MRT-LBM Simulation of Confinement Effects of a Two-Dimensional Particle Settling in a Newtonian Fluid

By means of extensive two-dimensional Direct Numerical Simulations utilizing a coupled Lattice Boltzmann Method -- Discrete Element Method approach, we analyzed the settling dynamics of a single disk-shaped particle in a Newtonian fluid, confined by lateral walls or periodic conditions. By varying the systems parameters we obtained particle's Reynolds number ranging from Re≃10 ^-4 to 10 ⁴ . This broad range of Re enables a comprehensive analysis of the settling dynamics in 2D across the viscous, visco-inertial and inertial settling regimes. With no-slip wall conditions, our simulations align well with literature data up to moderate Re. Beyond this threshold, increasing grid resolution and lower compressibility become essential. With periodic boundaries, the pressure beneath the particle scales with its buoyant weight divided by the periodic distance and does not depend on the settling dynamics. For all system parameters, the pressure drop across the particle follows the same scaling, with a pre-factor that depends to the Reynolds number. A sigmoidal function provides a good fit of this pre-factor, with two asymptotic values: 1 in the viscous regime and 2.5 in the inertial regime. Between this two regimes a transition occurs, corresponding to the visco-inertial regime. We also discuss the confinement effects, due to periodic conditions, on the settling dynamics. Interestingly, a confinement length scale is identified and is shown to scale with the inverse square of the Reynolds number in the viscous regime, while remaining constant at high Re.