Calculate smallest pore that will admit water

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In summary, the hydrophobicity of micropores can be explained by arguing that the capillary pressure in them is too high to allow water to penetrate. The contact angle is important in determining wetting behavior, but it is difficult to calculate.
  • #1
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:

[tex]P_c=\frac{2 \gamma Cos\theta}{r}[/tex]

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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  • #2
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?
 
  • #3
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.
 
  • #4
Calculate the Bond number, that will tell you.
 

FAQ: Calculate smallest pore that will admit water

1. What is the purpose of calculating the smallest pore that will admit water?

Calculating the smallest pore that will admit water is important for understanding the permeability of a material. This information can be used to determine the ability of a material to allow water or other fluids to pass through it.

2. How is the smallest pore size determined?

The smallest pore size can be determined by using various techniques such as mercury intrusion porosimetry or capillary flow porometry. These methods measure the size of pores based on the pressure needed to force fluids into the material.

3. What factors affect the calculation of the smallest pore that will admit water?

The calculation of the smallest pore size that will admit water is affected by several factors, including the properties of the material (such as pore size distribution and surface tension), the type of fluid being used, and the measurement technique being employed.

4. Why is it important to know the smallest pore size that will admit water?

Knowing the smallest pore size that will admit water is important for a variety of applications, including filtration, drug delivery, and environmental remediation. It can also provide valuable information about the structure and properties of a material.

5. Can the smallest pore size that will admit water change over time?

Yes, the smallest pore size that will admit water can change over time due to factors such as aging of the material, changes in environmental conditions, or the presence of contaminants. Therefore, it is important to regularly monitor and update these calculations as needed.

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