Towards a model of hydration-lubricated contact

Figure 1: Photo by Wes Hicks* on Unsplash

Have you ever tried to cross a small river by jumping from one emerging stone to another? I always try when I go on a walk! But I feel safer when these mossy/algae covered stones are dry. Hydrated stones are slippery. The article by Fang et al. [1] presented here describes hydration lubrication modelling although it does not talk about mosses or algae! Here, the lubrication mechanisms occur at a much smaller scale than any living cell. Indeed, what is known as the hydration layer only applies to the first molecular layers of water on the solid surface. And these layers have a key role in the surface separation of molecular lubrication.

One can find hydration water layers on ionic or hydrophilic surfaces in contact with aqueous liquids. In the present context, this layer can be very tightly bound to the surface and resist high compression and shear stress explain Fang et al., contrary to other hydrated layers which can be very fragile. Thanks to such layers, joints can accommodate various types of our body movements over the years! However, the complex interactions occurring between the solid and the layer and between the layers make this tribo-system difficult to model properly. A literature review shows that the main interactions to consider are van der Waals attraction p_{vdW}, short-range repulsion due to hydration force p_{hyd}, electrostatic repulsion p_{EDL} (known as Electrical Double Layer force), and the repulsive contact pressure p_{rep} obtained from the repulsive part of the Lennard-Jones potential. However, the authors report that so far, “there is no effective numerical model that describes the hydration contact characteristics and energy dissipation during sliding”. And this is why they propose theirs.

Figure 2: Interface pressure due to surface force as a function of surface separation in confined aqueous solution (from [1])

Film thickness computation

The components of their model can be summarized as follows:

  • Total contact pressure can be expressed by the sum of the four interactions: p_{sf} = p_{vdW} + p_{hyd} + p_{EDL} + p_{rep}. For further details about the summed terms, feel free to have a look at the full article! Figure 2 presents the different forces and their action depending on the surface separation.
  • The contact is considered as an elastic sphere on plane contact (see Figure 3 or this article) and therefore the loaded contact profile can be expressed as: h(x,y)=h_0+\frac{x^2+y^2}{2R}+u(x,y) with x and y the plane coordinates, h_0 the gap between rigid surfaces under a given load, R the sphere radius and u the elastic deformation which is here computed using the Boussinesq integral [2].
  • To close the mathematical equation set, the load force F should be balanced by the sum of the total contact pressure over the contact area:

        \[F=\iint p_{sf}(x,y) dx dy \]

Figure 3: Point contact

As one may notice, this model is based on continuum mechanics equations with inputs stemming from molecular size phenomena… but much less computation time than molecular dynamic computations while still providing an estimation of solid separation: h(x,y). The model resembles the elastohydrodynamic lubrication models, apart from the hydrodynamic pressure which is here replaced by other forces.


Fang et al. also included a friction model in their analysis. It is based on Eyring model and after integration of the shear stress over the contact area, the friction force f is obtained:

    \[ f=\iint \tau(x,y) dx dy \]

This computation is permitted by the knowledge of the film thickness h(x,y) which allows for obtaining the shear rate \dot{\gamma}. The shear stress can then be calculated by:

    \[ \tau=\dot{\gamma} \times \eta \]

Where \eta is viscosity of the lubricant. Provided that the model user possesses the different parameters to compute the four interactions, it is possible to obtain predictions on film thickness and friction. This is a good achievement. The authors then computed different cases under different loads resulting in different surface separations and friction forces.


Whereas hydration lubrication is the predominant lubrication mechanism in many applications that desperately need improvements (such as biolubrication or nanofriction) or at least a better understanding, it is a complex mechanism. This model certainly brings progress in the right direction as it is an innovative way to handle the topic and it proposes predictions on film thickness and friction.

This being said, it would be very interesting to assess the results of this model with experimental measurements or molecular dynamics results. Indeed, the limitations of the model are various as it contains different hypotheses to enable predictions. The aqueous solution and the bodies are described as continuous media, the solution is considered as a Newtonian fluid and the molecular interactions described by the interaction forces are hardly explained. As the approach provides a new tool to investigate hydration lubrication, I am eager to follow the progress of this research team and read their next publications. Don’t hesitate to have a look at this one for more information!

[1] Fang Y., Ma L., Wang X., Luo J. (2020) Numerical model for Hydration-Lubricated Contact and Its Friction Behavior at Nanoscale, Front. Mech. Eng. 6:564756

[2] Johnson K.L. (1987) Contact Mechanics, Cambridge, Cambridge University Press

* featured image reference

After a PhD thesis with SKF at the INSA de Lyon - LaMCoS dedicated to the lubrication of large size roller bearings, Jean-David joined SIMTEC ( to continue helping industries to develop their processes and products.

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