In order to account for diffusio-osmosis, Derjaguin proposed long ago that there is an excess pressure confined within a layer of typically a few nanometers in the vicinity of a solid surface immersed in a liquid and resulting from the interaction between the liquid and the surface. In the presence of a composition gradient in the liquid a confined pressure gradient parallel to the surface is therefore responsible for the diffusio-osmotic flow. This picture appears in contradiction with the contact theorem of colloidal science according to which such excess pressure does not exist. We propose a theoretical description for calculating hydrodynamic flows in inhomogeneous liquids in the vicinity of solid interfaces which is consistent with the contact theorem. This approach is based on a Gibbs free energy and a virtual work principle for calculating the driving forces in the liquid due to inhomogeneous composition along a capillary and to the interaction with the solid interfaces. Our approach allows us to show that the physics at play is the same in wetting or in diffusio-osmosis experiments, as one can go continuously from the latter to the former by making composition gradients sharper. We obtain an explicit expression for the diffusio-osmotic mobility which depends on the Gibbs free energy density in the vicinity of the interface and its dependance on the solute concentration in the liquid beyond the interfacial region, and which is inversely proportional to the liquid viscosity.

中文翻译：

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固体表面的扩散渗透和润湿：基于虚拟工作原理的统一描述

为了解决扩散渗透问题，德雅金（Derjaguin）很久以前就提出，在浸入液体的固体表面附近，通常在几纳米的层内存在一个过大的压力，这是由液体和表面之间的相互作用引起的。 。因此，在液体中存在成分梯度的情况下，平行于表面的封闭压力梯度是扩散渗透流的原因。这张图片看起来与胶体科学的接触定理矛盾，在接触定理中，不存在这种过大的压力。我们提出了一种理论描述，用于计算固体界面附近非均匀液体中的流体动力流，这与接触定理是一致的。该方法基于吉布斯自由能和虚拟功原理，用于计算由于沿毛细管的成分不均匀以及与固体界面的相互作用而导致的液体驱动力。我们的方法使我们能够证明，在润湿或扩散渗透实验中，所发挥的物理作用是相同的，因为通过使成分梯度更陡峭，可以从后者到前者连续进行。我们获得了弥散渗透迁移率的明确表达式，该表达式取决于界面附近的吉布斯自由能密度及其对界面区域以外液体中溶质浓度的依赖性，并且与液体粘度成反比。