Depth-averaged relations for granular-liquid uniform flows over mobile bed in a wide range of slope values

The behavior of liquid-granular flows, driven by gravity, is experimentally analyzed. Two types of free-surface uniform flow can take place, having different boundary conditions at the bottom. The first one runs over a fixed surface behaving as a solid (non-deformable) impermeable wall; the second one runs over a mobile-bed at rest, formed by the same loose grains and liquid of the flowing mixture. In the paper we will mark the differences between the two, but focus on the latter one. The experiments span over, and characterize, the possible flow regimes. In mobile-bed uniform flows it has been found that the Froude number reduces as the slope increases. Accordingly, there is an increment of the solid-concentration. These results are meaning that as slope increases a progressive dominance and thickening of frictional layers over collisional ones is taking place through the flow depth. Same behaviours have been observed by changing the type of grains in the flowing mixture. These findings contrast with the case of flows over a solid wall, where different trends are observed. Application of force balances by means of Coulomb law provides interesting confirmation of what observed and allows to take into account the surface-tension effects, which come into play when the particles on top are going to desaturate. Experimental data have also been employed to assess the applicability of kinetic theories to wet granular flows. Energy and momentum balances, under the hypothesis of no contribution in the liquid phase (except for the added mass concept) to shear stress and to the energy processes, are applied throughout the flow depth of the solid phase. Although depth-averaged quantities come out to have a trend similar to the experimental one, deficiencies in the theoretical approach, mainly due to its inability to represent frictional contacts, are clearly detected. Same conclusions may be drawn by applying the quite simple Bagnold theory. Altogether, a more appropriate theory able to deal with both collisional and frictional mechanisms, including the transition between, is demanded.