A full description of generalized drag in mixture mass flows

Drag plays an important role in the dynamics of mixture mass flows composed of viscous fluid and solid particles. Such flows often take place in environmental and engineering problems. We have analytically derived an enhanced generalized drag that completely describes the drag for any solid volume fraction in mixture mass flows. This provides a full analytical solution and physical basis for the dynamically evolving complex drag. Previous drag formulations were restricted, and produced singularities for large values of the solid volume fraction. Our new model removes singularity inherited by existing models. The analytical model shows different behavior for larger and smaller values of the solid volume fraction, and reveals a smooth variation of the drag coefficient as the solid volume fraction evolves during the flow. Dense to dilute distribution of particles in the mixture, mass flux and material parameters, including particle and fluid densities, characterize the new extended model that strongly determine the drag curve. In contrast to the previous models which tend to show singularity, the most important aspect of the new drag function is that, for any value of the solid fraction, it is sufficiently smooth. We highlight the importance of the new enhanced generalized drag model by comparing it with existing models. A strikingly new understanding is that for some values of the solid volume fraction, the drag takes its maximum, and then, decreases on either side of that particular value. Depending on the dilute to dense flows, two fundamentally different families of asymmetrical drag curves emerge. We have explained the physics behind these special behaviors of drag. With a benchmark simulation, we show that the new enhanced drag offers a great opportunity for the better and full dynamical simulation of a wide range of mixture mass flows. As the new. generalized drag reveals many essential physical phenomena, this can be applied in appropriately solving some challenging environmental and engineering problems related to complex multi-phase mixture mass flows including landslide and debris flows.