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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${latex}
where uip{latex}$\texfbf{u}_p^i${latex} is the velocity of particle i, Fiex{latex}$\textbf{f}_ex^i${latex} the forces exerted on it, and mp{latex}$m_p${latex} its mass.
In order to know accurately the hydrodynamic forces exerted on a particle one needs to resolve the flow to a scale significantly smaller than the particle diameter. This is computationnaly pro- hibitivecomputationally prohibitive. Instead, the hydrodynamic forces can be approximated roughly to be proportional to the drift velocity:
{latex}$\frac{d u ip = v − u ip dt τp
where τp = XXtextbf{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 ?Phase Model(DPM).