Drag on two coaxial rigid spheres moving along the axis of a cylinder filled with Carreau fluid

The boundary effect on the drag on two identical, rigid spheres moving along the axis of a long cylinder filled with a Carreau fluid for Reynolds number ranges from 0.1 to 40 is investigated. The influences of the key parameters of the problem under consideration, including the separation distance between two spheres, the relaxation time constant and the power-law index of a Carreau fluid, the Reynolds number, and the ratios (radius of sphere/radius of cylinder), on the drag acting on two spheres are investigated. We show that the boundary effect for the present case is more significant than that for the corresponding Newtonian fluid. The presence of the cylinder has the effect of enhancing the convective motion in the rear part of a sphere, thereby forming wakes and a reverse flow field, and this phenomenon is enhanced by the shear-thinning nature of a fluid. If the boundary effect is insignificant, the shear-thinning nature of a fluid has the effect of reducing the deviation of the ln(drag coefficient)-ln(Reynolds number) curve from a Stokesʹ-law-like relation. On the other hand, if it is significant, this deviation has a local minimum as the shear-thinning nature of a fluid varies.