Drag force on a circular cylinder midway between two parallel plates at Re ≪ 1 Part 2: moving uniformly (numerical and experimental)

To contribute to the determination of the hydrodynamic interactions between a long straight circular cylindrical particle and flow boundaries, we calculate the wall correction of the drag force exerted on a circular cylinder moving uniformly midway between two parallel plane walls, at very low Reynolds numbers. The wall correction factor is numerically and asymptotically investigated. Furthermore, we present a new experimental results for the drag force exerted on this straight circular cylinder. The Navier–Stokes and continuity equations are expressed in the stream function and vorticity formulation and are rewritten in an orthogonal system of curvilinear co-ordinates. These equations are solved with a finite-differences method. The accuracy of the numerical code is tested successfully through a comparison with theoretical and experimental results. In the lubrication regime the numerical calculations of the pressure and viscosity forces are in very good agreement with those obtained by asymptotic expansions. Combining the present results with those obtained in Poiseuille flow (Chem. Eng. Sci. 59 (15, part 1) (2004) 3215) we give the speed at which a force-free cylindrical particle would move with the fluid perpendicularly to it's axis between two planar walls in Poiseuille flow and corrected by wall effects.