In non-Newtonian fluids, the mass or heat transfer on particles are of major interest in many industrial processes using suspensions such as fluidized beds or microfluidics reactors. In all these problems we often face hydrodynamic and mass or thermal interactions between a single particle and others or between a single particle and some walls. In this study, such confined configurations can be modeled by a spherical particle translating parallel to the axis of a cylindrical tube. As the suspending fluid may be non-Newtonian, and before examining any possible additional viscoelastic effect on suspension, the first step in the understanding of the consequences of the principal non-Newtonian behavior is the study of the shear thickening or shear thinning (power law model) regarding the transfer phenomena. Then, when the particle translates along the axis of the tube in symmetrical configuration, we numerically solved the momentum and mass (or heat) transfer equations using the stream/vorticity functions formulation coupled to the singularity technique in order to make a numerical conformal mapping for the mesh. For Newtonian fluids, the successful comparisons firstly between our numerical results and asymptotical solutions obtained by us in the lubrication regime, and secondly between our results and those obtained by other authors in unlimited medium, confirm the validity of our approach. Thereby we extended this method to power law fluids. As the geometrical distribution of particles in suspensions is not at all symmetric, we study the influence of some geometrical disturbance breaking the symmetry of the system. To answer this question, we numerically investigate, using the finite volume method, the simple configuration of single spherical particles translating parallel to and in the off-axis position in the tube.
