Abstract
Two-dimensional Stokes flow around a circular cylinder in a microchannel is investigated based on Stokes approximation. The cylinder with arbitrary radius translates along the centerline of the channel, and plane Poiseuille flow exists upstream and downstream from the cylinder. The translating velocity of the cylinder and the magnitude of the Poiseuille flow are arbitrary. The Stokes flow is examined analytically using Papkovich-Fadle eigenfunction expansion and least square method. The stream function and the pressure distribution of the flow field are obtained and shown for some typical cases. The force exerted on the cylinder and the pressure drop due to the cylinder are calculated as functions of the radius of the cylinder. For a small radius of the cylinder, the results of the force are coincident with previous asymptotic expressions for the force. For a given average velocity of the Poiseuille flow in the channel, translational drift velocity of the cylinder is determined as a function of blockage factor. The drift velocity is slightly lower than the mean velocity of the Poiseuille flow component projected by the cylinder. The induced pressure drop due to the drifting cylinder in the Poiseuille flow is quite small. When the cylinder translates in the stagnant channel, a series of Moffatt eddies appears far from the cylinder in the channel, as expected. The size of the primary eddy increases with the radius of the cylinder.
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