Could you perhaps try dissolving a known weight of the particles, filter the solution, dry the filter and weigh it? Repeat with each different water/surfactant mix?
If the solids are too small to filter reliably, would a turbidity test work? For each surfactant-water mixture you would need to test with increasing amounts of the carbon particles, thoroughly mixed.
A TOC test might also do the trick, although you will have to do a bit of mathematical trickery and/or standardization work before starting your actual test. Specifically, you will need to know the percentage of carbon atoms within the particles, and the TOC of the surfactant.
These methods might be a bit too rough for a university project, and you'll need to fill in the blanks I've left, but perhaps they will get you thinking in the right direction. I can't honestly tell you what test your tutor is thinking of.