Dry granular flows down an inclined channel: experimental investigations on the frictional-collisional regime

This paper presents experimental results on dry granular flows down an inclined rough channel. Different flow regimes were identified depending on the Froude number. For Froude numbers exceeding a critical value (function of the channel slope), flow was characterized by a fairly linear velocity profile and a discharge equation in the form q varies with h(n) with q the flow rate per unit width, h the flow depth, and n an exponent in the range 2-3 (regime A). When the Froude number was lower than the critical value, the flow was characterized by a convex velocity profile and a discharge equation of the form q varies with h(n), with n ranging from 0.97 to 1.16, producing the striking result that the mean velocity was constant for a given inclination of the channel (regime B). Experimental data were used to test three theoretical models developed to describe dry granular flows in a frictional-collisional regime. Savage's model provides results that capture experimental trends well and yield the correct magnitude for velocity and discharge for regime A, but it reproduces the dependence of the discharge on the channel slope for only a narrow range of slopes [S. B. Savage, in U.S./Japan Seminar on New Models and Constitutive Relations in the Mechanics of Granular Materials, Ithaca, 1982, edited by J. T. Jenkins and M. Satake (Elsevier Science Publishers, Amsterdam, 1982), p. 261]. In contrast, Mills et al.'s model is less refined and requires fitting an input parameter to give the correct magnitude of velocity but it successfully accounts for the variation in the discharge with slope for regime A for a wide range of slopes [Mills, Loggia, and Tixier, Europhys. Lett. 45, 733 (1999); Eur. Phys. J. E 1, 5 (2000)]. Ancey and Evesque's model is also crude in determining the density profile but manages to provide velocity profiles and discharge equations in good agreement with experimental data for regime B [C. Ancey and P. Evesque, Phys. Rev. E 62, 8349 (2000)].