# Entropy question

1. Oct 18, 2009

### espen180

I remember reading a thread here on PF about how paper towels can absorb water. I think the answer was that the towel releases potential energy stored in the towel and lifts the water to a higher potential energy.

Let's examine the situation before and after the absorption.

Before, the water has a lot of freedom of movement and shape. After, it is held in place by the towel, severely decreasing it's freedom of movement. The towel itself does not change during the process (except for the areas where water is stored).

It seems to me that the entropy has decreased during this process. But that can't be, so I must be missing something. Is heat released during the absorption? Am I not concidering the complete system?

Any help will be appreciated.

2. Oct 18, 2009

### Andy Resnick

Interesting question... capillary rise is irreversible, so the entropy should increase. It's related to the more general problem of 'wetting'. I never thought of this before, tho. Not sure this problem has been treated before, either.

3. Oct 18, 2009

### Mapes

It's no problem if the entropy of the water decreases, as long as the Gibbs free energy of the water + paper towel decreases (assuming the system is at constant temperature and pressure). Presumably the surface energy of the paper towel material is lower when it's in contact with water, though I don't know the details. This reduction in energy would correspond with some amount of heat emission, as espen180 suggested.

4. Oct 19, 2009

### Andy Resnick

I don't think it's as simple as that. As I mentioned, capillary rise is a specific phenomenon of wetting, and wetting is poorly understood. Here's three examples:

1) Percolation. The main application is flow through a porous medium, but what's interesting (here) is when gravity is removed. Then, there is no stable state, and the instability is driven purely by geometry. There is a large number (possibly an infinite number) of equivalent states, corresponding to constant surface area while varying the particular voids that are filled. How does the entropy vary, and does this imply that even for viscous fluids partially filling a porous medium, the flow is reversible (isoentropic)?

2) Moving contact line. The microscopic details are not known, and indeed in the continuum model, the stress is infinite at the moving three-phase line. The no-slip boundary condition would seem to imply something about the local entropy, since the condition means we have a perfect understanding of the positions and velocities of the fluid atoms adjacent to a solid surface, but clearly contact lines do move with a finite energy (and isothermal conditions). Moving contact lines are generally not reversible (the contact angle undergoes hysteresis), but then a single moving drop is constantly producing entropy- even under isothermal conditions. How is the entropy manifested?

3) Coarsening. Binary mixtures undergo several dynamic processes (spinoidal decomposition/dewetting), coarsening/Ostwald ripening, etc. These are usually thought of in terms of the Gibbs free energy and occur at constant temperature and pressure. Are these isoentropic processes? It would seen not to be since they are irreversible, but again, how is the entropy manifested?