Kumaran V
Department of Chemical Engineering, Indian Institute of Science, Bangalore 560 012 India.
Phys Rev Lett. 2006 Jun 30;96(25):258002. doi: 10.1103/PhysRevLett.96.258002. Epub 2006 Jun 29.
The decay of the velocity autocorrelation function in a sheared granular flow is analyzed in the limit where the wavelength of fluctuations is larger than the "conduction length," so that energy is a nonconserved variable. The decay of the velocity autocorrelation function is much faster than that in a fluid at equilibrium for which energy is a conserved variable. Specifically, the autocorrelation function in a sheared granular flow decays proportional to t-3 in 2D and t-9/2 in 3D, in contrast with the decay proportional to t-1 in 2D and t-3/2 in 3D for a fluid at equilibrium. The renormalization of the viscosity due to mode coupling is evaluated using this form of the decay of the autocorrelation function. It is found that the logarithmic divergence in the viscosity in 2D, and the divergence of the Burnett coefficients in 3D, which is characteristic of a fluid of elastic particles at equilibrium, is absent in a sheared granular flow.
在波动波长大于“传导长度”的极限情况下，对剪切颗粒流中速度自相关函数的衰减进行了分析，使得能量成为一个非守恒变量。速度自相关函数的衰减比处于平衡态的流体快得多，在平衡态流体中能量是一个守恒变量。具体而言，剪切颗粒流中的自相关函数在二维中按t⁻³衰减，在三维中按t⁻⁹/²衰减，这与处于平衡态的流体在二维中按t⁻¹衰减、在三维中按t⁻³/²衰减形成对比。利用这种自相关函数的衰减形式来评估模式耦合导致的黏度重整化。结果发现，二维中黏度的对数发散以及三维中伯内特系数的发散（这是平衡态弹性颗粒流体的特征）在剪切颗粒流中并不存在。
