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How can we describe or model the spread of ice during the freezing of the surface of a still lake?
Premise: I live in a place where it is unquestionably wintertime in every aspect of the phrase. I was driving down the street and I drove by a lake. There was a recent and sudden temperature drop (from above freezing but still quite cold to well below freezing) overnight. The water had not yet frozen over.
It occurred to me while I was driving that the process of beginning the freezing process of the water at the interface of the water and the ambient air seemed to be counterintuitive. While I half (and admittedly naively) expected the ice to begin forming at the outside edges of the lake and continue to freeze inwards in a uniform fashion, the ice seemed to be beginning on one side of the lake only. I drove back by later on during the day, and the lack was nearly frozen over sans a bit of the side that was originally left unfrozen during my first observation.
The details are rather unimportant. I’m well aware of the fact that this was hardly a controlled environment, so the question remains to be how can we best describe or predict the nature of and changes within the interfaces of a substance and its surroundings during the a phase change of the substance? In particular, what’s prompting this question is the fact that there seemed to be a ‘preferred’ origin of the systematic spread of freezing. I’m curious as to why that might be and whether it is predictable. It could well just be dependent on the particular properties of the lake/general substance, but if so I’m curious as to what quantities influence these ready and obviously more rapid transitions.
My first intuition was that perhaps some parts of the lake are deeper and so there is a greater rate of heat transfer between the cold air/water interface and the volume of water below, resulting in that surface freezing more slowly in the long term. But, that doesn’t seem consistent with the fact that one of the edges of the lake remained entirely unfrozen until the end- most likely that edge was not a vertical drop and so would have fallen victim to earlier freezing as well. Presuming that the lake is a still body of water - are there any thoughts?

Variational wavefunctions and "spread" of potential in quantum mechanics
A particle in a box has an energy that decreases with the size of the box. In the general case, it is often said that a variational solution for a "narrow and deep" potential is higher in energy than a variational solution for a "wider and shallower" potential, by appealing to the particle in a box as a special case. The former wavefunction is said to be "more confined" in the former than the latter, and the act of being given more space to spread out is said to lower the energy variationally.
Question: are there rigorous mathematical statements of this argument?

The thickness of a non-spreadable liquid between two surfaces
There's this question I've come to when doing my research when working on polymer brushes; what I'm looking for is to find my reaction mixture thickness between two plates. So the setup is as follows: My bottom plate, with initiator on it. Then I put a drop of my reaction mixture on it which does not spread. Lastly, I put the top plate and the drop fills the gap between two plates and forms a film. I know how much the top plate weighs and the surface tension of drop and two plates, how can I calculate the film thickness between two plates? Here's my thought processes:
1.Should I look at the problem unsteady or steady? When thought of steady, I tried to equalize hydrodynamic pressure and weight of top plate but that did not match for the data of a paper working close to my work. They don't mention how they calculated their thickness.
2.Can I think of it simplistically? Like I know the volume of the drop that I put, I know the surface of the plate, then divide the volume by surface to get film thickness?

How does fire spread on a piece of paper?
If one lights the corner of a piece of paper with a match, the fire gradually spreads. What equation can be used to predict how the fire is going to spread spatially and temporally? At first, I thought thermodynamics would give answer to this question. But as far as I know, thermodynamics does not say anything about the dynamics of a system. So, how to tackle this question?

Does gas spread out equally everywhere?
"Gases can fill a container of any size or shape. It doesn't even matter how big the container is. The molecules still spread out to fill the whole space equally. That is one of their physical characteristics."
If a fixed quantity of gas is let out in a limited space, will it spread out equally and maintain a fixed gas distribution throughout the space?
Or, does it go where the gravitational pull is maximum? And what factors affect the distribution of gas in a given area?

Why does the wavefunction of a particle spread out after a measurement?
Quantum mechanics states that the wave packet of a particle "spreads-out" in position again after a measurement on this particle has been made. Is this spreading or "dispersion" caused by inherent properties of the wavefunction itself (eg according to the Uncertainty Principle), or is it due to the interaction with the environment (or both)? Does the wavefunction of a free, non-interacting particle also show this behaviour?

If an atom is put into motion will a constituent electron's wave spread over a LARGER region of space and will its energy be more dissipated?
My understanding is that a quantum event such as an electron moving between atomic levels takes place smoothly and continuously over a small discrete time interval during which time its energy will be relatively unstable.
Also an electron can spread out into a wave that extends over a region of space.
If an atom is put into motion will the electron's wave spread over a LARGER region of space than when stationary resulting in less energy per unit volume of space?

Why do electrons in a current spread apart, from their point of view?
There are many videos explaining how special relativity causes magnetism, with the most relevant part being that from the reference frame of the electrons, the positively charged ions in the wire have gotten closer together, and the negatively charged electrons have spread apart, a non-zero electric charge in a wire. We can determine that this must happen using the fact that in a lab reference frame, the wire is electrically neutral, and applying a Lorentz transformation to the electrons and ions. However, the electrons must see a different mechanism causing the space between them to increase. They need to see something pushing them apart. They don't know that the wire needs be electrically neutral in another reference frame. What's this mechanism that they see? Does it have anything to do with the period of time when they're accelerating?
I saw a bunch of questions that seemed similar to this one, but I didn't find any of the answers to be satisfactory. They all seemed to just explain how we know that the wire must be charged in different reference frames, using the Lorentz tranformation.

Why does the flame of a gas stove not spread backwards?
On lighting a gas stove the flame is active only above the burner. However, the gas input from beneath the burner and all the way to the pipeline contains gas fuel. Why doesn't it all ignite up ? I am guessing it may be due to the pressurised flow of the fuel in one direction but then I am unable to relate it to combustion, i.e., if a combustible substance is in contact of a source of ignition then it should start to burn.

If wave packets spread, why don't objects disappear?
If you have an electron moving in empty space, it will be represented by a wave packet. But packets can spread over time, that is, their width increases, with it's uncertainty in position increasing. Now, if I throw a basketball, why doesn't the basketball's packet spread as well? Wouldn't that cause its uncertainty in position to increase so much to the point it disappears?
EDIT: I realize I wasn't clear what I meant by disappear. Basically, suppose the wave packet is spread over the entire Solar System. Your field of vision covers only an extremely tiny part of the Solar System. Therefore, the probability that you will find the basketball that you threw in your field of vision is very small.