Calculate smallest pore that will admit water

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Discussion Overview

The discussion revolves around the calculation of the smallest pore size that will allow water to enter, particularly in the context of hydrophobicity research involving dried powders. Participants explore the relationship between surface tension, pore size, and contact angle, as well as the implications of these factors on fluid penetration in micropores.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant proposes using capillary pressure to explain the hydrophobicity of micropores, suggesting that high capillary pressure prevents water penetration at atmospheric pressure.
  • The formula for capillary pressure is presented, with a focus on the variables of surface tension, contact angle, and pore radius.
  • There is uncertainty about how to calculate the contact angle for powders given a known surface tension, raising the question of whether this approach is appropriate.
  • Another participant introduces Laplace's equation and its relevance to pressure differences at interfaces, noting that the contact angle is not directly included in this equation.
  • Young's equation is mentioned as a potential link to wetting behavior in small pores, suggesting it could provide boundary conditions for interface shapes.
  • A participant considers setting the contact angle to 90 degrees as a limiting case to simplify calculations, proposing to match the resulting pressure to atmospheric pressure.
  • There is a question raised about the significance of gravitational forces on a water droplet in the context of small pore sizes.
  • A suggestion is made to calculate the Bond number to assess the influence of gravity in this regime.

Areas of Agreement / Disagreement

Participants express differing views on the appropriate contact angle to use and the relevance of gravitational forces, indicating that multiple competing perspectives remain without consensus on the best approach to the problem.

Contextual Notes

Participants acknowledge limitations in their assumptions regarding contact angles and the applicability of certain equations, as well as the potential influence of gravity in small pore scenarios.

Bacat
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I am conducting some hydrophobicity research with dried powders. I have known mixtures of fluid from which I can calculate surface tension. I have data about the powders regarding which mixtures easily wet the surface and which bead up into drops. I also have BET surface area histograms which tell me the relative distributions of pore sizes on the powders.

I can correlate the surface tensions with the pore sizes and that's interesting, but I want to explain them also. I believe I can explain the hydrophobicity of micropores (about 10 angstroms in width or less) by arguing that the capillary pressure in them is too high to allow water to penetrate at atmospheric pressure. My question is how to calculate this pressure.

I know that capillary pressure is:

P_c=\frac{2 \gamma Cos\theta}{r}

where gamma is surface tension of the liquid, theta is the contact angle of the liquid at the solid interface, and r is the radius of a pore. I'm not sure how to calculate the contact angle for a powder given a known gamma. Is this the wrong approach?

I'm also not clear what the balancing force should be. I want to find the pore size which forbids entry of the fluid into the pore for a given gamma. I am assuming atmospheric pressure, so do I just need to find the r that makes P_c equal to P_atm?

Can I choose an arbitrary contact angle and get a reasonable estimate?
 
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Laplace's equation is the pressure *jump* across the interface; it's the excess pressure required. The contact angle does not properly figure in that equation.

Young's equation does involve the contact angle, and I'm sure relates to wetting in a small pore- if nothing else, it's the boundary condition for the interface shape and so involves Laplace's equation.

As for setting a contact angle, it's hard to say precisely what it would be, but for a hydrophobic material you could certainly assume a contact angle greater than 90 degrees.

Does that help?
 
I think I should just set theta equal to 90 degrees then, ie the limiting case. Then the pressure of interest is just the surface tension divided by the pore size. I think I just need to match this to atmospheric pressure.

Another question is whether a drop of water will have significant gravity forces in this regime.
 
Calculate the Bond number, that will tell you.
 

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