Félix G, Falk V, D'Ortona U
Laboratoire des Sciences du Génie Chimique, UPR 6811, CNRS, BP451, ENSIC, INPL, 1 rue Grandville, 54000 Nancy, France.
Eur Phys J E Soft Matter. 2007 Jan;22(1):25-31. doi: 10.1140/epje/e2007-00002-5. Epub 2007 Feb 16.
The flow of dry granular material in a half-filled rotating drum is studied. The thickness of the flowing zone is measured for several rotation speeds, drum sizes and beads sizes (size ratio between drum and beads ranging from 47 to 7400). Varying the rotation speed, a scaling law linking mean velocity vs. thickness of the flow, v approximately h(m), is deduced for each couple (beads, drum). The obtained exponent m is not always equal to 1, the value previously reported for a drum in litterature, but varies with the geometry of the system. For small size ratios, exponents higher than 1 are obtained due to a saturation of the flowing zone thickness. The exponent of the power law decreases with the size ratio, leading to exponents lower than 1 for high size ratios. These exponents imply that the velocity gradient of a dry granular flow in a rotating drum is not constant. More fundamentally, these results show that the flow of a granular material in a rotating drum is very sensible to the geometry, and that the deduction of the "rheology" of a granular medium flowing in such a geometry is not obvious.
研究了半满旋转鼓中干燥颗粒材料的流动情况。针对几种不同的转速、鼓尺寸和珠子尺寸（鼓与珠子的尺寸比范围为47至7400）测量了流动区域的厚度。通过改变转速，针对每一对（珠子、鼓）推导出了一个将平均速度与流动厚度联系起来的标度律，即v约为h(m)。所得到的指数m并不总是等于1（文献中先前报道的鼓的值），而是随系统的几何形状而变化。对于小尺寸比，由于流动区域厚度的饱和，得到的指数高于1。幂律的指数随尺寸比减小，导致大尺寸比时指数低于1。这些指数意味着旋转鼓中干燥颗粒流的速度梯度不是恒定的。更根本的是，这些结果表明颗粒材料在旋转鼓中的流动对几何形状非常敏感，并且推导在这种几何形状中流动的颗粒介质的“流变学”并非易事。
