Granular surface flows are important in industrial practice and natural systems, but the understanding of such flows is at present incomplete. We present a combined theoretical and experimental study of quasi-two-dimensional heap formation by pouring particles continuously at a point. Two cases are considered: open systems and closed systems. Experimental results show that the shear rate in the flowing layer is nearly independent of the mass flow rate, and the angle of static friction at the bed–layer interface increases with flow rate. Predictions of the model for the flowing layer thickness and interface angles are in good agreement with experiments.

An experimental study of the flow of different materials ͑steel balls, glass beads, and sand͒ in quasi-twodimensional rotating cylinders is carried out using flow visualization. The flow in the rotating cylinder comprises of a thin-flowing surface layer with the remaining particles rotating as a fixed bed. Experimental results indicate that the scaled layer thickness increases with increasing Froude number (Frϭ 2 R/g, where is the angular speed, R is the cylinder radius, and g the acceleration due to gravity͒ and with increase in size ratio (sϭd/R, where d is the particle diameter͒. The free surface profile, is nearly flat at low Fr and becomes increasingly S shaped with increasing Fr. The layer thickness profiles, which are symmetric at low Fr become skewed at high values of Fr and small s. The dynamic angles of repose for all the materials studied show a near-linear increase with rotational speed (). Scaling analysis of the experimental data shows that the shape of the scaled surface profiles and the scaled layer thickness profiles are nearly identical when Froude number and size ratio are held constant, for each material. The surface profiles and layer thickness profiles are also found to be nearly independent of the material used. The dynamic angle of repose (␤), however, does not scale with Fr and s and depends on the particle properties. The experimental results are compared to continuum models for flow in the layer. The models of Elperin and Vikhansky ͓Europhys. Lett. 42, 619 ͑1998͔͒ and Makse ͓Phys. Rev. Lett. 83, 3186 ͑1999͔͒ show good agreement at low Fr while that of Khakhar et al. ͓Phys. Fluids, 9, 31 ͑1997͔͒ gives good predictions over the entire range of parameters considered. An analysis of the data indicate that the velocity gradient (␥ ) is nearly constant along the layer at low Fr, and the value calculated at the layer midpoint varies as ␥ 0 ϰ͓g sin(␤ 0 Ϫ␤ s )/d cos ␤ s ͔ 1/2 for all the experimental data, where ␤ s is the static angle of repose and ␤ 0 is the interface angle at the layer midpoint. An extension of ''heap'' models ͑BCRE, BRdG͒ is used to predict the interface angle profiles, which are in reasonable agreement with experimental measurements.

Motivated by examples of erosive incision of channels in sand, we investigate the motion of individual grains in a granular bed driven by a laminar fluid to give us new insights into the relationship between hydrodynamic stress and surface granular flow. A closed cell of rectangular cross-section is partially filled with glass beads and a constant fluid flux Q flows through the cell. The refractive indices of the fluid and the glass beads are matched and the cell is illuminated with a laser sheet, allowing us to image individual beads. The bed erodes to a rest height h r which depends on Q. The Shields threshold criterion assumes that the non-dimensional ratio θ of the viscous stress on the bed to the hydrostatic pressure difference across a grain is sufficient to predict the granular flux. Furthermore, the Shields criterion states that the granular flux is non-zero only for θ > θ c . We find that the Shields criterion describes the observed relationship h r ∝ Q 1/2 when the bed height is offset by approximately half a grain diameter. Introducing this offset in the estimation of θ yields a collapse of the measured Einstein number q * to a power-law function of θ − θ c with exponent 1.75 ± 0.25. The dynamics of the bed height relaxation are well described by the power law relationship between the granular flux and the bed stress.

We show that the velocity correlations in uniform dense granular flows inside a silo are similar to the hydrodynamic response of an elastic hard-sphere liquid. The measurements are made using These effects were later described by hydrodynamic and mode-coupling theories [4,5], and are said to be in excellent agreement with direct observations in colloidal systems [6,7]. Thus correlations are observed even in simple dense liquids where particles interact elastically.In granular systems, because inelasticity and friction is important whenever grains come The experimental apparatus consists of a glass silo chamber with dimensions shown in Fig. 1(a). Glass beads with diameter d = 1 ± 0.1 mm drain from the silo into a bottom collecting chamber through an exit slot. The flow rate is set by varying the width w of the slot. A minimum width (w = 3.25d) was needed to observe steady flow, and the data reported here was obtained for w = 3.5d, 4d, 5d and 6d. To measure the flow away from the sidewalls, the entire system is immersed in an interstitial fluid [16] with the same refractive index (≈ 1.52) as the glass beads. The fluid displaced in the bottom chamber is channeled through a mesh via side chambers (not shown) into the silo at the top. This arrangement was found to effectively reduce counter flow of the interstitial fluid through the exit slot.The grains are visualized by adding a fluorescent dye to the fluid [14]. As illustrated in Fig. 1(a), a plane inside the silo, which is less than 0.1d thick, is illuminated using a 50-mW laser and a cylindrical lens, and imaged through the front wall with a digital camera.Typical images for two different planes, wherein the particles appear dark against a bright background, are shown in insets to Fig. 1(b),(c). The apparent size of the particles depends

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