1. Optical Phenomena
It all started with a question “why wet spots look dark?”.
Apparently wet spots look darker if viewed from the same side as that of the light source, however if we observe light passing through same spot from the other side, it looks brighter instead.
So the word “dark” is not a very accurate word to describe how a wet spot looks like after all–Here is better description, a wet spot looks more transparent than a dry spot. Here are some possible explanations:
- Fibers sticking together
When the paper/cloth gets wet, the water only gets into the fibers, it does not stay in the gaps between fibers. Then, because of the surface tension of water, the fibers tend to stick together, leaving bigger gaps between fibers and letting more light to pass.
- Light’s wavelength is shorter in water
Assuming that the fibers are opaque, light beam passing through the paper will be diffracted by the fibers. Since light’s wavelength is smaller in water, the light is less diffracted in water, i.e. more focused. Thus, the intensity of light that passes through the paper will be greater. Another way to see this is, light with smaller wavelength will “see” relatively bigger holes and accordingly easier to pass through them.
- Refractive index of paper/cloth
If the wavelengths of light within the visible spectrum are much smaller than the dimensions of the fibers, then we can say that certain wave train of light is in a fiber. The molecules composing the fibers will respond to the light by radiating electromagnetic wave. This “new light” will interfere with the “old light” in such a way which results in delayed light(advanced in phase)– This can be easily shown by using a phasor diagram. Thus, effectively, the light covers a smaller phase each second, in other words it has a lower phase velocity than the speed of light. As we know, the quantity that measures the effective phase velocity of light is called refractive index. Note again that the refractive index that we are referring to here is the refractive index of a single fiber, not the refractive index of a group of fibers. The refractive index of a fiber (cellulose) can be found by googling to be n=1.48. When we get the cloth wet, the air between the fibers is replaced by water–Water has index of refraction(n=1.33) much closer to that of fiber ( n=1.48) than air(n=1) has. Thus, each time a light beam encounters a fiber, it is bent much less than it would be with dry cloth. Therefore, in average, a light beam can pass through many more fibers before its deflected significantly. So more of the light ends up travelling forward into the fabric.
First, I need to kill the first theory…If the whole paper is immersed in water, It will still appears more transparent than it would be in air. Therefore the first theory failed to survive. If the whole gaps is filled with water, the surface tension force acting on a single fiber will be directed in all direction, thus there is no effect at all, the fibers won’t fluff. The same thing happens with paintbrush’s bristles when you put it in water. The bristles will stick together after you pull it out from the water.
The two remaining theories predict that if we change the water with another liquid with higher refractive index, then the paper will be more transparent. To test this hypothesis, we did an experiment:
We take a piece of paper and we put several drop of water (n=1.33) on a place and several drop of glycerin (n=1.47) on other place. At a glance, their transparency look almost the same, and the water spot is more wavy than the glycerin one and also glycerin is easier to permeate into paper than water do. Human’s eye capability to differ intensities is not reliable, so we measure the intensity of laser beam that pass through the paper with photodiode.
the photodiode is behind the paper
The measurement shows that the glycerin spot is more transparent than the water spot! Therefore it agrees with the two remaining theories!!
There is a tie breaker experiment… If the “refractive index” theory’s effect is more dominant, a paper will be invincible when immersed in liquid that has refractive index similar to that of cellulose (maybe it won’t work because some paper is colored), if the “diffraction” theory is right there will be no local maximum of transparency.
There is an argument that disadvantage the “diffraction” theory. Since diffraction depends on wavelengths it means that blue light, yellow light and red light is diffracted differently. Bluer light is less diffracted while redder light is strongly diffracted. Therefore it means that when white beam is diffracted, it will look slightly bluer. But in reality it doesn’t , so it is either the “diffraction” theory is wrong or our vision is not accurate enough. Yet another argument, it doesn’t matter whether it is more focused or not, the total intensity of light that passes through the hole is still the same. More focused–>less interference, less focused–>more interference, it doesn’t make any difference.
I think the “refractive index” theory makes a lot of sense, but I am not sure.
Another interesting phenomenon will show up if you put a wet paper on a surface and stick it; the transparency will increases significantly. The explanation comes like this, if we stick a paper into a surface, the light beam can get out through the same hole it goes in. Almost all the light that comes in can comes out, effectively it is like passing through the layer once, just like when you can see through a cloth that’s right in front of your eyes. We can see that the change in the intensity is quite large, because the effects is not added up, but it is multiplied. So when your shirt gets wet, lifting the shirt away from your skin will pretty much reduce the transparency.
2. Mechanical Phenomena
While playing with papers to find out some ideas to answer previous question, I found five more questions to think of:
- Why is it easier to tear wet paper than dry paper?
Paper is made of small cellulose fibers tangled together like spaghetti, they can stick together by relying on friction force only. If you put water on it, it will lower the friction force between those fibers, thus they can slide over more easily, hence much easier to be tore.
- How does paper make sound when it is teared?
I have two explanation for this:
a) The sound is produced by snapping the fibers. When we are tearing the paper, we stretch some part of the paper until it reach the breaking tension of the fiber and suddenly the fibers snapped. The fibers are elastic, when it is stretched and suddenly cut into two, it is like stretching a spring and release it. Thus the fibers will vibrate as a spring, the greater it is stretched, the bigger the sound will be.
b) The sound is produced by the stick-slip movement between fibers. It is the same effect that happen to your screeching door, it is a rapid transition between moving and stopping. Thus the frequency of sound produced is related to the time characteristic of the moving and stopping process.
- Why dry paper make more sound than wet paper?
a) When the paper is wet, the water gets into the fiber , increasing its mass. Thus the frequency of vibration is much more lower than before, and maybe get out from human’s frequency range. And also because the friction is lower, the fibers can slide over easily, therefore not many fibers will get snapped.
b) When the paper is wet, the coefficient of friction between fibers is greatly reduced. Thus not much kinetic energy of the fibers is converted into sound energy.(screeching explanation)
- Why dry paper produces greater sound if we tear it faster?
–There will be more fibers snapped per second or there will be more screeching fibers at the same time. The sound from different parts of the paper interfere constructively, the wavelength of sound wave in the human’s hearing range is maybe long enough to account this effect.
– The tearing is fast enough that the elastic wave in the paper has not traveled quite far in the tearing process. Thus the tearing force is focussed on a small region ,therefore those fibers within the region have very large amplitudes. And also the smaller the number of fibers participating in the vibration, the higher the frequency will be.
- Why wet paper is more stretched than dry paper?
When the paper is dry, the fibers are pulled one side or the other which then creates tension. The entangled fibers are bent to some radius of curvature, because they are elastic they want to go back to their original shape(larger radius of curvature).They tend to get apart but friction force holds them together. When the paper gets wet, it lowers its static friction, therefore some strongly pulled fibers that previously unable to defeat the friction force are now able to slip off. Thus the paper will appears stretched and more wavy, and retain its shape even thought it is dried.
- What is the difference if we fold the paper before tearing it?
Usually the voice will be smaller. It is because we cannot tear it in a short time. A folded paper can produce larger voice than a non folded paper of the same size if we can tear it fast enough.
Edit:I found a better explanation that seems more convincing to me. I tried sliding two edges of paper perpendicularly, surprisingly the sound produced by doing that is pretty similar with the one produced by tearing paper. It seems that the sound produced is due to the transversal vibration of the whole paper, the friction or the fibers snapping merely acts as driving force. and notice if you hold the paper near the sliding point, the frequency of sound produced becomes higher because the shorter the vibrating paper’s length the higher the frequency is(only short wavelengths of standing wave are allowed).Now which one gives more dominant driving force, friction or snapping fibers?
I think friction is more dominant, because sliding the edges gives a similar sound even without involving any snapping process. Also if we slide it faster, the frequency will be higher.