Khan Zeina S, Morris Stephen W
Department of Physics, University of Toronto, 60 St. George Street, Toronto, Ontario, Canada M5S 1A7.
Phys Rev Lett. 2005 Feb 4;94(4):048002. doi: 10.1103/PhysRevLett.94.048002. Epub 2005 Jan 31.
Granular mixtures segregate radially by size when tumbled in a partially filled horizontal drum. The smaller component moves toward the axis of rotation and forms a buried core, which then splits into axial bands. Models have generally assumed that the axial segregation is opposed by diffusion. Using narrow pulses of the smaller component as initial conditions, we have characterized axial transport in the core. We find that the axial advance of the segregated core is well described by a self-similar concentration profile whose width scales as talpha, with alpha approximately 0.3<1/2. Thus, the process is subdiffusive rather than diffusive as previously assumed. We compare our results to two one-dimensional model equations which contain self-similarity and subdiffusion: a linear fractional diffusion model and the nonlinear porous medium equation.
当在部分填充的水平转鼓中翻滚时，颗粒混合物会按尺寸进行径向分离。较小的组分向旋转轴移动并形成一个埋藏的核心，然后该核心会分裂成轴向带。模型通常假定轴向分离受到扩散的阻碍。以较小组分的窄脉冲作为初始条件，我们对核心中的轴向输运进行了表征。我们发现，分离核心的轴向推进可以用一个自相似浓度分布很好地描述，其宽度按tα缩放，α约为0.3<1/2。因此，该过程是次扩散的，而不是如先前假定的扩散过程。我们将我们的结果与两个包含自相似性和次扩散的一维模型方程进行了比较：一个线性分数扩散模型和非线性多孔介质方程。
