Abstract
We have used a finite-difference scheme to solve the Navier-Stokes equations for the steady flow inside and outside viscous spheres in a fluid of different properties. Hence, we obtained the hydrodynamic forces and the steady-state drag coefficient of the spheres. The computational technique we have used enables us to extend the results to Reynolds numbers between 0 and 1,000. The viscosity ratio of the computations ranges between 0 (inviscid bubble) and infinity (solid particle). The method presented here makes use of a two-layer concept for the computational domain outside the sphere. The first layer is a very thin one [O(Re−1/2)] and is positioned at the interface of the sphere. The second layer is based on an exponential function and covers the rest of the domain. The computations yield the friction and the form drag of the sphere. It is observed that both the Reynolds number and the viscosity ratio play a major role on the value of the hydrodynamic force and the drag coefficient. If all other conditions are the same, there is a negligible effect of the density ratio on the drag coefficient of viscous spheres.
