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The contact line (CL) is where solid, liquid and vapor phases meet, and Young's equation describes the macroscopic force balance of the interfacial tensions between these three phases. These interfacial tensions are related to the nanoscale stress inhomogeneity appearing around the interface, and for curved CLs, eg a three-dimensional droplet, another force known as the line tension must be included in Young's equation. The line tension has units of force, acting parallel to the CL, and is required to incorporate the extra stress inhomogeneity around the CL into the force balance. Considering this feature, Bey et al. [J. Chem. Phys. \textbf{152}, 094707 (2020)] reported a mechanical approach to extract the value of line tension $\taul$ from molecular dynamics (MD) simulations. In this study, we show a novel thermodynamics interpretation of the line tension as the free energy per CL length, and based on this interpretation, through MD simulations of a quasi-static detachment process of a quasi-two-dimensional droplet from a solid surface, we obtained the value $\taul$ as a function of the contact angle. The simulation scheme is considered to be an extension of a thermodynamic integration method, previously used to calculate the solid-liquid and solid-vapor interfacial tensions through a detachment process, extended here to the three phase system. The obtained value agreed well with the result by Bey et al. and show the validity of thermodynamic integration at the three-phase interface., Comment: 9 figures

We present TTCF4LAMMPS, a toolkit for performing non-equilibrium molecular dynamics (NEMD) simulations to study fluid behaviour at low shear rates using the LAMMPS software. By combining direct NEMD simulations and the transient-time correlation function (TTCF) technique, we study the behaviour of fluids over shear rates spanning $15$ orders of magnitude. We present two example systems consisting of simple monatomic systems: one containing a bulk liquid and another with a liquid layer confined between two solid walls. The small bulk system is suitable for testing on personal computers, while the larger confined system requires high-performance computing (HPC) resources. We demonstrate that the TTCF formalism can successfully detect the system response for arbitrarily weak external fields. We provide a brief mathematical explanation for this feature. Although we showcase the method for simple monatomic systems, TTCF can be readily extended to study more complex molecular fluids. Moreover, in addition to shear flows, the method can be extended to investigate elongational or mixed flows as well as thermal or electric fields. The reasonably high computational cost needed for the method is offset by the two following benefits: i) the cost is independent of the magnitude of the external field, and ii) the simulations can be made highly efficient on HPC architectures by exploiting the parallel design of LAMMPS. We expect the toolkit to be useful for computational researchers striving to study the nonequilibrium behaviour of fluids under experimentally-accessible conditions., Comment: 33 pages, 10 figures. Scripts available at the following link https://github.com/edwardsmith999/TTCF

Computer simulation is an important tool for scientific progress, especially when lab experiments are either extremely costly and difficult or lack the required resolution. However, all of the simulation methods come with limitations. In molecular dynamics (MD) simulation, the length and time scales that can be captured are limited, while computational fluid dynamics (CFD) methods are built on a range of assumptions, from the continuum hypothesis itself, to a variety of closure assumptions. To address these issues, the coupling of different methodologies provides a way to retain the best of both methods. Here, we provide a perspective on multiscale simulation based on the coupling of MD and CFD with each a distinct part of the simulation domain. This style of coupling allows molecular detail to be present only where it is needed, so CFD can model larger scales than possible with MD alone. We present a unified perspective of the literature, showing the links between state and flux coupling and discuss the various assumptions required for both. A unique challenge in such coupled simulation is obtaining averages and constraining local parts of a molecular simulation. We highlight that incorrect localisation has resulted in an error in the literature for both pressure tensor and coupling constraints. We then finish with some applications, focused on the simulation of fluids. Thus, we hope to motivate further research in this exciting area with applications across the spectrum of scientific disciplines., Comment: 21 pages, 8 figures perspective paper submitted to Physical Chemistry Chemical Physics (PCCP)

We derive the transient-time correlation function (TTCF) expression for the computation of phase variables of inhomogenous confined atomistic fluids undergoing boundary-driven planar shear (Couette) flow at constant pressure. Using nonequilibrium molecular dynamics simulations, we then apply the TTCF formalism to the computation of the shear stress and the slip velocity for atomistic fluids at realistic low shear rates, in systems under constant pressure and constant volume. We show that, compared to direct averaging of multiple trajectories, the TTCF method dramatically improves the accuracy of the results at low shear rates, and that it is suitable to investigate the tribology and rheology of atomistically detailed confined fluids at realistic flow rates.

Time-reversible dynamical simulations of nonequilibrium systems exemplify both Loschmidt's and Zerm\'elo's paradoxes. That is, computational time-reversible simulations invariably produce solutions consistent with the {\it irreversible} Second Law of Thermodynamics (Loschmidt's) as well as {\it periodic} in the time (Zerm\'elo's, illustrating Poincar\'e recurrence). Understanding these paradoxical aspects of time-reversible systems is enhanced here by studying the simplest pair of such model systems. The first is time-reversible, but nevertheless dissipative and periodic, the piecewise-linear compressible Baker Map. The fractal properties of that two-dimensional map are mirrored by an even simpler example, the one-dimensional random walk, confined to the unit interval. As a further puzzle the two models yield ambiguities in determining the fractals' information dimensions. These puzzles, including the classical paradoxes, are reviewed and explored here. We review our investigations presented in Budapest in 1997 and end with presentday questions posed as the Snook Prize Problems in 2020 and 2021., Comment: Eighteen pages with 11 Figures

The local pressure tensor is non-unique, a fact which has generated confusion and debate in the seventy years since the seminal work by Irving Kirkwood. This non-uniqueness is normally attributed to the interaction path between molecules, especially in the interfacial-science community. In this work we reframe this discussion of non-uniqueness in terms of the location, or reference frame, used to measure the pressure. By using a general mathematical description of the liquid-vapour interface, we obtain a reference frame that moves with the interface through time, providing a new insight into the pressure. We compare this instantaneous moving reference frame with the fixed Eulerian one. Through this process, we show the requirement that normal pressure balance at the moving surface is satisfied by surface fluxes, however an additional corrective term based on surface curvature is required for the average pressure in a volume. We make the case that a focus on the path of integration is the cause of much of the confusion in the literature. Using an explicit reference frame with a more general derivation of pressure clarifies some of the issues of uniqueness in the pressure tensor and provides a pressure tensor which is defined at any instant in time and valid away from thermodynamic equilibrium., Comment: 26 pages (preprint) and 9 figures

Understanding what happens inside the rippling and dancing surface of a liquid remains one of the great challenges of fluid dynamics. Using molecular dynamics (MD) 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-vapour 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 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-vapour instabilities., Comment: 52 pages, 8 figures

The surfactant-driven spreading of droplets is an essential process in many applications ranging from coating flow technology to enhanced oil recovery. Despite the significant advancement in describing spreading processes in surfactant-laden droplets, including the exciting phenomena of superspreading, many features of the underlying mechanisms require further understanding. Here, we have carried out molecular dynamics simulations of a coarse-grained model with a force-field obtained from the statistical associating fluid theory to study droplets laden with common and superspreading surfactants. We have confirmed the important elements of the superspreading mechanism, i.e. the adsorption of surfactant at the contact line and the fast replenishment of surfactant from the bulk. Through a detailed comparison of a range of droplets with different surfactants, our analysis has indicated that the ability of surfactant to adsorb at the interfaces is the key feature of the superspreading mechanism. To this end, surfactants that tend to form aggregates and have a strong hydrophobic attraction in the aggregated cores prevent the fast replenishment of the interfaces, resulting in reduced spreading ability. We also show that various surfactant properties, such as diffusion and architecture, play a secondary role in the spreading process. Moreover, we discuss various drop properties such as the height, contact angle, and surfactant surface concentration, highlighting differences between superspreading and common surfactants. We anticipate that our study will provide further insight for applications requiring the control of wetting., Comment: 26 pages, 11 figures