颗粒介质中的粘滞系数

将颗粒介质看成是等效均匀介质, 其中的声衰减系数和声速等于该颗粒介质中的相应的量值(它们可由作者的理论给出), 等效静态密度可以用二元混合规则求得. 此外, 根据浓颗粒介质中相互作用的声传播理论, 当入射波为平面波时, 相互作用的次级波仍然是平面波. 在这样的情况下, 可以将三维非线性方程组简化为一维情况, 从而算得浓颗粒介质中的粘滞系数, 结果表明, 颗粒介质中的粘滞系数不仅依赖于颗粒的体积分数而且还与频率有关. 根据推导过程可知, 对比于爱因斯坦理论所能应用的限制, 本文的结果可以更广泛地应用于实际介质.

Viscosity coefficient in granular medium

A granular medium can be regarded as an equivalent uniform medium, of which the attenuation coefficient and the acoustic speed are obtained from the author's theory published elsewhere. The equivalent static density can be given by the mixed rule. According to the author's sound propagation theory in the granular medium, furthermore, the secondary waves are plane waves as well when the incidental sound wave is plane wave. In these cases, the three-dimensional equations can be simplified into a one-dimensional equation, and an expression for the viscosity coefficient in concentrated granular medium can be obtained. The theoretical results show that the viscosity coefficient depends on not only the volume fraction of the grains, but also sound frequency. On the other hand, the theory given in this paper can be used in the realistic cases, where less restrictions will be imposed on the applications than the Einstein's theory.