颗粒介质的结构及热力学

Granular structure and the nonequilibrium thermodynamics

颗粒介质具有远程无序和近程有序的结构,是产生动力学不均匀性(dynamical heterogeneity)和复杂不可逆过程的根源.本文分析了颗粒介质的结构特征、变形和能量耗散之间的内在关联,讨论了颗粒介质的弹性,提出了流变应变增量、耦合应变增量和弹性应变增量的应变增量分解方式.沿用非平衡热力学框架,引入表征运动无序的动理学颗粒温度Tk和表征弹性应力涨落的构型温度Tc,作为非平衡态变量,建立了双颗粒温度热力学(two-granular-temperature thermodynamics,TGT理论),注重分析了不可逆过程中的热力学力和流,并与著名的砂土内变量热力学进行了对比.

Granular materials posses disorder structures which are the origin of dynamical heterogeneity. On the basis of non-equilibrium thermodynamics, the structure characteristics, complex deformations, and energy dissipations are analysed. Based on the photoelastic tests, the granular elasticity is discussed. The strain increments are classified into three categories. By means of the non-equilibrium thermodynamics, two granular temperatures, Tk, Tc, are introduced as the state variables, which denote the fluctuations of the kinetic energy and the elastic energy, respectively. Further, a two-granular-temperature thermodynamics（i.e. TGT theory） are developed for granular materials. The thermodynamic forces and fluxes are particularly analyzed. TGT theory is also compared with the previous internal variable thermodynamics for sands（IVT theory） developed a few decades ago. It is found that from TGT the Gibbs free energy in the IVT theory can be deduced, and the energy dissipation function can be apparently expressed from TGT theory.