Condensation droplets on a mirror surface. Forces at work. – Image by Vincent Summers
My question concerns condensation. What dictates how droplets form, then combine with each other? When you blow warm breath onto a cool surface, at first nothing appears to happen. Keep it up and droplets appear. These small droplets merge into bigger droplets. What physical laws dictate how this occurs? Also, what role does gravity play on vertical surfaces such as a chilled bottle of beer, producing tiny rivulets of moisture running down the sides? –Dan.
Initial Commentary
The answer, which follows, although it has some basis in well-known physical principles, depends in part upon observation, mental visualization, and (finally) blatant speculation.
This is an interesting procedure, since so many of life’s mundane occurrences are in reality quite fascinating when closely examined.
Condensation droplets. Notice the flattened hemispheres. Image by rkit
Initial Condensation
We breathe in and breathe out, exhaling water vapor at a temperature of approximately 34ºC (93.2ºF). We may exhale onto a mirror in order to wipe it clean with a tissue.
Actually, a mirror is excellent for discussion purposes. The glass of most mirrors is formulated from silicon dioxide. Fused silicon dioxide is polar, and thus glass is polar. Since water is also polar, it readily adheres to glass. No scratches or other surface imperfections are necessary.
What is polarity? It is an uneven distribution of molecular electric charges. (One end is positive, one end is negative.) Ends of molecules with opposite charges attach themselves to one another.
Simply put, moisture droplets adhere by electrical charges.
Opposing Forces at Work
Water molecule. Note the two electrical poles. Image by Vincent Summers
Our breath deposits tiny drops of moisture on a mirror. However, any moisture already present on a mirror’s surface tends to evaporate due to vapor pressure. If the relative humidity of the air at the mirror’s surface is sufficiently high and is constant, we will build up a foggy film. But if we stop exhaling and the humidity is low, the droplets quickly evaporate.
What enables continuous bombardment of the mirror’s surface with moist air to eventually build up droplets of moisture? As moisture molecules continue to bombard the mirror, some of them strike where there already are adherent water molecules. Hydrogen bonding causes the newcomers to bond to those already present. As the droplet radius increases in size, other physics factors play an increasing role.
The Other Factors
Two of those other factors are gravity and surface tension. Now we are all acquainted with gravity, but what precisely is surface tension? The Oxford Dictionary tells us that it is,
The water strider stays afloat by means of surface tension. PD Image by the3cats
The tension of the surface film of a liquid caused by the attraction of the particles in the surface layer by the bulk of the liquid, which tends to minimize surface area.
The particles mentioned in the above definition are polar, that is electrically charged, molecules of water. Those particles within a drop of condensation all thoroughly bond to one another. But the outermost layer has no particles above to bond to, so those particles bond to the particles below with even greater fervor, forcing the drop into its somewhat spherical shape.
The vessel of minimum surface area that contains the maximum volume is a sphere. It would seem logical then that condensation would resemble somewhat flattened hemispheres.
As the radius of each drop increases, so does the pull of gravity on each droplet, spreading the droplet out. Surface tension pulls the droplet up and together, so it does not lose its spherical shape too rapidly.
Eventually, if the source of additional moisture continues at a sufficient rate, gravity will win out and the drops will become rivulets or sheets of moisture. This is especially so on a well-cooled vertical surface such as a beer bottle.
The difference in the case of the beer bottle is that its chilled surface condenses a sizeable percentage of the water vapor in the atmosphere around it, no matter what the relative humidity may be.
Physics, Water, and Condensation
Observing the behavior of water condensing on the surface of glass is science you can experience at home. For more information about surface tension, cohesion, adhesion, and more, please check the resources for this article.
Dewpoint is a more useful measure of moisture in the air than humidity. The dewpoint is the temperature at which moisture will condense. When the ground radiates at night, its temperature drops. If it drops below the dewpoint, dew forms (hence the name). If the temperature is below freezing, frost forms. If a mirror is below the dewpoint of the adjacent air, water will condense on it. The dewpoint of human breath is around 90 degrees F. But when we exhale, it immediately mixes with the ambient air. We can get condensation at room temperature only if an object is very close — for example the lens of a pair of spectacles held very close to the mouth. When the temperature is very cold, the water vapor in breath can condense before it mixes with the ambient air and evaporates.
Vincent Summers says
Great additional information, Jon. This is the kind of material I love to think about.
OP here, this is a great answer, and it totally makes sense! It must be that the force of surface tension has a threshold that cannot withstand that of gravity, so when the droplets get too massive, they succumb and become rivulets! Thank you for putting to rest my burning science question!!!
It takes someone to ask the question. I remember staying at my grandmother’s house as a child. She had no television and if it rained we couldn’t play in the garden. My main occupation in those days was watching the raindrops gather on the window pane and condense into rivulets.
If glass is polar, then is one side of the glass a different polarity from the other? Does condensation react or form in a different way on one side of the glass compared with the other?
Vincent Summers says
A pane of glass contains quite a few molecules. The polarity of one side is similar to that of the other. The humidity on the outside obviously differs from that on the other side, as may the temperature. Otherwise, identical conditions exist and behavior is the same.