The pressure in interfaces having cylindrical geometry

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.

Thermo-osmotic pressure and resistance to mass transport in a vapor-gap membrane

We have investigated the transport of fluid through a vapor-gap membrane. The transport due to a membrane temperature difference was investigated under isobaric as well as non-isobaric conditions. Such a concept is relevant for water cleaning and power production purposes. A coarse-grained water model was used for modelling transport through pores of different diameters and lengths. The wall-fluid interactions were set so as to mimic hydrophobic interactions between water and membrane. The mass transport through the membrane scaled linearly with the applied temperature difference. Soret equilibria were obtained when the thermo-osmotic pressure was 18 bar K-1. The state of the Soret equilibrium did not depend on the pore size or pore length as expected. We show that the Soret equilibrium cannot be sustained by a gradient in vapor pressure. The fluxes of heat and mass were used to compute the total resistances to the transport of heat and mass.

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.

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.