An Application Of The Hanks Stability Parameter For The Macroviscous-inertial Transition In The Surface Flow Of A Neutrally Buoyant Suspension

This paper focuses on the evaluation of the regime transition in the surface flow of a neutrally buoyant suspension. The revisiting of the 1954 Bagnold paper made by Hunt et al. (2002) showed that the choice of the non-dimensional parameter afterwards known as Bagnold number for evaluating the transition between macroviscous and grain-inertial regime is at least doubtful. Here, a different approach, based on the universal stability parameter of Hanks (1963a, b), is proposed. The application of this transition criterion to the case of the incompressible uniform surface flow of a liquid-solid mixture shows that the Reynolds number is the parameter that really controls the transition between the flow regimes. The critical value of the Reynolds number is a function of the solid volume fraction of the mixture. This value is derived assuming that the critical value of the Hanks stability parameter does not change when referring to the ensemble averaged momentum equations of the continuous phase rather than to the classical Navier-Stokes equations. The present analysis shows that highly concentrated neutrally buoyant suspensions can be characterized by the macroviscous regime even if the Reynolds number is not small, up to an order of 10 5 . Thus, one should pay attention in applying at real scale laws obtained through experiments performed at laboratory scale.