Experimental study on the equilibrium position of a falling sphere in a circular tube flow

At the low slip Reynolds numbers (Re_s) range, a falling sphere in a tube flow is usually expected to approach an equilibrium position along the tube axis monotonically. In the present work, an unusual phenomenon is observed experimentally in quiescent and flowing fluids, where an irrotational sphere falls along an off-axis straight line. The sphere-tube diameter ratios (λ) are 0.186–0.403, and the Re_s are 36 - 169, calculated based on the slip velocities and the diameters of the spheres. The results reveal that the equilibrium position is related to sphere size and flow conditions. In the quiescent fluid case, the radial equilibrium position of a sphere gradually shifts toward the axis as the sphere size increases. In the flowing fluid, the equilibrium position of a sphere exhibits two different tendencies—a small sphere moves toward the axis with increasing channel Reynolds numbers Re_t, while a large sphere migrates toward the wall. In addition, an examination of the variation in the drag coefficients of the spheres in different flow conditions reveals that the drag coefficient of a sphere decreases in a tube flow compared with quiescent fluid.