AI 中文总结
研究二元液体混合物中重力控制的非平衡卡西米尔压力，用涨落流体动力学表明平板过剩压力由\(k_{\mathrm{RO}}L\)标度函数描述，大间距时按\(1/(k_{\mathrm{RO}}L)\)衰减，力可吸引或排斥，还提出测量该力的实验装置及估计力大小。
AI 中文摘要
我们研究了在等温二元液体混合物中的非平衡卡西米尔压力。该混合物保持在与重力平行的空间恒定且静止的浓度梯度中，并被限制在厚度为\(L\)的三维平板内，平板由与重力场和外加梯度平行的两个无限大平板界定。我们假设在相同非平衡条件下，液体混合物占据平板的内部和外部。利用涨落流体动力学，我们表明平板上产生的有限尺寸过剩压力由无量纲变量\(k_{\mathrm{RO}}L\)的标度函数描述，其中\(k_{\mathrm{RO}}\)是重力诱导的滚降波矢。在大间距时，这种卡西米尔压力按\(1/(k_{\mathrm{RO}}L)\)衰减。根据混合物的热力学性质，相应的力可以是吸引的或排斥的，而对于理想溶液则消失。由于混合物假设远离其共溶临界点，这里研究的卡西米尔压力完全是非平衡起源的，并且在没有外加浓度梯度时消失。最后，我们提出了一个可能测量这种力的实验装置，由两个光学捕获的胶体粒子浸没在扩散到上层纯水的致密水胶体悬浮液中组成，并估计了所得力的预期大小。
英文摘要
We investigate the non-equilibrium Casimir pressure in an isothermal binary liquid mixture maintained in a spatially constant and stationary concentration gradient parallel to gravity and confined within a three-dimensional slab of thickness $L$, bounded by two infinite plates parallel to both the gravitational field and the imposed gradient. We assume that the liquid mixture, under the same non-equilibrium conditions, occupies both the interior and the exterior of the slab. Using fluctuating hydrodynamics, we show that the resulting finite-size excess pressure on the plates is described by a scaling function of the dimensionless variable $k_{\mathrm{RO}}L$, where $k_{\mathrm{RO}}$ is the gravity-induced roll-off wavevector. At large separations, this Casimir pressure decays as $1/(k_{\mathrm{RO}}L)$. Depending on the thermodynamic properties of the mixture, the corresponding force can be either attractive or repulsive, while it vanishes for ideal solutions. Since the mixture is assumed to be far from its consolute critical point, the Casimir pressure investigated here is entirely of non-equilibrium origin and it vanishes in the absence of the imposed concentration gradient. Finally, we propose an experimental setup where this force might be measured, consisting of two optically trapped colloidal particles immersed in a dense aqueous colloidal suspension diffusing into an overlying layer of pure water, estimating the expected magnitude of the resulting force.
