Publications
39 results found
Smith ER, Theodorakis PE, 2024, Multiscale simulation of fluids: coupling molecular and continuum., Phys Chem Chem Phys, Vol: 26, Pages: 724-744
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 same 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 the two main types of coupling, state and flux, and discuss the varying assumptions in their use. 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. 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.
Rahman MR, Shen L, Ewen JP, et al., 2023, Non-equilibrium molecular simulations of thin film rupture, JOURNAL OF CHEMICAL PHYSICS, Vol: 158, ISSN: 0021-9606
Shi K, Smith ER, Santiso EE, et al., 2023, A perspective on the microscopic pressure (stress) tensor: History, current understanding, and future challenges, JOURNAL OF CHEMICAL PHYSICS, Vol: 158, ISSN: 0021-9606
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- Citations: 13
Ewen J, Maffioli L, Smith E, et al., 2022, Slip and stress from low strain-rate nonequilibrium molecular dynamics: The transient-time correlation function technique, The Journal of Chemical Physics, Vol: 156, Pages: 1-11, ISSN: 0021-9606
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.
Rahman M, Shen L, Ewen J, et al., 2022, The intrinsic fragility of the liquid-vapor interface: a stress network perspective, Langmuir: the ACS journal of surfaces and colloids, Vol: 38, Pages: 4669-4679, ISSN: 0743-7463
The evolution of the liquid-vapour interface of a Lennard-Jones fluid is examined with molecular dynamics simulations using the intrinsic sampling method. Results suggest, in agreement with capillary wave theory, clear damping of the density profiles as the temperature is increased. We identify a linear variation of the space-filling nature (fractal dimension) of the stress-clusters at the intrinsic surface with increasing surface tension, or equivalently, with decreasing temperature. A percolation analysis of these stress networks indicates that the stress field is more disjointed at higher temperatures. This leads to more fragile interfaces that result in a reduction in surface tension at higher temperature.
Kalderon M, Smith E, O'Sullivan C, 2022, Comparative analysis of porosity coarse-graining techniques for discrete element simulations of dense particulate systems, Computational Particle Mechanics, Vol: 9, Pages: 199-219, ISSN: 2196-4378
The discrete element method (DEM) is a well-established approach to study granular materials in numerous fields of application; each granular particle is modelled individually to predict the overall behaviour. This behaviour can be then extracted by averaging, or coarse graining, the sample using a suitable method. The choice of appropriate coarse-graining method entails a compromise between accuracy and computational cost, especially in the large-scale simulations typically required by industry. A number of coarse-graining methods have been proposed in the literature, and these are reviewed and categorized in this work. Within this contribution, two novel porosity coarse-graining strategies are proposed including a voxel method where a secondary dense grid of “pixel cells” is implemented adopting a binary logic for the coarse graining and a hybrid method where both analytical formulas and pixels are utilized. The proposed methods are compared with four coarse-graining schemes that have been documented in the literature, including the particle centroid method, an analytical method, a method which solves the diffusion equation and an approach which employs averaging using kernels. The novel methods are validated for problems in both two and three dimensions through comparison with the “accurate” analytical method. It is shown that, once validated, both the proposed schemes can approximate the exact solutions quite accurately; however, there is a high computational cost associated with the voxel method. The accuracy of both methods can be adjusted allowing the user to decide between accuracy and computational time. A detailed comparison is then presented for all six schemes considering “accuracy”, “smoothness” and “computational cost”. Optimal parameters are obtained for all six methods, and recommendations for coarse-graining DEM samples are discussed.
Smith ER, 2022, The importance of reference frame for pressure at the liquid-vapour interface, MOLECULAR SIMULATION, Vol: 48, Pages: 57-72, ISSN: 0892-7022
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- Citations: 8
Hoover WG, Hoover CG, Smith ER, 2022, Nonequilibrium Time Reversibility with Maps and Walks, ENTROPY, Vol: 24
Wen J, Dini D, Hu H, et al., 2021, Molecular droplets vs bubbles: Effect of curvature on surface tension and Tolman length, PHYSICS OF FLUIDS, Vol: 33, ISSN: 1070-6631
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- Citations: 10
Lavino AD, Smith E, Magnini M, et al., 2021, Surface topography effects on pool boiling via non-equilibrium molecular dynamics simulations., Langmuir: the ACS journal of surfaces and colloids, Vol: 37, Pages: 5731-5744, ISSN: 0743-7463
In this work, we investigate nucleate pool boiling via non-equilibrium molecular dynamics simulations. The effect of nano-structured surface topography on nucleation and transition to a film-like boiling regime is studied at the molecular scale, by varying the cavity aspect ratio, wall superheat, and wettability through a systematic parametric analysis conducted on a Lennard-Jones (LJ) system. The interplay of the aforementioned factors is rationalized by means of a classical nucleation theory-based model. The solid surface is heated uniformly from the bottom in order to induce the nanobubble nucleation. Insight into the cavity behavior in heat transfer problems is achieved by looking at temperature and heat flux profiles inside the cavity itself, as well as at the time of nucleation, for different operating conditions. The role of the cavity size in controlling the vapor embryo formation is highlighted, and its dependence on the other investigated parameters is summarized in a phase diagram. Our results show that heterogeneity at the nanoscale plays a key role in determining pool boiling heat transfer performance, suggesting a promising approach to optimize nanostructured surfaces for energy and thermal management applications.
Che H, O'Sullivan C, Sufian A, et al., 2021, A novel CFD-DEM coarse-graining method based on the Voronoi tessellation, Powder Technology, Vol: 384, Pages: 479-493, ISSN: 0032-5910
In unresolved flow CFD-DEM simulations, the porosity values for each CFD cell are determined using a coarse-graining algorithm. While this approach enables coupled simulations of representative numbers of particles, the influence of the porosity local to the particles on the fluid-particle interaction force is not captured. This contribution considers a two-grid coarse-graining method that determines a local porosity for each particle using a radical Voronoi tessellation of the system. A relatively fine, regular point cloud is used to map these local porosity data to the CFD cells. The method is evaluated using two different cases considering both disperse and tightly packed particles. The data show that the method conserves porosity data, is reasonably grid-independent and can generate a relatively smooth porosity field. The new method can more accurately predict the fluid-particle interactive force for polydisperse particle system than alternative methods that have been implemented in unresolved CFD-DEM codes.
Heyes DM, Dini D, Smith ER, 2021, Viscuit and the fluctuation theorem investigation of shear viscosity by molecular dynamics simulations: the information and the noise, Journal of Chemical Physics, Vol: 154, ISSN: 0021-9606
The shear viscosity, η, of model liquids and solids is investigated within the framework of the viscuit and Fluctuation Theorem (FT) probability distribution function (PDF) theories, following Heyes et al. [J. Chem. Phys. 152, 194504 (2020)] using equilibrium molecular dynamics (MD) simulations on Lennard-Jones and Weeks–Chandler–Andersen model systems. The viscosity can be obtained in equilibrium MD simulation from the first moment of the viscuit PDF, which is shown for finite simulation lengths to give a less noisy plateau region than the Green–Kubo method. Two other formulas for the shear viscosity in terms of the viscuit and PDF analysis are also derived. A separation of the time-dependent average negative and positive viscuits extrapolated from the noise dominated region to zero time provides another route to η. The third method involves the relative number of positive and negative viscuits and their PDF standard deviations on the two sides for an equilibrium system. For the FT and finite shear rates, accurate analytic expressions for the relative number of positive to negative block average shear stresses is derived assuming a shifted Gaussian PDF, which is shown to agree well with non-equilibrium molecular dynamics simulations. A similar treatment of the positive and negative block average contributions to the viscosity is also shown to match the simulation data very well.
Smith ER, Braga C, 2020, Hydrodynamics across a fluctuating interface, JOURNAL OF CHEMICAL PHYSICS, Vol: 153, ISSN: 0021-9606
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- Citations: 4
Heyes DM, Dini D, Smith ER, 2020, Statistical analysis and molecular dynamics simulations of the thermal conductivity of lennard–Jones solids including their pressure and temperature dependencies, Physica Status Solidi B: Basic Solid State Physics, Vol: 257, Pages: 1-14, ISSN: 0370-1972
Aspects of the thermal conductivity, λ, of a Lennard–Jones (LJ) solid along an isotherm and the sublimation line are studied using equilibrium molecular dynamics (MD) simulations. A reformulation of the Green–Kubo time correlation function expression for λ in the form of a probability distribution function (PDF) of single trajectory contributions (STC) exhibits the same characteristic statistical trends as found previously for liquids, even at high pressures and low temperatures. The analysis reveals that for short periods of time the thermal conductivity can be negative. This feature is evident along the sublimation line isobar and a low‐temperature isotherm going to high densities. Along the isobar and isotherm lines, λ is to a good approximation a power law in temperature and density, respectively. This behavior is used in a more general thermodynamics‐based analysis description of the state point dependence of the thermal conductivity. The heat flux autocorrelation function increasingly develops a damped oscillatory appearance as pressure increases or temperature decreases, consistent with the phonon formulation of thermal conductivity.
Heyes DM, Dini D, Smith ER, 2020, Single trajectory transport coefficients and the energy landscape by molecular dynamics simulations, JOURNAL OF CHEMICAL PHYSICS, Vol: 152, ISSN: 0021-9606
Smith E, Trevelyan D, Ramos-Fernandez E, et al., 2020, CPL library - a minimal framework for coupled particle and continuum simulation, Computer Physics Communications, Vol: 250, Pages: 1-11, ISSN: 0010-4655
We present an open-source library for coupling particle codes, such as molecular dynamics (MD) or the discrete element method (DEM), and grid based computational fluid dynamics (CFD). The application is focused on domain decomposition coupling, where a particle and continuum software model different parts of a single simulation domain with information exchange. This focus allows a simple library to be developed, with core mapping and communication handled by just four functions. Emphasis is on scaling on supercomputers, a tested cross-language library, deployment with containers and well-documented simple examples. Building on this core, a template is provided to facilitate the user development of common features for coupling, such as averaging routines and functions to apply constraint forces. The interface code for LAMMPS and OpenFOAM is provided to both include molecular detail in a continuum solver and model fluids flowing through a granular system. Two novel development features are highlighted which will be useful in the development of the next generation of multi-scale software: (i) The division of coupled code into a smaller blocks with testing over a range of processor topologies. (ii) The use of coupled mocking to facilitate coverage of various parts of the code and allow rapid prototyping. These two features aim to help users develop coupled models in a test-driven manner and focus on the physics of the problem instead of just software development. All presented code is open-source with detailed documentation on the dedicated website (cpl-library.org) permitting useful aspects to be evaluated and adopted in other projects.
Ewen J, Ramos Fernandez E, Smith E, et al., 2020, Nonequilibrium Molecular Dynamics Simulations of Tribological Systems, Modeling and Simulation of Tribological Problems in Technology, Editors: Paggi, Hills, Publisher: Springer Nature, Pages: 95-130, ISBN: 978-3-030-20376-4
Theodorakis PE, Smith ER, Muller EA, 2019, Spreading of aqueous droplets with common and superspreading surfactants. A molecular dynamics study, COLLOIDS AND SURFACES A-PHYSICOCHEMICAL AND ENGINEERING ASPECTS, Vol: 581, ISSN: 0927-7757
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- Citations: 12
Theodorakis PE, Smith ER, Craster RV, et al., 2019, Molecular dynamics simulation of the super spreading of surfactant-laden droplets. A review, Fluids, Vol: 4, Pages: 1-23, ISSN: 2311-5521
Superspreading is the rapid and complete spreading of surfactant-laden droplets on hydrophobic substrates. This phenomenon has been studied for many decades by experiment, theory, and simulation, but it has been only recently that molecular-level simulation has provided significant insights into the underlying mechanisms of superspreading thanks to the development of accurate force-fields and the increase of computational capabilities. Here, we review the main advances in this area that have surfaced from Molecular Dynamics simulation of all-atom and coarse-grained models highlighting and contrasting the main results and discussing various elements of the proposed mechanisms for superspreading. We anticipate that this review will stimulate further research on the interpretation of experimental results and the design of surfactants for applications requiring efficient spreading, such as coating technology.
Heyes D, Smith ER, Dini D, 2019, Shear stress relaxation and diffusion in simple liquids by molecular dynamics simulations: Analytic expressions and paths to viscosity, The Journal of Chemical Physics, Vol: 150, ISSN: 0021-9606
The results are reported of an equilibrium molecular dynamics simulation study of the shear viscosity, η, and self-diffusion coefficient, D, of the Lennard-Jones liquid using the Green-Kubo (GK) method. Semiempirical analytic expressions for both GK time correlation functions were fitted to the simulation data and used to derive analytic expressions for the time dependent diffusion coefficient and shear viscosity, and also the correlation function frequency transforms. In the case of the shear viscosity for a state point near the triple point, a sech function was found to fit the correlation function significantly better than a gaussian in the ballistic short time regime. A reformulation of the shear GK formula in terms of a time series of time integrals (“viscuits”) and contributions to the viscosity from components based on the initial stress (“visclets”) enable the GK expressions to be recast in terms of probability distributions which could be used in coarse grained stochastic models of nanoscale flow. The visclet treatment shows that stress relaxation is statistically independent of the initial stress for equilibrium and metastable liquids, suggesting that shear stress relaxation in liquids is diffusion controlled. By contrast, the velocity autocorrelation function is sensitive to the initial velocity. Weak oscillations and a plateau at intermediate times originate to a greater extent from the high velocity tail of the Maxwell-Boltzmann velocity distribution. Simple approximate analytic expressions for the mean square displacement and the self Van Hove correlation function are also derived.
Smith ER, Daivis PJ, Todd BD, 2019, Measuring heat flux beyond Fourier's law, JOURNAL OF CHEMICAL PHYSICS, Vol: 150, ISSN: 0021-9606
Braga C, Smith E, Nold A, et al., 2018, The pressure tensor across a liquid-vapour interface, Journal of Chemical Physics, Vol: 149, ISSN: 0021-9606
Inhomogeneous fluids exhibit physical properties that are neither uniform nor isotropic. The pressure tensor is a case in point, key to the mechanical description of the interfacial region. Kirkwood and Buff and, later, Irving and Kirkwood, obtained a formal treatment based on the analysis of the pressure across a planar surface [J. G. Kirkwood and F. P. Buff, J. Chem. Phys. 17(3), 338 (1949); J. H. Irving and J. G. Kirkwood, J. Chem. Phys. 18, 817 (1950)]. We propose a generalisation of Irving and Kirkwood’s argument to fluctuating, non-planar surfaces and obtain an expression for the pressure tensor that is not smeared by thermal fluctuations at the molecular scale and corresponding capillary waves [F. P. Buff et al., Phys. Rev. Lett. 15, 621–623 (1965)]. We observe the emergence of surface tension, defined as an excess tangential stress, acting exactly across the dividing surface at the sharpest molecular resolution. The new statistical mechanical expressions extend current treatments to fluctuating inhomogeneous systems far from equilibrium.
Heyes D, Dini D, Smith E, 2018, Incremental viscosity by non-equilibrium molecular dynamics and the Eyring model, Journal of Chemical Physics, Vol: 148, ISSN: 0021-9606
The viscoelastic behavior of sheared fluids is calculated by Non-Equilibrium Molecular Dynamics(NEMD) simulation, and complementary analytic solutions of a time-dependent extension of Eyring’smodel (EM) for shear thinning are derived. It is argued that an “incremental viscosity,”ηi, or IV whichis the derivative of the steady state stress with respect to the shear rate is a better measure of the physicalstate of the system than the conventional definition of the shear rate dependent viscosity (i.e., the shearstress divided by the strain rate). The stress relaxation function,Ci(t), associated withηiis consistentwith Boltzmann’s superposition principle and is computed by NEMD and the EM. The IV of the Eyringmodel is shown to be a special case of the Carreau formula for shear thinning. An analytic solutionfor the transient time correlation function for the EM is derived. An extension of the EM to allow forsignificant local shear stress fluctuations on a molecular level, represented by a gaussian distribution,is shown to have the same analytic form as the original EM but with the EM stress replaced by its timeand spatial average. Even at high shear rates and on small scales, the probability distribution functionis almost gaussian (apart from in the wings) with the peak shifted by the shear. The Eyring formulaapproximately satisfies the Fluctuation Theorem, which may in part explain its success in representingthe shear thinning curves of a wide range of different types of chemical systems.
Smith ER, Theodorakis PE, Craster RV, et al., 2018, Moving contact lines: linking molecular dynamics and continuum-scale modeling, Langmuir, Vol: 34, Pages: 12501-12518, ISSN: 0743-7463
Despite decades of research, the modeling of moving contact lines has remained a formidable challenge in fluid dynamics whose resolution will impact numerous industrial, biological, and daily life applications. On the one hand, molecular dynamics (MD) simulation has the ability to provide unique insight into the microscopic details that determine the dynamic behavior of the contact line, which is not possible with either continuum-scale simulations or experiments. On the other hand, continuum-based models provide a link to the macroscopic description of the system. In this Feature Article, we explore the complex range of physical factors, including the presence of surfactants, which governs the contact line motion through MD simulations. We also discuss links between continuum- and molecular-scale modeling and highlight the opportunities for future developments in this area.
Heyes D, Dini D, Smith E, et al., 2017, Nanowire stretching by Non-equilibrium Molecular Dynamics, Physica Status Solidi B: Basic Solid State Physics, Vol: 254, ISSN: 0370-1972
Non-equilibrium Molecular Dynamics (NEMD) simulations of a stretched Lennard-Jones (LJ) model single crystal nanowire with square cross-section are carried out. The microstructural and mechanical properties are examined as a function of strain and strain rate. The instantaneous Poisson's ratio and Young's modulus are shown to be strongly time (strain) dependent from the start of the pulling process. The structural transformation as a result of straining initially involves the (100) layers moving further apart and then slipping at ca. math formula when the shear slip stress along that direction is about 1% of the shear modulus, which is typical of plastic deformation of noble gas solid crystals, and in accordance with Schmid's law.
Smith E, Heyes D, Dini D, 2017, Towards the Irving Kirkwood limit of the mechanical stress tensor, Journal of Chemical Physics, Vol: 146, ISSN: 1089-7690
The probability density functions (PDFs) of the local measure of pressure as a function of the sampling volume are computed for a model Lennard-Jones (LJ) fluid using the Method of Planes (MOP) and Volume Averaging (VA) techniques. This builds on the study of Heyes, Dini, and Smith [J. Chem. Phys. 145, 104504 (2016)] which only considered the VA method for larger subvolumes. The focus here is typically on much smaller subvolumes than considered previously, which tend to the Irving-Kirkwood limit where the pressure tensor is defined at a point. The PDFs from the MOP and VA routes are compared for cubic subvolumes, V=ℓ3. Using very high grid-resolution and box-counting analysis, we also show that any measurement of pressure in a molecular system will fail to exactly capture the molecular configuration. This suggests that it is impossible to obtain the pressure in the Irving-Kirkwood limit using the commonly employed grid based averaging techniques. More importantly, below ℓ≈3 in LJ reduced units, the PDFs depart from Gaussian statistics, and for ℓ=1.0, a double peaked PDF is observed in the MOP but not VA pressure distributions. This departure from a Gaussian shape means that the average pressure is not the most representative or common value to arise. In addition to contributing to our understanding of local pressure formulas, this work shows a clear lower limit on the validity of simply taking the average value when coarse graining pressure from molecular (and colloidal) systems.
Smith ER, Müller EA, Craster RV, et al., 2016, A Langevin model for fluctuating contact angle behaviour parametrised using molecular dynamics, Soft Matter, Vol: 12, Pages: 9604-9615, ISSN: 1744-6848
Molecular dynamics simulations are employed to develop a theoretical model to predict the fluid-solid contact angle as a function of wall-sliding speed incorporating thermal fluctuations. A liquid bridge between counter-sliding walls is studied, with liquid-vapour interface-tracking, to explore the impact of wall-sliding speed on contact angle. The behaviour of the macroscopic contact angle varies linearly over a range of capillary numbers beyond which the liquid bridge pinches off, a behaviour supported by experimental results. Nonetheless, the liquid bridge provides an ideal test case to study molecular scale thermal fluctuations, which are shown to be well described by Gaussian distributions. A Langevin model for contact angle is parametrised to incorporate the mean, fluctuation and auto-correlations over a range of sliding speeds and temperatures. The resulting equations can be used as a proxy for the fully-detailed molecular dynamics simulation allowing them to be integrated within a continuum-scale solver.
Heyes DM, Dini D, Smith ER, 2016, Equilibrium fluctuations of liquid state static properties in a subvolume by molecular dynamics, Journal of Chemical Physics, Vol: 145, ISSN: 1089-7690
System property fluctuations increasingly dominate a physical process as the sampling volume decreases. The purpose of this work is to explore how the fluctuation statistics of various thermodynamic properties depend on the sampling volume, using molecular dynamics (MD) simulations. First an examination of various expressions for calculating the bulk pressure of a bulk liquid is made, which includes a decomposition of the virial expression into two terms, one of which is the Method of Planes (MOP) applied to the faces of the cubic simulation cell. Then an analysis is made of the fluctuations of local density, temperature, pressure, and shear stress as a function of sampling volume (SV). Cubic and spherical shaped SVs were used within a spatially homogeneous LJ liquid at a state point along the melting curve. It is shown that the MD-generated probability distribution functions (PDFs) of all of these properties are to a good approximation Gaussian even for SV containing only a few molecules (∼10), with the variances being inversely proportional to the SV volume, Ω. For small subvolumes the shear stress PDF fits better to a Gaussian than the pressure PDF. A new stochastic sampling technique to implement the volume averaging definition of the pressure tensor is presented, which is employed for cubic, spherical, thin cubic, and spherical shell SV. This method is more efficient for less symmetric SV shapes.
Smith ER, 2015, A molecular dynamics simulation of the turbulent Couette minimal flow unit, Physics of Fluids, Vol: 27, ISSN: 1070-6631
A molecular dynamics simulation of planar Couette flow is presented for the minimalchannel in which turbulence structures can be sustained. Evolution over a single break-down and regeneration cycle is compared to computational fluid dynamics simula-tions. Qualitative similar structures are observed and turbulent statistics show excellentquantitative agreement. The molecular scale law of the wall is presented in whichstick-slip molecular wall-fluid interactions replace the no-slip conditions. The impactof grid resolution is explored and the observed structures are seen to be dependenton averaging time and length scales. The kinetic energy spectra show that a range ofscales are present in the molecular system and that spectral content is dependent onthe grid resolution employed. The subgrid velocity of the molecules is studied usingjoint probability density functions, molecular trajectories, diffusion, and Lagrangianstatistics. The importance of sub-grid scales, relevance of the Kolmogorov lengthscale,and implications of molecular turbulence are discussed.
Smith ER, Heyes DM, Dini D, et al., 2015, A localized momentum constraint for non-equilibrium molecular dynamics simulations, JOURNAL OF CHEMICAL PHYSICS, Vol: 142, ISSN: 0021-9606
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- Citations: 5
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