Abstract
The present experimental study examines the behaviour of slow granular flows, focusing on the details of particle patterns and motions over the depth of a sheared layer. A conveyor belt circuit enclosed in an inclined flume is used to generate steady uniform open-channel flows of dry granules. Particle positions near the transparent sidewall are extracted from video sequences. The Voronoï diagram is then used to characterise the configurations formed by neighbouring grains and to assist particle tracking over successive frames. This allows a qualitative visualisation of the internal structure of the flowing layer, as well as quantitative measurements of lattice defect density and granular velocities at different depths. The response of the depth profiles to different conveyor belt speeds is examined. In addition to the mean and fluctuating velocities, we probe the time and space correlations of the fluctuations.
Similar content being viewed by others
References
Jenkins, J.T., Savage, S.B.: A theory for the rapid flow of identical, smooth, nearly elastic particles. J. Fluid Mech. 130, 186–202 (1983)
Azanza, E., Chevoir, F., Moucheront, P.: Experimental study of collisional granular flows down an inclined plane. J. Fluid Mech. 400, 199–227 (1999)
Zhang, Y., Campbell, C.S.: The interface between fluid-like and solid-like behavior in two-dimensional granular flows. J. Fluid Mech. 237, 541–568 (1992)
Aharonov, E., Sparks, D.: Rigidity phase transition in granular packings. Phys. Rev. E , 60(6), 6890–6896 (1999)
Savage, S.B.: Analyses of slow high-concentration flows of granular materials. J. Fluid Mech. 377, 1–26 (1998)
Pouliquen, O., Forterre, Y., Le Dizes, S.: Slow dense granular flows as a self-induced process. Adv. Complex Systems. 4(4), 441–450 (2001)
Davies, T.R.H.: Debris flow surges – a laboratory investigation. Mitteilungen der Versuchsanstalt für Wasserbau, Hydrologie und Glaziologie, Nr. 96, ETH Zürich, (1988)
Hübl, J., Steinwendtner, H.: Estimation of rheological properties of viscous debris flow using a belt conveyor. Phys. Chem. Earth B, 25(9), 751–755 (2000)
Jain, N., Ottino, J.M., Lueptow, R.M.: An experimental study of the flowing granular layer in a rotating tumbler. Phys. Fluids 14(2), 572–582 (2002)
Hsiau, S.S., Shieh, Y.M.: Fluctuations and self-diffusion of sheared granular material flows. J. Rheol. 43, 1049–1066 (1999)
Drake, T.G.: Structural features in granular flows. J. Geophys. Res. 95(B6), 8681–8696 (1990)
Okabe, A., Boots, B., Sugihara, K.: Spatial Tesselations: Concepts and Applications of Voronoï Diagrams. Wiley, (1992)
Richard, P., Oger, L., Lemaitre, J., Samson, L., Medvedev, N.N.: Application of the Voronoï tesselation to study transport and segregation of grains inside 2D and 3D packings of spheres. Gran. Matter 1, 203–211 (1999)
Capart, H., Young, D.L., Zech, Y.: Voronoï imaging methods for the measurement of granular flows. Exp. Fluids 32, 121–135 (2002)
Bonamy, D., Daviaud, F., Laurent, L., Mills, P.: Texture of granular surface flows: experimental investigation and biphasic non-local model. Gran. Matter 4, 183–190 (2003)
Spinewine, B., Capart, H., Larcher, M., Zech, Y.: Three-dimensional Voronoï imaging methods for the measurement of near-wall particulate flows. Exp. Fluids 34, 227–241 (2003)
Allen, M.P., Frenkel, D., Gignac, W.: A Monte Carlo simulation study of the two-dimensional melting mechanism. J. Chem. Phys. 78(6), Part II: 4206–4222 (1983)
Kenkel, N.C., Hoskins, J.A., Hoskins, W.D.: Edge effects in the use of area polygons to study competition. Ecology 70, 272–274 (1989)
Adrian, R.J.: Particle-imaging techniques for experimental fluid mechanics. Annu. Rev. Fluid Mech. 23, 261–304 (1991)
Guler, M., Edil, T.B., Bosscher, P.J.: Measurement of particle movement in granular soils using image analysis. J. Comp. Civ. Eng. 13(2), 116–122 (1999)
Veber, P., Dahl, J., Hermansson, R.: Study of the phenomena affecting the accuracy of a video-based Particle Tracking Velocimetry technique. Exp. Fluids 22, 482–488 (1997)
Armanini, A., Capart, H., Fraccarollo, L., Larcher, M.: Rheological stratification in experimental free-surface flows of granular-liquid mixtures. J. Fluid Mech. 532, 269–319 (2005)
van Noije, T.P.C., Ernst, M.H.: Cahn-Hilliard theory for unstable granular fluids. Phys. Rev. E, 61(2), 1765–1782 (2000)
Utter, B., Behringer, R.P.: Self-diffusion in dense granular shear flows. Phys. Rev. E, 69, 031308–1–12 (2004)
Campbell, C.S.: Self-diffusion in granular shear flows. J. Fluid Mech. 348, 85–101 (1997)
Savage, S.B., Dai, R.: Studies of granular shear flows. Wall slip velocities, 'layering' and self-diffusion. Mech. Mater. 16, 225–238 (1993)
Le Caer, G., Ho, J.S.: The Voronoï tesselation generated from eigenvalues of complex random matrixes. J. Phys. A, 23, 3279–3295 (1990)
Caram, H., Hong, D.C.: Random-walk approach to granular flows. Phys. Rev. Lett. 67(7), 828–831 (1991)
Rouse, H.: Modern conceptions of the mechanics of fluid turbulence. Trans. ASCE 102, 532–536 (1937)
Kelley, W.G., Peterson, A.C.: Difference equations. Harcourt Academic Press, (2001)
Campbell, C.S.: The stress tensor for simple shear flows of a granular material. J. Fluid Mech. 203, 449–473 (1989)
Wildman, R.D., Huntley, J.M., Hansen, J.-P.: Self-diffusion of grains in a two-dimensional vibrofluidized bed. Phys. Rev. E, 60(6), 7066–7075 (1999)
Batchelor, G.K.: The Theory of Homogeneous Turbulence. Cambridge Univ. Press, (1970)
Alder, B.J., Wainwright, T.E.: Decay of the velocity autocorrelation function. Phys. Rev. A, 1(1), 18–21 (1970)
Isobe, M.: Velocity statistics in two-dimensional granular turbulence. Phys. Rev. E, 68, 040301–1–4 (2003)
Author information
Authors and Affiliations
Additional information
A. T. H. Perng - Former affiliation: Department of Civil Engineering, National Central University, Taiwan
Rights and permissions
About this article
Cite this article
Perng, A., Capart, H. & Chou, H. Granular configurations, motions, and correlations in slow uniform flows driven by an inclined conveyor belt. Granular Matter 8, 5–17 (2006). https://doi.org/10.1007/s10035-005-0213-2
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10035-005-0213-2