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The suspended particles are considered as rigid spheres of same diameter d, and density {latex}{\large$$\rho_p$$}{latex}. Newton's second law written for the particle i stipulates:
{latex}{\large $$m_p \frac{d \mathbf{u}_p^i}{dt}=\mathbf{f}_{ex}^i$$}{latex}
where {latex}{\large$$\mathbf{u}_p^i$$}{latex} is the velocity of particle i, {latex}{\large $$\mathbf{f}_{ex}^i$$}{latex} the forces exerted on it, and {latex}{\large $$m_p$$}{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 [ref3]:
{latex}{\large $$\frac{d \mathbf{u}_p^i}{dt}=\frac{\mathbf{u}_f-\mathbf{u}_p^i}{\tau_p}$$}{latex}
where {latex}{\large $$\tau_p$$_p=\rho_p D^2/(18\mu)$$}{latex} is known as the particle response time, {latex}{\large $$\rho_p$$}{latex} the particle density and D the particle diameter. 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).