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In the Nile Red video Making ferrofluid from scratch a suspension of small magnetite ($\ce{Fe^{2+}Fe_2^{3+}O_4^{2−}}$) particles is produced from a combination of ferrous chloride and ferric chloride.

The nanoparticles are then given a coating of oleic acid ($\ce{CH3(CH2)7CH=CH(CH2)7COOH}$) to provide steric stabilization to prevent aggregation, then dissolved in kerosene.

After about 23:20:

…the magnetite isn’t truly dissolving, it’s going into suspension. This is because the nanoparticles aren’t soluble in the solvent, but they’re small enough that they can still easily get dispersed.

The oleic acid coating that helps with this, by preventing two particles from coming too close together, and by also allowing them to interact with the non-polar solvent. The result of this is a stable suspension known as a colloid, where it’s almost like the magnetite being dissolved.

As an exercise I'd like to estimate the maximum size of the oleic acid-coated magnetite particles that can be stable in this solution. Some considerations are:

  1. While the magnetite particles themselves have a high density (over 5 g/cm3), the oleic acid molecules might be arranged radially making the volume of the complete particle much larger than the magnetite core.

  2. While large magnetite particles would sink quickly to the bottom due to gravity, the thermal agitation (Brownian motion) at room temperature is sufficient to keep these in colloidal suspension if they are small enough. This suggest that there might be some ratio of $k_B T$ with some expression of gravitational potential energy.

Question: How would I go about estimating the maximum size of the magnetite nanoparticles that could remain in stable suspension in this case?

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  • $\begingroup$ Assuming you could make a more dilute colloid (not the black blob) without changing anything essential, i.e., particle sizes, how about Mie scattering? Per wiki, this is used for particle sizing when the particles are below 50 microns. The reference is ISO 13321:2009. Or maybe the Tyndall effect could give an estimate of the range of particle sizes. $\endgroup$
    – Ed V
    Commented Feb 12, 2020 at 0:10
  • $\begingroup$ @EdV by estimate I mean using pencil and paper or thinking or a white board, not a real measurement. I've asked for a way to estimate the maximum size that won't settle out of suspension. $\endgroup$
    – uhoh
    Commented Feb 12, 2020 at 7:55
  • $\begingroup$ I hope you get an answer: every paper I find is way too complicated. Based on the fact that Brownian motion is modeled using the diffusion equation (in part), I would assume spherical particles should have diameters small enough so that the diffusion model is valid. But there are so many factors: particle density, viscosity, fluid density, and so on. My wild guess, just a hunch, is that particle diameter must be less than 10% of the diffusion length in the fluid. I really hope you get an answer so I can see how bad I guessed! $\endgroup$
    – Ed V
    Commented Feb 17, 2020 at 0:11
  • $\begingroup$ @EdV I don't know about the oleic acid "wrapping" and the effective density of the coated particles, but I have a hunch that the maximum density will come from the same effect that keeps the argon from falling to the bottom of a closed box of air. Thus my comment about"some ratio of $k_B T$ with some expression of gravitational potential energy". $\endgroup$
    – uhoh
    Commented Feb 17, 2020 at 4:03

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