Transport mechanisms of fluids under nanoscale confinements

Abstract

The presence of fluids confined to the nanoscale has been known for some time in nature, as observed in geological formations, e.g. light hydrocarbon fluids trapped in shale reservoirs, or in biological systems, e.g. water in aquaporins. However, it is only recently that technological advances have stimulated interest in studying fluid behaviour under such conditions in more detail, due to the disruptive potential of engineering applications at these scales. Three important characteristic lengths can be identified in these flows, namely the molecular mean free path λ (denoting the average distance travelled by particles between collisions), the diameter of fluid constituent particles σ, and the channel size L. At the microscale, λ may be become comparable to L, leading to an increased collision frequency with the confining walls rather than with other particles. In this scenario, the gas is no longer in quasi-local thermodynamic equilibrium state as assumed by continuum fluid dynamics, and the Boltzmann equation must be used to accurately describe its behaviour. At the nanoscale, where L is comparable to σ, excluded volume effects and non-locality of collisions become significant. Consequently, the Boltzmann description becomes invalid and alternative kinetic models, such as the Enskog equation, or a more fundamental approach, such as molecular dynamics simulations, must be considered. This thesis aims to contribute to the understanding of transport phenomena at the nanoscale, spanning fluid conditions from the dense to the rarefied gas, and considering different channel sizes, geometries, and surface roughnesses. In order to do so, a fluid composed of hard spheres confined between mathematical surfaces has been studied because, despite its simplicity, this model retains the essential physics of more realistic systems.

Self-diffusion of atoms is the simplest transport mechanism, and yet it is not fully understood in the context of molecularly confined flows. Firstly, in this thesis, a systematic study of this process was carried out for a fluid within a slit geometry, delimited by two infinite parallel plates. One of the most distinctive features of the fluid behaviour in confined conditions is the preferential fluid structuring that occurs next to the walls, due to the limited mobility of particles in the normal direction to the wall. To clarify a source of debate in the literature, it is proved that, despite the strong fluid inhomogeneities, the self-diffusivity based on the Einstein relation can still be used to describe Fickian diffusion under molecular confinements, the latter being explicitly computed in simulations by tracking the dynamics of tagged particles. The interplay of the underlying diffusion mechanisms, i.e. molecular and Knudsen diffusion, is then identified, by differentiating between fluid-fluid and fluid-wall collisions. The key finding is that the Bosanquet formula, previously used for describing the diffusive transport of rarefied gases, also provides a good semi-analytical description of self-diffusivities for dense fluids under tight confinements, as long as the channel size is not smaller than five molecular diameters. Importantly, this allows one to predict the self-diffusion coefficient in a wide range of Knudsen numbers, including the transition regime, which was not possible before.

Although diffusion is believed to dominate the fluid transport at the nanoscale, it is shown that the Fick first law fails to describe the surprising fluid behaviour that occurs within confined straight channels. For example, since Knudsen’s experimental work circa 1910, it has been known that the Poiseuille mass flow rate along microchannels features a stationary point as the fluid density decreases, referred to as the Knudsen minimum. However, when the characteristic length L is further decreased, this minimum has been reported to disappear and the mass flow rate monotonically increases over the entire range of flow regimes. Using an analytical procedure, in this work it is shown, for the first time, that this vanishing occurs because the decay of the mass flow rate, due to the decreasing density effects, is overcome by the enhancing contribution to the flow provided by the fluid velocity slip at the wall. The latter phenomena become more important in tight geometries, ultimately being capable of modifying the flow dynamics.

The physical mechanisms underlying fluid slippage at walls are not well understood at the nanoscale, where dense and confinement effects add several complexities. For example, it is unclear to what extent the Navier-Stokes equations with slip boundary conditions can accurately describe the fluid behaviour under molecular confinements. Furthermore, the effects of fluid density and confinement as well as the surface properties, such as curvature and microscopic roughness, on velocity slip are not fully understood. Using a simple fluid-wall framework, it is shown that the interfacial friction coefficient, which is inversely proportional to the slip length, is linear with the peak fluid density at the wall, regardless of the nominal density, confinement ratio, and wall curvature. The peak density turns out to increase as the nominal density increases, with a mild dependence on confinement and curvature. Furthermore, the friction coefficient scales according to the Smoluchowski prefactor with respect to the influence of the accommodation coefficient, similar to the case of a rarefied gas where the same gas-surface dynamics are considered – despite the physics next to the wall are very different.

Altogether, these results represent a significant step forward in understanding the mechanisms of fluid flow in molecular-scale systems, and have important implications for the design and optimisation of nanofluidic devices.