Does Capillary Flow in a Tube Create a Pressure Gradient?

[Niles]

I'm trying to understand capillary flow in a tube. I've found this http://folk.uio.no/eaker/thesis/node11.html that explains some aspects of it, the system is illustrated here,

So the (black) non-wetting fluid resides to the left and the (white) wetting fluid is to the right. Say that we are looking at a pore in a piece of chalk/rock and that the outlet (to the right) is a big reservoir of wetting fluid, whereas the inlet to the left is merely the end of the pore. Given this setup, I can't quite figure out how the inlet pressure pL relates to the outlet pressure pR.

They can't be equal since the capillary forces must introduce a pressure gradient which "pushes" the non-wetting phase out, given that the solid boundary is wetting. Given this, I would anticipate that pR<pL.

Is this reasoning correct?

 

[eljose79]

Hello there,

Thank you for your inquiry about capillary flow in a tube. The link you provided does indeed provide some helpful information about the topic. You are correct in your understanding that the inlet pressure (pL) and outlet pressure (pR) cannot be equal in this scenario. The capillary forces do indeed introduce a pressure gradient which pushes the non-wetting phase out.

To fully understand the relationship between pL and pR, we need to consider the concept of capillary pressure. Capillary pressure is the difference in pressure between the wetting and non-wetting fluids in a porous medium, such as the pore in a piece of chalk/rock. In this case, the wetting fluid is the white fluid and the non-wetting fluid is the black fluid.

The capillary pressure is affected by several factors, including the surface tension between the two fluids, the contact angle between the fluids and the solid boundary, and the pore geometry. In your scenario, the solid boundary is wetting, meaning that the contact angle between the fluid and the solid surface is less than 90 degrees. This results in a positive capillary pressure, which means that the pressure in the wetting fluid (pR) is higher than the pressure in the non-wetting fluid (pL).

In summary, your reasoning is correct. The outlet pressure (pR) will be higher than the inlet pressure (pL) due to the capillary forces pushing the non-wetting phase out. I hope this helps clarify the relationship between pL and pR in capillary flow. Let me know if you have any further questions.