To contribute to the existing knowledge of the
hydrodynamic force exerted on a spherical particle placed in the
axis of a cylinder, at small Reynolds numbers, the influence of
the uniform and Poiseuille flows on the wall correction factor are
numerically and asymptotically investigated. The Stokes and
continuity equations are expressed in the stream function and
vorticity formulation and are rewritten in an orthogonal system of
curvilinear coordinates. These equations are solved using a
finite differences method. The generation of the grid was carried
out by the singularities method. The accuracy of the numerical
code is tested through comparison with theoretical and
experimental results. In both cases we numerically calculated the
separate contributions of the pressure and viscosity forces. In
concentrated regime these numerical calculations are in very good
agreement with those obtained by asymptotic expansions. This
analysis allowed us to show the prevalence of the pressure term
over the viscosity one in the lubrication regime contrary to what
happened for the dilute regime. All our numerical and asymptotical
results compared with those of Bungay et al. (Int. J. Multiphase Flow 1,
25–56 (1973)) seem to give a response to this problem argued for a long time.