# Tag Info

15

The surface of any fluid has an associated energy-per-unit-area, known as the surface energy, a.k.a. surface tension. This energy is not a property of the fluid alone, but of the fluid and the medium it is in contact with. In your case you would have associated surface energies for the water-air interface, $e_{wa}$, as well as for the water-paper interface, ...

5

The physics behind this is the same capillary action that causes water to move up narrow cylindrical channels. Tissue paper is extremely porous, but the pores are sufficiently narrow that the cohesion between water molecules (actually driven by the Coulomb interaction, since water molecules are polar) and adhesion between the water and the surfaces of the ...

5

Your problem is highly nontrivial. The theoretical tool to be used is the renormalization group, which extracts the relevant dynamics of the large scales of the system. But if we were able to use it "in a blind way", then we would have a technique to study the macroscopic dynamics of any microscopic system... and this would made a lot of my colleagues ...

3

The keyword for porous flows is Darcy's flow, which is based on the Darcy law guiding the field of mass flux instead of velocity: $$\vec{q}=-K\nabla p$$ $\vec{q}:=\vec{u} \cdot \text{porosity}$, so it is equivalent to normal flow only for homogeneous media. This equation comes from averaging the NS over porous volume; however, as you can see, it is very ...

1

For the input parameters provided, your velocity estimate is reasonable but probably not accurate. Reason is that Darcy's law assumes Stokes (small Reynolds number) flow. For the parameters provided, together with a density of 1 kg/m3, and substituting a flow length scale of 0.001 m, the Reynolds number reaches a value around 10. This means that the flow ...

1

The previous answer tells you why the water moves up but doesn't explain where the energy comes from. In order for water to move up and thereby gain gravitational potential energy, you need to have some energy loss somewhere else to compensate. Some of the energy comes from the random molecular movement of heat which extends the edge of the water itself up ...

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