Slow motion of a circular cylinder in a plane Poiseuille flow in a microchannel

The slow motion of a circular cylinder in a plane Poiseuille flow in a microchannel is analyzed for a wide range of cylinder radii and positions across the channel. The cylinder translates parallel to the channel walls and rotates about its axis. The Stokes approximation is used and the problem is solved analytically using the Papkovich-Fadle eigenfunction expansion and the least-squares method. The stream function and the pressure distribution of the flow field are obtained as results. The force and moment exerted on the cylinder, and the pressure change far from the cylinder, are calculated and shown as functions of the size and location of the cylinder. The results confirm some reciprocal relations exactly. In particular, the translational and rotational velocities of the drifting cylinder in the existing Poiseuille flow are determined. The induced pressure change, when the cylinder drifts in the Poiseuille flow, is also calculated. Some typical streamline patterns, depending on the size and location of the cylinder, are shown and discussed. When the cylinder translates and/or rotates in the channel blocked at infinity, a series of Moffatt eddies appears far from the cylinder in the channel, as expected. (C) 2014 AIP Publishing LLC.