Clarke Nigel, Gibbions Nigel, Long Didier R
Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, UK.
Soft Matter. 2020 Apr 14;16(14):3485-3497. doi: 10.1039/c9sm02118c. Epub 2020 Mar 25.
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.
为了解释扩散渗透现象，德亚金早在很久以前就提出，在浸入液体的固体表面附近，存在一层通常为几纳米厚的受限超额压力，这是由液体与表面之间的相互作用产生的。因此，在液体中存在成分梯度的情况下，与表面平行的受限压力梯度导致了扩散渗透流。这一图景似乎与胶体科学的接触定理相矛盾，根据该定理，不存在这种超额压力。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学流动，该描述与接触定理一致。这种方法基于吉布斯自由能和虚功原理，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在液体中产生的驱动力。我们的方法使我们能够表明，在润湿或扩散渗透实验中起作用的物理原理是相同的，因为通过使成分梯度更陡，可以从后者连续过渡到前者。我们得到了扩散渗透迁移率的显式表达式，它取决于界面附近的吉布斯自由能密度及其对界面区域之外液体中溶质浓度的依赖性，并且与液体粘度成反比。
