Can you explain the meaning of the symbols in these formulas?
I could answer with less effort, knowing that.
What are these Ro, Rg, Rf and Rm?
Also, what is the Vs supposed to represent?
My first impression is that the log formula would be based on an assumption regarding the size distribution at the entrance of the separator. I would guess it represents the ratio of fines actually collected to the amount of fines that could be collected.
This would justify the word "efficiency". Calculations might be done assuming a Rosin-Rammler curve.
I will check later, in the hope that you can find the meaning of the symbols.