On the Transition from Bulk to Ordered Form of Water: A Theoretical Model to Calculate Adhesion Force Due to Capillary and van der Waals Interaction

Abstract

The adhesion force due to capillary interaction between two hydrophilic surfaces is strongly dependent on the partial pressure of water and is often calculated using the Kelvin equation. The validity of the Kelvin equation is questionable at low relative humidity (RH) of water, like in high vacuum and dry nitrogen environments, where water is only present as layers of several molecules thick at the surfaces. A model from ordered to bulk form of water has been developed using the Brunauer, Emmett, and Teller adsorption model. The results show that the adhesion force calculated using the Young–Laplace and Kelvin equations at low (5–30 %) RH is underestimated. The total adhesion force shows changes when the RH is changed from 0 to 100 %. In dry conditions, at RH below 10 %, the total adhesion force is contributed by the van der Waals interaction due to solid–solid contact. The total adhesion force then increases and remains constant being equal to the superposition of van der Waals interaction due to solid–solid contact and van der Waals interaction due to adsorbed water layers on the surfaces. The total adhesion force further increases slowly with the increase in RH incorporating capillary forces and then decreases at very high RH due to screening of van der Waals forces. This change in adhesion force occurs from solid–solid interaction to ordered form of water at low RH and from ordered form to bulk form of water at high RH along with the screening effect of van der Waals interaction. The results have been compared with the experiments and it has been seen that at small length scales, the model is in agreement with the existing experimental data. However, at large length scales roughness of the surfaces should be taken into account.