Inertial migration of a non-neutrally buoyant particle in a linear shear flow with thermal convection

Abstract

We perform numerical simulations on inertial migration of a non-neutrally buoyant particle with a density ratio of 0.98-1.02 in a linear shear flow dominated channel with a Reynolds number up to 500 in the presence of thermal convection using a double-population lattice Boltzmann method. It is found that under the isothermal condition, the particle with a larger density difference from the fluid will either settle to the bottom of the channel or float to the top of the channel, while the particle with a smaller particle-fluid density difference remains suspended in the channel due to the inertial lift force. The presence of thermal convection (characterized by the Grashof number Gr) induces an additional downward lift force, which results in distinctive migration behaviors that depend on whether the particle density is larger or smaller than that of the fluid. For a particle heavier than the fluid, the settling is enhanced by thermal convection due to the synergistic effect of the thermal lift force and the gravitational force. The critical Reynolds number for lifting the particle increases compared with the isothermal case and is linearly correlated with the dimensionless density ratio (σ). On the other hand, for a particle lighter than the fluid, an empirical dimensionless number Gr∗, defined as Gr/[σ(1.59Re+9.31)], is introduced to characterize the particle migration. It is discovered that the particle's equilibrium position depends on whether it migrates to the top wall or remains suspended in the shear flow under the isothermal condition. For the former case, when thermal convection is introduced, the particle stays at the top wall when Gr∗<1, and becomes suspended in the channel when Gr∗>1.