# Force required to break electrostatic bonds between granular matter

I'm working with a powder mass that is separated into different samples, each having a varying degree of water and oil content. They're stored for a fixed amount of time and then conditioned to reach a loose state for testing. Now the electrostatic forces and capillary bridge during storage lead to lump formation, that I've to destroy by providing vibratory force. The tendency was that for increased water and oil content there were bigger lumps, which needed more force to break up. I wanted to gain a rough estimate of the required vibratory force and relate it to the fluid content.

Looking at electrostatic forces, I wanted to estimate how much attractive force 2 particles would have. The problem I'm having is in understanding the application of Coulomb's law to gain my rough estimate. The force of attraction between 2 particles separated by distance r with charge q each is, $$F = \frac{q^2}{4\pi\epsilon r^2}$$ where $\epsilon$ is the permittivity of the media.

Now since oil and water have higher $\epsilon$, the force between the particles is lesser, for particles that are equidistant. But this result is counter intuitive, since I need more force to break up the lumps when water and oil content is higher. Has the Coulomb's force F a completely different interpretation, than the strength of the electrostatic bond holding 2 particles together?

I understand that permittivity means, that the lines of electric force can be better oriented, but I find it counterintuitive that particles in air have more force between them, than in water, unless my understanding of the meaning of F is false. Also, is there an alternate formula to estimate how strong the electrostatic bond between 2 particles is, which would allow me to estimate how much force I need to break them?

• For the wet particles you have the capillary forces produced by the liquid layer between the solid particles. It is harder to separate wet particles than dry ones. Sand castles depend on this property. Electrostatic attraction may or may not be present. Do you have some evidence that the particles are charged? – nasu Sep 22 '17 at 12:32
• The particles have between 3.5 to 5% water and between 4 to 8% oil content. I assumed capillary bridges wouldn't alone explain lump size differences. I am yet to estimate the actual amount of charge, because I'd like to know first if that would even allow me to answer the force required question. Generally speaking, assuming there was charge, I'd like to know if the Coulomb equation would actually help me answer the question. – Franz K Sep 22 '17 at 12:49
• I don't think you should consider electrostatic forces. The effect of the liquid is complex enough. Whereas for dry powder you may expect some development of electrostatic charges due to the friction between particles, in a wet medium I find it unlikely. I would try to connect the amount of liquid to the number of the liquid bridges and the geometry of the capillary layer. I suppose this is discussed in the literature about particulate composite. The amount of wetting realized by a specific amount of filler is an essential parameter. – nasu Sep 22 '17 at 12:56