after the ice starts to form on top and then along the internal walls of the bucket, the frozen base and the circular rim begin to thicken. The rest of the forming crystals grow until they reach the middle of the bucket. With molecules that are more tightly bound, the ice at point A cannot flow out of the bucket as it did when it was in a liquid state. But the air space in the bucket above the slant will be occupied as the ice from the freezing core expands and pushes upwards. The bucket, as a result, even though on a slant, gets completely filled with ice, which also expands against the bottom, deforming the plastic base.

If you slide the ice back into the bucket and wait for a warm day to melt it, water will reveal its intrinsic color. Most glass containers aren’t large enough for water to absorb enough red light to reveal a perceptible hue of greenish blue. Too often we get the false impression that water is transparent. But the white walls of the bucket will provide enough internal reflection to increase the path length, and water’s color becomes noticeable. I’ve ventured a little deeper into that idea in this blog entry. If you’re not interested, hopefully I’ve nevertheless shown that there are some side-benefits to saving water and energy while collecting rain.


The Joys of Walking Across An Icy Field

Education has met its goals, not necessarily when it has landed you a dream job—which I think is an illusion for the vast majority of people who have slaved in the past and who are working now— but when it can intensify the sensual and intellectual pleasures of the simplest acts of life—like walking to work.

Same field as being described but from another day.

Weather-wise, we have had an erratic month of February in Montreal, with more than the usual cycles of freezing and melting. One day, after a morning of snow and an afternoon of freezing rain, the snowscape was glazed with a thick, milky ice, thick enough to support the weight of a toddler. It was cold for a few days afterwards, but subsequent rain transformed the veneer. I was reminded that with every subzero drop, the forms of snow and ice, like the size of all crystals, depend on how quickly the temperature drops and on the impurities and imperfections that seed them. During my 2 km-walk that morning, I experienced different textures and densities.  This is because sources of dust, pools of water,  their depth and amount of surface exposed to air are all variable and not every spot is equally affected by wind and footsteps.

Over two thousand five hundred footsteps that gave me an uplifting return on by body’s investment in adenosine triphosphate, ATP. (For the uninitiated, ATP is not a drug.  It is the currency of cells, the facilitator for all of our energy-requiring reactions. It’s what chloroplasts produce when photosynthesizing before creating glucose, and it is what our cells create when oxygen breaks down the metabolites of that same sugar. )

As I felt the unmonotonous sequence of pressures around my boots, each different area that I walked on created a unique sound  Since childhood, my favourite sound of that type is that of thin ice shattering above an air pocket. I was also reminded that the frictional coefficient of naturally-formed ice varies significantly. That morning no one else braved the -22 oC windchill factor. So with no one watching, I was a free 54-year old, giving myself a little run and testing to see how far I’d glide on various sections of the ice field.

The way light interacted with all the surfaces also accentuated their differences. There were sparkles from icy particles acting as tiny prisms; there were lakes of yellow-orange as the rising sun caught expanses of smooth surfaces; and other parts of the frozen field glistened with different hues. Every hue corresponded to a different frequency, suggesting a unique interaction of matter with light energy.

103_9405Another benefit of immersing myself into the walk was that it lifted the weight of the thoughts about the oncoming day. It also dissipated any of the usual worries that the condensation of water in my breath was beginning to accumulate and cool my neck-warmer. If anything, the journey was far too short. I was tempted to turn 180 degrees and repeat the walk with even more attention to detail…Oh but, wait, I said to myself. The fact that I did not indulge in an extended trek was not a wasted opportunity. After all, there was the journey home that afternoon.

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