Scientifically explain how you can do raindrops that should not exist mathematically

Rain grain falling from the sky is actually impossible existence mathematically, and it seems that it is impossible for rain to fall on the ground originally. When it comes to scientific consideration why it is impossible for raindrops to exist mathematically, why is there actually raindrops?

Why Raindrops Are Mathematically Impossible - YouTube


There are many physical phenomena related to raindrops. For example, "condensation" where water molecules gather ... ...


"Viscosity" or ...


"Air resistance" etc.


Strictly speaking, raindrops, which are falling water, are shaped like jellyfish by air resistance and are not like the illustration on the right.


Consider mathematically and physically how to make raindrops.


Generally it is easy to make raindrops, it is easy to start making raindrops at first, as water temperature goes down, water vapor becomes liquid water, then that water gathers and becomes water drops.


However, the phenomenon "water gathers and becomes water drops" actually can not happen mathematically.


Water has the property of trying to reduce the surface area, and has the property that water molecules gather in a spherical shape without stretching each other and spreading.


Thanks to this, small water droplets are spherical ... ...


Drops of water fall on small coins.


To put it in more detail, water absorbs energy when "increasing the surface area", and releases energy when "increasing the volume".


If the waterdrop has sufficient size, the amount of energy released by volume increase will be sufficiently larger than the energy absorbed by increasing the surface area. This is related to the fact that the volume is proportional to the cube of the radius and the surface area is proportional to the square of the radius. In other words, volume is easy to increase.


This is the state of energy (10 3 cubic) obtained by increasing the volume> state of losing energy (10 squared) by increasing the surface area.


However, as the water droplet becomes smaller, the talk is different, and it is completely opposite state of 0.1 cube <0.1 squared.


In other words, it is more convenient to increase the surface area by splitting the water droplet smaller than to increase the volume with a certain size as the boundary.


There is a contradictory world where water droplets tend to be smaller and those which are more likely to be larger, with a certain size as the border.


When drawing a graph of y = x² - x³, it has a local maximum at x = 2/3.


This maximum value is "a certain size", and smaller waterdrops are easier to get smaller than this.


Mathematically, in a range smaller than 1, it is natural to say that the square graph always becomes larger than the cube power graph. In other words, it means that very small water molecules do not gather and become large water droplets.


However, it actually rains.


It is extremely rare for five water molecules to become 10 water molecules, and the probability that this will be 50, and the "size" of several million is unlimitedly equal to zero, that is impossible .


But, if you want to know why it will rain, you can see the movie 'Rain's Dirty Little Secret'.


So the following movie is the answer.

Rain's Dirty Little Secret - YouTube


Mathematically no raindrops fall on the earth.


This is because "small" water molecules that hover in the air do not gather naturally and become water drops.


However, water molecules have characteristics that are very easy to associate with each other.


That is why water has this shape.


Water molecules in the air may cling to clumps ... ...


Unity is cut off by adding heat (energy), and it may become separated.


The water molecules in the air become water drops at the temperature called "Dew Point" (dew point).


However, this is a story that is applicable when many water molecules gather and become a huge mass.


In the case of a small water molecule block, because the curve is steep, the number of intermediate water molecules in the vicinity of water molecules is small and the cohesion is weak ......


When energy is applied, the bond is broken and water molecules often jump out.


In other words, the water molecules jumping out are larger than the added water molecules, the mass of water molecules will not be larger but rather smaller.


With "a certain size" that was also found in the previous movie, the water molecules take two states, which are more likely to be smaller and more likely to be larger.


What is this "certain size", a mass of 150 million water molecules.


In probability theory there is also a mass of water molecules that gets together and grows. However, for example, if there are millions of 5 water molecules in the size range of a golf ball, there is only one little that can grow into 10 masses of water molecules.


In addition, in the case of a mass of 50 water molecules, there is only one in the range of 16 million kilometers in diameter.


It is impossible for a few hundred million years to wait for a "certain size" of 1.5 million water molecules to birth naturally by passing through the probability equal to zero as much as possible.


However, there are small foreign dust like small dust in the air. And some of them are ants of "some size".


If water molecules coincide with this little dust dust ......


It is no wonder that a mass of water exceeding "a certain size" appeared in the air ... ...


Because it is bigger than a certain size, water collects and it gets even bigger.


And, the lump of water molecules that grew larger ......


We gathered as clouds ......


It will rain.


In other words, water drops were born on the earth, it started to rain, and life was brought up thanks to small garbage that catches the air.