Physics-based analysis of the hydrodynamic stress in a fluid-particle system

The paper begins by showing how standard results on the average hydrodynamic stress in a uniform fluid-particle system follow from a direct, elementary application of Cauchy's stress principle. The same principle applied to the angular momentum balance proves the emergence, at the mesoscale, of an antisymmetric component of the volume-averaged hydrodynamic stress irrespective of the particle Reynolds number. Several arguments are presented to show the physical origin of this result and to explain how the averaging process causes its appearance at the mesoscale in spite of the symmetry of the microscale stress. Examples are given for zero and finite Reynolds number, and for potential flow. For this last case, the antisymmetric stress component vanishes, but the Cauchy principle proves nevertheless useful to derive in a straightforward way known results and to clarify their physical nature. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3365950]