Scientifically speaking, how and why does sweating (soldering) copper pipes work?
I think @ArchonOSX has a good answer, but I'd like to expand a bit more on it (having a background in welding, brazing, and soldering).

Going point by point:


Flux typically promotes bonding between the base metals and the solder. It does this by cleaning the metal (removing surface contaminants), deoxidizing the metal, and preventing further oxidation. Hot metal tends to oxidize more quickly than cold metal, but the flux will remove oxygen (either by absorption, adsorption, or oxidation of the flux itself) where it is applied.


If all your flux burns (or gets oxidized) before you've finished brazing the joint, then the solder will be less likely to flow where you need it because the base metals will tend to oxidize. Solder doesn't bond as well with oxidized surfaces, so instead, it balls-up and drips off.
This is possible, but difficult. Unless you were in an anaerobic environment (and even then it might not work) you'd probably not get a good bond.
Wikipedia is pretty good on this one.

You want the metal to be uniformly heated so thermal expansion is uniform, so wicking is uniform, so everything is uniform. Copper, being a good electrical conductor, is also a very good heat conductor. If you only heat the joint, you might find it cools relatively quickly due to surrounding copper cooling the joint.


Not right at the joint (right away). When you are promoting solder flow, then you do want to focus the flame very tightly.
Yes, to heat the surrounding pipe initially.
Yes, because the metal here is also often a bit thicker than anywhere else, so it takes the most energy to heat up to brazing temperatures.

Capillary action is an interesting phenomenon that occurs when one material can "wet" another. Wetting is a process where the surface energy is lowered when the liquid-phase material is in contact with the solid-phase material. Some liquids, like mercury, don't wet others, like glass (forming an upward meniscus). Water does the opposite, wetting glass. The surface energy must be lower than the surface tension of the liquid to prevent beading (balling-up, which you see when the flux burns off). In small spaces, this wetting capability can cause a column of liquid to rise against gravity. For non-wetting materials, the opposite tends to happen.


I think I answered this part above.
When this happens, it's because the molten solder cannot wet the copper. Flux lowers the surface energy of the bare copper (another of its functions), which is how it promotes wicking, but if the copper isn't hot enough, it won't wet either.



HOWEVER, everything I just described indicates that the solder is on the surface of the copper (adsorptive or adhesive). In fact, the solder is able to form a localized alloy with the base metal that penetrates some distance into the base metal. This is why brazing (and soldering) can be quite strong, even compared to welding. This is an absorptive process and occurs because the higher temperatures allow copper atoms to move enough within their lattices to allow for an alloy to form. This process adds to the effects described before.