Lateral migration of a neutrally buoyant particle in Couette flow with thermal convection

•The equilibrium position is located below the centerline when both walls are hot.•The equilibrium positions are well characterised by the Richardson number and size ratio.•Bifurcation of the equilibrium position occurs when the temperature of two walls are different.•The critical Reynolds number at the transition point follows a power law of the size ratio.A numerical investigation of lateral migration of a neutrally buoyant particle in Couette flow with two different thermal boundary conditions is performed using a lattice Boltzmann method coupled with a discrete element method. The effects of the channel Reynolds number (Re), the Grashof number (Gr) as well as the particle size on the migration behaviour are explored in detail. It was found that when both the top and bottom walls are hot, the equilibrium positions are located below the centerline for all the particle sizes studied, which can be well characterised using a dimensionless force ratio determined by the Richardson number (Ri=Gr/Re2) and the confinement ratio. With the increase of the force ratio, the equilibrium position moves towards the bottom wall. On the other hand, when the top wall is cold and the bottom wall is hot, a transition of the equilibrium position is observed, which switches from below the centerline to above the centerline as the particle size is increased above a certain threshold. It is discovered that the critical Reynolds number at transition can be well described by a power law of the confinement ratio. Furthermore, it is also found that the variation of the equilibrium positions above the centerline is governed by a new dimensionless parameter Gr/Re for a fixed particle size, which is attributed to the finite size effect