[Cooper]

Hi,

The picture below is from my physical chemistry textbook (Atkins 9th Ed.). After reading this several times and asking my teacher, I am still having trouble understanding what's going on with capillary action.

So the pressure immediately below the meniscus is [tex]p_{ext}-\frac{2\gamma}{r}[/tex]. But what allows the two pressures on either side of the meniscus to be different? Shouldn't this change in pressure cause movement until the pressures are equal? Is this because the surface tension makes up for the lack of pressure below the meniscus? To be honest, I'm still not really sure what surface tension really is. My book just defines it as a constant of proportionality...

So back to the figure, is the book saying because the pressure pushing on the water immediately adjacent to the tube is p_ext, it pushes the water up the tube, because the pressure of water at the top of the tube is less by 2γ/r?

Then, further down, when it says the hydrostatic pressure matches the pressure difference 2γ/r, I am having trouble picturing what is going on. So the pressure exerted at the bottom of the tube is obviously greater than at the top, and this makes up for the lack of pressure at the top when compared to the outside?

Sorry there are so many questions! I want to make sure I really get this.

[Corribus]

Rather than just jumping into equations, I think a better approach is to first understand why things happen. Equations only quantify things.

In a two phase system of water in air, water forms (spherical, with no gravity) droplets. As you probably understand already, this is because water molecules are happier to interact with each other than with molecules of air.  For any given volume of water, a spherical droplet has the smallest area of surface where water is contacting air. We call this minimizing the surface energy - there is an energy of interaction between water and air at the surface of the droplet. This is why water droplets are not cubes. Surface tension is a measure of the strength of the cohesive forces holding the substance together. A substance with a higher surface tension has stronger forces holding it together - molecules of the substance are very happy being together and it takes a larger amount of energy to disrupt their integrity. The total surface energy between two substances depends on this strength of cohesion in each phase, and the strength of adhesion between the phases.

Now take that droplet and put it on a piece of glass. What happens? Now we have three phases to consider. Water interacts with itself. It interacts with air. And it interacts with the glass surface. We already know that the interaction between the water and the air is unfavorable. Glass is hydrophilic - water likes to interact with glass, in fact it likes to contact glass more than it likes to contact itself. So, water spreads along the glass. This can be expressed as a "spreading force" or a "wetting force" - or a pressure if you consider the area over which the force is acting. But when the water droplet spreads, it becomes less spherical, and thus has more surface in contact with the air, which we said is not favorable. Therefore the degree to which the water spreads is a delicate balance between the energy of interaction between water molecules themselves (cohesive forces) and both the energy of interaction between water and the glass (favorable) and the energy of interaction between water and air (unfavorable).

This is often expressed as a "contact angle", which is a measure of how spherical the water droplet remains when it's put on a surface. On a hydrophobic surface, like a waxy leaf, there is very little driving force to spread/wet, so the water droplet remains spherical to minimize both water-surface and water-air interactions, and the contact angle is large. On a hydrophilic surface, there is a large driving force to spread/wet, so the water droplet loses spherical character, at least until the forces driving spreading are balanced by the forces acting to minimize water-air interaction. Spreading isn't indefinite, in other words. The droplet isn't a sphere, but it's not an infinitely thin coating either,as it would be in an idealized infinitely superhydrophilic surface. It's somewhere in the middle.

The argument above should help you understand capillary action. When a capillary tube is put into water, there is a driving force for the water to spread along the glass - or a pressure, if you prefer to think of it that way - because the interactions between water and glass are favorable. A narrower tube gives more relative surface area for contact between the water and glass (and less surface area for contact between the water and air), which means the water travels further up a narrow tube. This is exactly the same as the case of water spreading  along a horizontal surface, except now the system is contextualized by gravity. The height the fluid travels in the capillary is determined by equilibrium between all of these forces.

The equation the book talks about is derived from the Young-Laplace Equation, which you can learn more about here:

http://en.wikipedia.org/wiki/Young-Laplace_equation