General Definition of Particle-fluid-particle Stress in Multiphase Flows

Particle-particle interactions result in a stress in a dense system. For systems containing small amount of viscous liquids, the particle interaction becomes particle-fluid-particle interaction through the liquid bridges between particles. In this case we have clear definition of the particle-fluid-particle stress which appears in the momentum equation for the particle phase. As the liquid amount increases, the liquid bridges cannot be clearly identified, while there is no reason for the particle-fluid-particle stress to disappear from the momentum equation.

In this presentation, we start from the ensemble averaging method to show that the stress can be defined using particle forces conditionally averaged on the nearest neighbor. These forces are not necessary interaction forces between particles, but statistical correlations given the nearest pair. The assumption of pair interaction is not necessary; therefore, this definition is valid for finite volume fractions. The stress is defined as an integral over the space surrounding a particle. The use of the nearest neighbor quantities ensures convergence of the integral.