Lateral force on a rigid sphere in large-inertia laminar pipe flow

We present a prediction of the lateral force exerted on a rigid neutrally buoyant sphere in circular cross-section Poiseuille flow. The force is calculated with the method of matched asymptotic expansions. We investigate the influence of the pipe Reynolds number in the range 1-2000 on the equilibrium position and the magnitude of the lateral force. We show that the predicted lift force in a circular geometry is qualitatively similar to, but quantitatively different from, that in a plane channel. The predicted force in the pipe is significantly smaller than the channel result, and the zero of the force which determines the equilibrium radial position of a suspended particle lies closer to the centreline in the pipe.