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The suspended particles are considered as rigid spheres of same diameter d, and density {latex}$\rho_p${latex}. Newton's second law written for the particle i stipulates:
{latex}$m_p \frac{d \textbf{u}_p^i}{dt}=\textbf{f}_ex^i${ex}^i${latex}
where {latex}$\textbf{u}_p^i${latex} is the velocity of particle i, {latex}$\textbf{f}_ex^i${ex}^i${latex} the forces exerted on it, and {latex}$m_p${latex} its mass.
In order to know accurately the hydrodynamic forces exerted on a particle one needs to resolve the flow to a scale significantly smaller than the particle diameter. This is computationally prohibitive. Instead, the hydrodynamic forces can be approximated roughly to be proportional to the drift velocity:
{latex}$\frac{d \textbf{u}_p^i}{dt}=\frac{\textbf{v}-\textbf{u}_p^i}{\tau_p}${latex}
where {latex}$\tau_p${latex} is known as the particle response time. This equation needs to be solved for all particles present in the domain. This is done in Fluent via the module: Discrete Phase Model(DPM).