The inertial migration of a neutrally buoyant particle in a rectangular pipe is investigated by lattice Boltzmann simulations. The hydrodynamic force on the particle is evaluated by the method of stress-integration and the sphere surface mesh generation technique. The lift forces at different positions, which are a component of the hydrodynamic forces and are vertical to the x-axis at steady state in constrained simulations, are calculated numerically. The particle equilibrium position is deduced at the point of zero lift force, and a stable or unstable equilibrium position is obtained by analyzing the lift force near the point of zero lift force. The dependence of the particle size and flow Reynolds number on the particle equilibrium positions is investigated. The lift force can be used to predict the moving behaviour of the particle confined by more complicated walls.
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