How Does Capillary Action Work?

There's a good chance this is one of those "everyone knows but  me" questions, but since I write this blog purely for my own amusement you're just going to have to live with that.

Anyway, I got to wondering about capillary action via the usual route; I left the end of a towel or something hanging into the sink, which still had a bit of water in it, the other week.  About eight hours later, the towel was completely saturated with water in clear defiance of gravity.  This phenomena is called "capillary action" and is familiar to basically anyone who has encountered water and fabric in some combination in their lifetimes, but when I got to thinking about it I realized my poorly-thought-out mental justification for it ("it's just like a really slow siphon!") made no goddamn sense on a bunch of different levels.  To the internet!

You know what you never, ever run into in electrical engineering?  Fluid dynamics.  I'd argue that this is one of the best reasons to go into electrical engineering, but the fact that we make up for it with horrible things like electromagnetics and quantum mechanics kind of undercuts that.  Anyway, the point is that beyond the basic physics it shares with other things (e.g. diffusion) I know next to nothing about why liquids do whatever it is they do, including weird shit like climbing up fabric.

Apparently capillary action isn't exclusive to fabrics; it's something that will happen in lots of porous materials, including things like bricks and cinder blocks.  The key to the whole thing is narrow channels through the material.  Stick some water in a narrow, vertical-ish tube (the most idealized demonstration of this is a thin glass tube partly immersed in water; see below) and you've suddenly got two pretty big forces to think about.  Surface tension is the first one, which will cause the surface of our narrow water-channel to form something called a "concave meniscus", which is a fancy term for a liquid surface where the level at the edges is higher than the level at the center (the smaller the channel, the greater the meniscus curvature and the higher the surface tension). The formation of a concave meniscus is dependent on there being an attractive force between the liquid and the channel material; assuming our liquid is water, we'd need to make the channel out of something hydrophilic, like glass.

Idealized capillary force demonstration.  A narrow glass tube is placed in a bath of water; surface tension and liquid cohesion "pull" the water up the tube to some height where their force is exactly balanced by gravity.

Next you've got the interaction between the capillary medium and the water to consider.  A concave meniscus of water in a channel of hydrophilic material is going to have its edges drawn upward by adhesion forces between the water and the sides of the channel.  As the edges of the water meniscus move up the channel, surface tension and general cohesion of the water molecules ensures that the rest of the surface, as well as the water behind it, is also drawn upward to preserve the shape of the meniscus.

So you've got a combination of adhesion and surface tension creating an upward force that's stronger than the downward force of gravity on the mass of the water.  Obviously that can't last forever; the capillary force is constant with height (assuming a constant-width channel) while the force of gravity is going to increase as more mass (water) is drawn up into the channel.  At some point they'll balance and water will stop "flowing" upward.  This balance point depends largely on the channel diameter (smaller diameter = greater surface tension force, remember?), although the channel wall material (specifically, the hydrophilic-ness thereof) is obviously going to play a role. There's probably a really simple equation for the critical height of the water level in a capillary tube, so if that's of interest to you definitely look it up!

Now extrapolate that out to a porous medium like fabric or a paper towel.  The pores are basically thousands of very tiny channels, and we know from the fact that you can get them wet that paper towels and most cellulose-based fabrics are pretty hydrophilic.  Add in the fact that most of our pores/channels aren't even going to be perfectly vertical (reducing gravity's counter-force) and you've got a really good situation for capillary action to do its work.  In most cases, such as the towel in the sink that inspired this, capillary action can easily lift a decent volume of water up a distance of several inches if you give it enough time to work. 

Water climbs up a brick, which is basically an assload of microscopic glass channels from a fluid-dynamic standpoint

Besides making a mess of my counter that one time, capillary action has some legitimate applications.  It's basically the mechanism by which things like paper towels absorb water, which as most people know is just all kinds of handy.  It's also the mechanism by which certain fabrics "wick" sweat away from the body.  It actually encroaches on my field a little bit too; people building microfluidic and nanofluidic devices (small devices designed to move tiny amounts of liquid around strategically, in order to sort DNA and detect chemicals and things) rely heavily on capillary forces to do their work, since extremely narrow channels mean extremely strong capillary forces.

Per usual, thanks to Wikipedia for making me feel dumb.