momentum exchange method for particle force

Hello All,

I am trying to implement this paper :
Iglberger, Klaus, Nils Thürey, and Ulrich Rüde. “Simulation of moving particles in 3D with the Lattice Boltzmann method.” Computers & Mathematics with Applications 55.7 (2008): 1461-1468.

For calculating the momentum/Force on the particle the paper uses momentum exchange approach which is :

Force on fluid cell = sum over all neighboring particles( sum over all Lattice Directions * ea(f(Xb) + f(Xf))))

where f(Xb) is the distribution functions in cell near to the particle boundary and f(Xf) is the distribution function at the fluid cell near to the particle boundary .

My question is if a cell is or was a Particle cell at some instant of time, what could be the distribution function in the particle ?

Is this distribution function same as fluid cell distribution ?

Any suggestion is helfpful