Bingham Plastics

first I must say, that I am new to both fluid dynamics and LBM (like 1 year old :slight_smile: )

So I would like to derive an A term in an equilibrium distribution function:
for Bingham plastics. Or at least I would like to find a derived solution. I have found only a paper: Lattice Boltzmann modeling of Bingham plastics, but the equilibrium function looks quite different then ussual and I can not see if it is correct because I do not know how to derive it.

So could you please point me to any paper / book where there is complete derivation of A term of the equation for Bingham plastic or similar? Or could you at least point me to any paper describing Bingham plastics for LBM aside from the mentioned one?

Best regards,
Oldrich Svec