Belardinelli Daniele, Sbragaglia Mauro, Benzi Roberto, Ciliberto Sergio
Department of Physics & INFN, University of Rome "Tor Vergata", Via della Ricerca Scientifica 1, 00133, Rome, Italy.
Laboratoire de Physique de Ecole Normale Superieure de Lyon (CNRS UMR5672), 46 Allée d'Italie, 69364, Lyon, France.
Phys Rev E. 2019 Jun;99(6-1):063302. doi: 10.1103/PhysRevE.99.063302.
In recent years the lattice Boltzmann (LB) methodology has been fruitfully extended to include the effects of thermal fluctuations. So far, all studied cases pertain to equilibrium fluctuations, i.e., fluctuations with respect to an equilibrium background state. In this paper we take a step further and present results of fluctuating LB simulations of a binary mixture confined between two parallel walls in the presence of a constant concentration gradient in the wall-to-wall direction. This is a paradigmatic setup for the study of nonequilibrium (NE) fluctuations, i.e., fluctuations with respect to a nonequilibrium state. We analyze the dependence of the structure factors for the hydrodynamical fields on the wave vector q in both the directions parallel and perpendicular to the walls, highlighting the long-range (∼|q|^{-4}) nature of correlations in the NE framework. Results at the small scales (high wave numbers) quantitatively agree with the predictions of fluctuating hydrodynamics without fitting parameters. At larger scales (low wave numbers), however, results show finite-size effects induced by confinement and call for further studies aimed at controlling boundary conditions in the fluctuating LB framework as well as compressibility effects. Moreover, in the presence of a nonideal equation of state of the mixture, we also observe that the (spatially homogeneous) average pressure changes, due to a genuinely new contribution triggered by NE fluctuations. These NE pressure effects are studied at changing the system size and the concentration gradient. Taken all together, we argue that the results of this article are useful and instrumental to boost the applicability of the fluctuating LB methodology in the framework of NE fluctuations, possibly in conjunction with experiments.
近年来，格子玻尔兹曼（LB）方法已成功扩展到包括热涨落的影响。到目前为止，所有研究的案例都涉及平衡涨落，即相对于平衡背景状态的涨落。在本文中，我们更进一步，给出了在两平行壁之间存在壁间恒定浓度梯度的情况下，二元混合物的涨落LB模拟结果。这是研究非平衡（NE）涨落的典型设置，即相对于非平衡状态的涨落。我们分析了流体动力学场的结构因子在平行和垂直于壁的两个方向上对波矢q的依赖性，突出了NE框架中相关性的长程（～|q|⁻⁴）性质。小尺度（高波数）的结果在不拟合参数的情况下与涨落流体动力学的预测定量一致。然而，在较大尺度（低波数）下，结果显示了由限制引起的有限尺寸效应，并呼吁进一步研究以控制涨落LB框架中的边界条件以及可压缩性效应。此外，在混合物存在非理想状态方程的情况下，我们还观察到，由于NE涨落引发的全新贡献，（空间均匀的）平均压力发生了变化。我们在改变系统尺寸和浓度梯度的情况下研究了这些NE压力效应。综上所述，我们认为本文的结果对于提高涨落LB方法在NE涨落框架中的适用性是有用的且有帮助的，可能与实验相结合。
