Estimating water transport in carbon nanotubes: a critical review and inclusion of scale effects

The quasi-frictionless water flow across graphitic surfaces offers vast opportunities for a wide range of applications from biomedical science to energy. However, the conflicting experimental results impede a clear understanding of the transport mechanism and desired flow control. Existing literature proposes numerous modifications and updated boundary conditions to extend classical hydrodynamic theories for nanoflows, yet a consensus or definitive conclusion remains elusive. This study presents a critical review of the proposed modifications of the pressure driven flow or the Hagen-Poiseuille (HP) equations to estimate the flow enhancement through carbon nanotubes (CNTs). For such a case, we performed (semi-)classical molecular dynamics simulations of water flow in various sizes of CNTs, applied the different forms of boundary definitions from the literature, and derived HP equation models by implementing these modifications. By aggregating seven distinct experimental datasets, we tested various flow enhancement models against our measurements. Our findings indicate that including the interfacial layering-based dynamic slip-definition in the proposed HP equations yields accurate estimations. While considering interfacial viscosity predicts the individual CNT experiments well, using the experimental viscosity yields better estimations of measurements for the water flow enhancement through membranes of CNTs. This critical review testing existing literature demonstrates how to refine continuum fluid mechanics to predict water flow enhancement at the nanoscale providing holistic multiscale modeling.

A perspective on the microscopic pressure (stress) tensor: History, current understanding, and future challenges

The pressure tensor (equivalent to the negative stress tensor) at both microscopic and macroscopic levels is fundamental to many aspects of engineering and science, including fluid dynamics, solid mechanics, biophysics, and thermodynamics. In this Perspective, we review methods to calculate the microscopic pressure tensor. Connections between different pressure forms for equilibrium and nonequilibrium systems are established. We also point out several challenges in the field, including the historical controversies over the definition of the microscopic pressure tensor; the difficulties with many-body and long-range potentials; the insufficiency of software and computational tools; and the lack of experimental routes to probe the pressure tensor at the nanoscale. Possible future directions are suggested.

Local Thermodynamic Description of Isothermal Single-Phase Flow in Simple Porous Media

Darcy’s law for porous media transport is given a new local thermodynamic basis in terms of the grand potential of confined fluids. The local effective pressure gradient is determined using non-equilibrium molecular dynamics, and the hydraulic conductivity and permeability are investigated. The transport coefficients are determined for single-phase flow in face-centered cubic lattices of solid spheres. The porosity changed from that in the closest packing of spheres to near unity in a pure fluid, while the fluid mass density varied from that of a dilute gas to a dense liquid. The permeability varied between $$5.7 \times {10^{-20}} \hbox {m}^2$$ 5.7 × 10 - 20 m 2 and $$5.5 \times {10^{-17}} \hbox {m}^2$$ 5.5 × 10 - 17 m 2 , showing a porosity-dependent Klinkenberg effect. Both transport coefficients depended on the average fluid mass density and porosity but in different ways. These results set the stage for a non-equilibrium thermodynamic investigation of coupled transport of multi-phase fluids in complex media.

Multiphase PdCu nanoparticles with improved C1 selectivity in ethanol oxidation

PdCu/CNT-300 catalysts with a mixed crystalline phase were successfully prepared. The introduction of Cu elements and the presence of a phase interface in the mixed phase facilitated electron transfer and increased the rate of the EOR.

Can we define a unique microscopic pressure in inhomogeneous fluids?

The estimation of a microscopic pressure tensor in an adsorbed thin film on a planar surface remains a challenge in both experiment and theory. While the normal pressure is well-defined for a planar surface, the tangential pressure at a point is not uniquely defined at the nanoscale. We report a new method that allows us to calculate the local pressure tensor and its spatial integral using an arbitrary contour definition of the "virial-route" local pressure tensor. We show that by integrating the local tangential pressure over a small region of space, roughly the range of the intermolecular forces, it is possible to define a coarse-grained tangential pressure that appears to be unique and free from ambiguities in the definition of the local pressure tensor. We support our argument by presenting the results for more than ten types of contour definitions of the local pressure tensor. By defining the coarse-grained tangential pressure, we can also find the effective thickness of the adsorbed layer and, in the case of a porous material, the statistical pore width. The coarse-grained in-layer and in-pore tangential pressures are determined for Lennard-Jones argon adsorbed in realistic carbon slit pores, providing a better understanding of the pressure enhancement for strongly wetting systems.

Nanothermodynamic Description and Molecular Simulation of a Single-Phase Fluid in a Slit Pore

We have described for the first time the thermodynamic state of a highly confined single-phase and single-component fluid in a slit pore using Hill's thermodynamics of small systems. Hill's theory has been named nanothermodynamics. We started by constructing an ensemble of slit pores for controlled temperature, volume, surface area, and chemical potential. We have presented the integral and differential properties according to Hill, and used them to define the disjoining pressure on the new basis. We identified all thermodynamic pressures by their mechanical counterparts in a consistent manner, and have given evidence that the identification holds true using molecular simulations. We computed the entropy and energy densities, and found in agreement with the literature, that the structures at the wall are of an energetic, not entropic nature. We have shown that the subdivision potential is unequal to zero for small wall surface areas. We have showed how Hill's method can be used to find new Maxwell relations of a confined fluid, in addition to a scaling relation, which applies when the walls are far enough apart. By this expansion of nanothermodynamics, we have set the stage for further developments of the thermodynamics of confined fluids, a field that is central in nanotechnology.

Hydrodynamics across a fluctuating interface

Understanding what happens inside the rippling and dancing surface of a liquid remains one of the great challenges of fluid dynamics. Using molecular dynamics, we can pick apart the interface structure and understand surface tension. In this work, we derive an exact mechanical formulation of hydrodynamics for a liquid-vapor interface using a control volume, which moves with the surface. This mathematical framework provides the local definition of hydrodynamic fluxes at any point on the surface. These are represented not only by the flux of molecules and intermolecular interactions acting across the surface but also as a result of the instantaneous local curvature and movement of the surface itself. By explicitly including the surface dynamics in the equations of motion, we demonstrate an exact balance between kinetic and configurational pressure normal to the surface. The hydrodynamic analysis makes no assumptions regarding the probability distribution function, so it is valid for any system arbitrarily far from thermodynamic equilibrium. The presented equations provide a theoretical basis for the study of time-evolving interface phenomena, such as bubble nucleation, droplet dynamics, and liquid-vapor instabilities.

Microscopic Pressure Tensor in Cylindrical Geometry: Pressure of Water in a Carbon Nanotube

The microscopic pressure tensor plays an important role in understanding the mechanical stability, transport, and high-pressure phenomena of confined phases. The lack of an exact formulation to account for the long-range Coulombic contribution to the local pressure tensor in cylindrical geometries prevents the characterization of molecular fluids confined in cylindrical pores. To address this problem, we first derive the local cylindrical pressure tensor for Lennard-Jones fluids based on the Harasima (H) definition, which is expected to be compatible with the Ewald summation method. The test of the H-definition pressure equations in a homogeneous system shows that the radial and azimuthal pressure have unphysical radial dependence near the origin, while the axial pressure gives physically meaningful values. We propose an alternative contour definition that is more appropriate for cylindrical geometry and show that it leads to physically realistic results for all three pressure tensor components. With this definition, the radial and azimuthal pressures are of Irving-Kirkwood (IK) type, and the axial pressure is of Harasima type. Because of the practical interest in the axial pressure, we develop a Harasima/Ewald (H/E) method for calculating the long-range Coulombic contribution to the local axial pressure for rigid molecules. As an application, the axial pressure profile of water inside and outside a (20, 20) single-wall carbon nanotube is determined. The H/E method is compared to the IK method, which assumes a spherically truncated Coulombic potential. Detailed analysis of the pressure profile by both methods shows that the water confined in the nanotube is in a stretched state overall in the axial direction.