Using finite difference methods, we study numerically the dynamics of a single spherical object (cylinder) in a two-dimensional box filled with viscous fluid under the influence of gravity. The algorithm is validated using the analytic result of the terminal velocity ${\mathrm{U}}_{\mathrm{\infty }}$ in the creeping flow limit. We focus on the dependence of ${\mathrm{U}}_{\mathrm{\infty }}$ on the cylinder diameter D and the box size L. By extrapolating the numerically obtained terminal velocities to the Stokes' limit L→∞ (D/L→0) for various cylinder diameters, we seek a universal relation ${\mathrm{U}}_{\mathrm{\infty }}$(D/L)=${\mathrm{U}}_{\mathrm{\infty }}$(0)f(D/L) in analogy to the three-dimensional result for spheres in the creeping flow limit. We will present f(D/L) as power series in D/L, and discuss its validity.

DOI:https://doi.org/10.1103/PhysRevE.55.2808