Modeling the phase interaction in the momentum equations of a fluid-solid mixture

Abstract

The phase interaction term in the momentum equations for the flow of a fluid-solid mixture is derived using a control volume/control surface approach. This approach has been used by the authors in an earlier work to obtain the solid phase stress. An extension of this approach provides a consistent derivation for the necessary constitutive equations for a laminar flow of a dilute fluid-solid mixture. A fundamental difference is observed between the present model and other models in the literature. The diffusion/anti-diffusion phenomenon caused by the concentration gradient is discussed. The resulting governing equations are applied to the case of a vertical flow where the phase interaction term is first evaluated according to a previous model in the literature, and then to the one presently obtained. The resulting solutions show that a significant difference exists in the flow behavior described by the two solutions.