Abstract.

The application of a temperature gradient along a fluid-solid interface generates stresses in the fluid causing “thermo-osmotic” flow. Much of the understanding of this phenomenon is based on Derjaguin's work relating thermo-osmotic flows to the mechano-caloric effect, namely, the interfacial heat flow induced by a pressure gradient. This is done by using Onsager's reciprocity relationship for the equivalence of the thermo-osmotic and mechano-caloric cross-term transport coefficients. Both Derjaguin theory and Onsager framework for out-of-equilibrium systems are formulated in macroscopic thermodynamics terms and lack a clear interpretation at the molecular level. Here, we use statistical-mechanical tools to derive expressions for the transport cross-coefficients and, thereby, to directly demonstrate their equality. This is done for two basic models: i) an incopressible continuum solvent containing non-interacting solute particles, and ii) a single-component fluid without thermal expansivity. The derivation of the mechano-caloric coefficient appears to be remarkably simple, and provides a simple interpretation for the connection between interfacial heat and particle fluxes. We use this interpretation to consider yet another example, which is an electrolyte interacting with a uniformly charged surface in the strong screening (Debye-Hückel) regime.

Graphical abstract

中文翻译：

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Onsager互惠关系和Derjaguin热渗透理论的简单统计力学解释。

摘要。

沿着流体-固体界面施加温度梯度会在流体中产生应力，从而引起“热渗透”流动。对这种现象的大部分理解是基于Derjaguin的工作，该工作将热渗透流与机械热效应（即由压力梯度引起的界面热流）联系起来。这是通过使用Onsager的对等关系来实现热渗透和机械热跨项传输系数的等价关系。Derjaguin理论和Onsager失衡体系的框架都是用宏观热力学术语来表述的，在分子水平上缺乏清晰的解释。在这里，我们使用统计机械工具来导出运输交叉系数的表达式，从而直接证明它们的相等性。这是针对两个基本模型完成的：i）包含非相互作用溶质颗粒的不可压连续介质溶剂，以及ii）没有热膨胀性的单组分流体。机械热系数的推导似乎非常简单，并且为界面热与颗粒通量之间的关系提供了简单的解释。我们使用这种解释来考虑另一个示例，该示例是在强屏蔽（Debye-Hückel）方案中电解质与均匀带电的表面相互作用。并为界面热和颗粒通量之间的关系提供了简单的解释。我们使用这种解释来考虑另一个示例，该示例是在强屏蔽（Debye-Hückel）方案中电解质与均匀带电的表面相互作用。并为界面热和颗粒通量之间的关系提供了简单的解释。我们使用这种解释来考虑另一个示例，该示例是在强屏蔽（Debye-Hückel）方案中电解质与均匀带电的表面相互作用。

图形概要