Buoyant flows

In real two-phase (debris) mass flows there exists a strong coupling between the solid and the fluid momentum transfer, where the solid's normal stress is reduced by buoyancy, which in turn diminishes the frictional resistance, enhances the pressure gradient, and reduces the drag on the solid component. Buoyancy is an important aspect of two-phase debris flow, because it enhances flow mobility (longer travel distances) by reducing the frictional resistance in the mixture. Buoyancy is present as long as there is fluid in the mixture. It reduces the solid normal stress, solid lateral normal stresses, and the basal shear stress (thus, frictional resistance) by a factor ($1-\gamma$), where $\gamma$ is the density ratio between the fluid and the solid phases. The effect is substantial when the density ratio ($\gamma$) is large (e.g., in the natural debris flow).

If the flow is neutrally buoyant, i.e., $\gamma =1$, (see, e.g., Bagnold, 1954) the debris mass is fluidized and moves longer travel distances. This can happen in highly viscous natural debris flows. For neutrally buoyant flows, Coulomb friction disappears, the lateral solid pressure gradient vanishes, the drag coefficient is zero, and the basal slope effect on the solid phase also vanishes. In this limiting case, the only remaining solid force is due to gravity, and thus the force associated with buoyancy. Under these conditions of hydrodynamic support of the particles by the fluid, the debris mass is fully fluidized (or lubricated) and moves very economically, promoting long travel distances. Compared to buoyant flow, the neutrally buoyant flow shows completely different behaviour. For the latter case, the solid and fluid phases move together, the debris bulk mass is fluidized, the front moves substantially farther, the tail lags behind, and the overall flow height is also reduced. When $\gamma =0$, the flow does not experience any buoyancy effect. Then the effective frictional shear stress for the solid phase is that of pure granular flow. In this case the force due to the pressure gradient is altered, the drag is high and the effect of the virtual mass disappears in the solid momentum. All this leads to slowing down the motion.