(21f) Dynamics of Surface Flow during Heap Formation

Surface flows comprise a shallow layer of material flowing over a static region of the same material. These flows are important in nature in phenomena such as lava flow, avalanches, sedimentation at river bed , sand dunes as well as in industrial processes like transportation of material, storage in silos and mixing in rotary kilns. The flow rate is the only independent parameter in such flows and the interface between the flowing layer and static region depends on the flow, determining the surface angle and the depth of flowing layer.

Steady state surface flows have been studied by means of experiments in heaps and rotating cylinders [1-5] but transient behavior of such flows have not been studied much. du Pont et al. [6] looked at the instantaneous velocity profile within the flowing layer during avalanches in a rotating cylinder. The velocity profile is found to be purely exponential over the depth. The profiles are found to be self-similar with a decay length independent of time.

To model surface flows, depth averaged conservation equations defined over the surface layer have been widely used in literature [7-10]. The system is not a closed one as there is interchange of material between the flowing and the static regime. The rate of erosion of the bed or deposition on the bed is dependent on interchange velocity and is an important factor for surface flows. The interchange velocity is predicted by different models based on various assumptions. Experimental determination of interchange velocity during transient flow can serve as a robust tool to examine the models.

Here we present an experimental study of transient flow during heap formation in a quasi 2D open heap system. The objective of the work is to gain an understanding of the rate of deposition and erosion in surface flows. Using video photography and image analysis technique we have determined the spatio-temporal variation of macroscopic properties like height of the free surface and interface, layer thickness, interchange velocity, mean velocity and local flux. The variation of the parameters during the process shows a qualitatively similar behavior over the entire range (35 g/s - 160 g/s) of mass flow rate studied. All the parameters show a sudden change immediately after outflow begins. Steady state angle of repose is found to increase with mass flow rate. It is found that time scale of the process is inversely proportional to the mass flow rate. Some of the existing theoretical models [7-10] are compared with the experimental results.

References

1. D. Bonamy, F. Daviaud and L. Laurent, Experimental study of granular surface flows via a fast camera: A continuous description, Phys. Fluids, 14 (2002), 1666-1673.
2. N. Jain, J. M. Ottino and R. M. Lueptow, An experimental study of the flowing granular layer in a rotating tumbler, Phys. Fluids, 14 (2002), 572-582.
3. N. Taberlet, P. Richard, A. Valance, W. Losert, J. M. Pasini, J. T. Jenkins and R. Delannay, Superstable granular heap in a thin channel, Phys. Rev. Lett., 91 (2003), 264301.
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6. S. Courrech du Pont, R. Fischer, P. Gondret, B. Perrin and M. Rabaud, Instantaneous velocity profiles during granular avalanches, Phys. Rev. Lett., 94 (2005), 048003.
7. J. P. Bouchad, M. Cates, J. Ravi Prakash and S. F. Edwards, A model for the dynamics of sandpile surface, J. Phys. Paris I, 4 (1994), 1383-1409.
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