剪切相关（近临界）模型流体在约束中的粘度
Viscosity of a sheared correlated (near-critical) model fluid in confinement
摘要：
二阶相变的特征在于序参量波动的空间相关长度的发散。对于封闭系统，这是已知的，导致显着的平衡物理现象，包括有限尺寸效应和临界卡西米尔力。我们在这里探索一些非平衡方面的这些影响在稳态的外力的作用所造成的：通过分析模型的相关流体剪切下，空间上由两个平行的板，我们研究（高斯）朗道-金兹伯格理论的设置内产生的粘度。具体来说，我们引入一个模型，其中流体动力学速度场（服从斯托克斯方程）耦合到一个序参量与耗散动力学。将体系统中著名的Green-Kubo关系推广到了受限系统中。这表明，导致在一个非本地的斯托克斯方程的流体流动，由于相关的波动。由此产生的有效剪切粘度表现出普遍的以及非普遍的贡献，我们详细研究。特别地，从体行为的偏离是普遍的，取决于相关长度和膜厚度$L$的比率。此外，在临界点处，粘度与$\ell/L$成比例，其中$\ell$是动态长度尺度。这些发现预计是实验观察到的，特别是对于系统的体积粘度的临界波动的影响。
英文摘要：
Second-order phase transitions are characterized by a divergence of the spatial correlation length of the order parameter fluctuations. For confined systems, this is known to lead to remarkable equilibrium physical phenomena, including finite-size effects and critical Casimir forces. We explore here some non-equilibrium aspects of these effects in the stationary state resulting from the action of external forces: by analyzing a model of a correlated fluid under shear, spatially confined by two parallel plates, we study the resulting viscosity within the setting of (Gaussian) Landau-Ginzburg theory. Specifically, we introduce a model in which the hydrodynamic velocity field (obeying the Stokes equation) is coupled to an order parameter with dissipative dynamics. The well-known Green-Kubo relation for bulk systems is generalized for confined systems. This is shown to result in a non-local Stokes equation for the fluid flow, due to the correlated fluctuations. The resulting effective shear viscosity shows universal as well as non-universal contributions, which we study in detail. In particular, the deviation from the bulk behavior is universal, depending on the ratio of the correlation length and the film thickness $L$. In addition, at the critical point the viscosity is proportional to $\ell/L$, where $\ell$ is a dynamic length scale. These findings are expected to be experimentally observable, especially for systems where the bulk viscosity is affected by critical fluctuations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
