The interior of nanoscale crystals experiences stress that compensates for the capillary forces[1] and that can be very large, in the order of ...1 GPa[2].

1. FLUID SATURATION AND CAPILLARY PRESSURE http://homepages.see.leeds.ac.uk/~earpwjg/PG_EN/CD%20Contents/GGL-66565%20Petrophysics%20English/Chapter%204.PDF

2. On the impact of capillarity for strength at the nanoscale

https://www.nature.com/articles/s41467-017-01434-2.pdf

Please also take the effect of velocity of the moving liquid/air interface into account. See for instance

Daniel Bonn, Jens Eggers, Joseph Indekeu, Jacques Meunier, and Etienne Rolley

Rev. Mod. Phys. 81, 739 – Published 27 May 2009

The influence of the indenter shapes and various parameters on the magnitude of the capillary force on the basis of models describs the wet adhesion of indenters and substrates joined by liquid bridges. Different dependences of the capillary force on the indenter shapes and the geometric parameters are observed. The results can be applicable to the micro- and nano-indentation experiments. It shows that the measured hardness is underestimated due to the effect of the capillary force.

Review this articke

The capillary force in micro- and nano-indentation with different indenter shapes

Article The capillary force in micro- and nano-indentation with diff...

The capillary force in micro- and nano-indentation with different indenter shapes

Capillarity at the nanoscale

From microfluidic applications to nanofluidic phenomena

Details in the attached article

Article Capillarity at the nanoscale

Capillarity is a rather old topic in physical chemistry (the

theories of Young and Laplace were developed in the early

19th century), however on the nanoscale it is very much alive,

both fundamentally as well as in different engineering fields.

To illustrate this, accurate experimental data to support the

validity of the Young-Laplace equation in nanometre gaps

was presented only at the beginning of the 1980’s.2 Examples

of important applications in the field of chemistry and

nanotechnology are, respectively, electrospray and AFM

based liquid deposition. Electrospray is an important topic

in this review because of its significance in analytical chemistry

(mass-spectrometry) being probably the most prominent

soft-ionization method for bio-molecules. On a fundamental

level, the Taylor cone illustrates the concept of electrocapillarity

which requires an extension of the Young-Laplace

equation to include electrical stress as an extra term affecting

the curvature of the meniscus for a given hydrostatic pressure

drop.

Critical Review of Fluid Flow Physics at Micro- to Nano‐scale Porous Media Applications in the Energy Sector

https://www.hindawi.com/journals/amse/2018/9565240/

World’s energy demand is expected to grow approximately by 25–37% between 2014 and 2040 per some estimates. In order to secure the future energy supply while also reducing the global carbon footprints, new avenues are being explored to produce energy that is efficient and clean. Some major technologies that are either already contributing to this objective or can potentially contribute in the future include (i) electrokinetic energy conversion devices that power wide variety of applications, (ii) water desalination using synthetically created nanosized membranes, (iii) extraction of hydrocarbons from ultra-tight shale formations, and (iv) storage of hydrogen. Optimum utilization of these technologies requires understanding of fluid transport at micro- to nanosized pores and developing theoretical models that capture the physics of fluid flow at these scales to predict their performance. Understanding the material of the medium together with the physics of fluid flow is important because they are often coupled together in addition to the importance of their role independently; for instance, properties of a rock matrix (material) are important in shale to locate regions with hydrocarbons as well as in designing a hydraulic fracturing job that is strongly affected by the rock’s material properties. As another example, properties of the material are used to control the performance of electrokinetic devices. While it is evident from the literature that more emphasis is given to studying the material of these systems, similar emphasis must be given to study the physics of fluid flow. Incomplete or insufficient physics for the fluid flow can lead to untapped potential of these applications that can be used to increase their performance.

Micro- to Nano‐scale

The attached article may be useful

Self-Assembly of Chip-Size Components with Cavity Structures:

High-Precision Alignment and Direct Bonding without Thermal

Compression for Hetero Integration