Why are Fluid Densities So Low in Carbon Nanotubes?

The equilibrium density of fluids under nanoconfinement can differ substantially from their bulk density. Using a mean-field approach to describe the energetic landscape near the carbon nanotube (CNT) wall, we obtain analytical results describing the lengthscales associated with the layering observed at the fluid-CNT interface. When combined with molecular simulation results for the fluid density in the layered region, this approach allows us to derive a closed-form prediction for the overall equilibrium fluid density as a function of the CNT radius that is in excellent agreement with molecular dynamics simulations. We also show how aspects of this theory can be extended to describe water confined within CNTs and find good agreement with results from the literature

Statistical Error in Particle Simulations of Low Mach Number Flows

We present predictions for the statistical error due to finite sampling in the presence of thermal fluctuations in molecular simulation algorithms. Expressions for the fluid velocity, density and temperature are derived using equilibrium statistical mechanics. The results show that the number of samples needed to adequately resolve the flow-field scales as the inverse square of the Mach number. The theoretical results are verified for a dilute gas using direct Monte Carlo simulations. The agreement between theory and simulation verifies that the use of equilibrium theory is justified.Singapore-MIT Alliance (SMA

An alternative approach to efficient simulation of micro/nanoscale phonon transport

Starting from the recently proposed energy-based deviational formulation for solving the Boltzmann equation [J.-P. Peraud and N. G. Hadjiconstantinou, Phys. Rev. B 84, 2011], which provides significant computational speedup compared to standard Monte Carlo methods for small deviations from equilibrium, we show that additional computational benefits are possible in the limit that the governing equation can be linearized. The proposed method exploits the observation that under linearized conditions (small temperature differences) the trajectories of individual deviational particles can be decoupled and thus simulated independently; this leads to a particularly simple and efficient algorithm for simulating steady and transient problems in arbitrary three-dimensional geometries, without introducing any additional approximation.Comment: 4 pages, 2 figure

Parabolic temperature profile and second-order temperature jump of a slightly rarefied gas in an unsteady two-surface problem

The behavior of a slightly rarefied monatomic gas between two parallel plates whose temperature grows slowly and linearly in time is investigated on the basis of the kinetic theory of gases. This problem is shown to be equivalent to a boundary-value problem of the steady linearized Boltzmann equation describing a rarefied gas subject to constant volumetric heating. The latter has been recently studied by Radtke, Hadjiconstantinou, Takata, and Aoki (RHTA) as a means of extracting the second-order temperature jump coefficient. This correspondence between the two problems gives a natural interpretation to the volumetric heating source and explains why the second-order temperature jump observed by RHTA is not covered by the general theory of slip flow for steady problems. A systematic asymptotic analysis of the time-dependent problem for small Knudsen numbers is carried out and the complete fluid-dynamic description, as well as the related half-space problems that determine the structure of the Knudsen layer and the coefficients of temperature jump, are obtained. Finally, a numerical solution is presented for both the Bhatnagar-Gross-Krook model and hard-sphere molecules. The jump coefficient is also calculated by the use of a symmetry relation; excellent agreement is found with the result of the numerical computation. The asymptotic solution and associated second-order jump coefficient obtained in the present paper agree well with the results by RHTA that are obtained by a low variance stochastic method

Statistical Error in Particle Simulations of Hydrodynamic Phenomena

We present predictions for the statistical error due to finite sampling in the presence of thermal fluctuations in molecular simulation algorithms. Specifically, we establish how these errors depend on Mach number, Knudsen number, number of particles, etc. Expressions for the common hydrodynamic variables of interest such as flow velocity, temperature, density, pressure, shear stress and heat flux are derived using equilibrium statistical mechanics. Both volume-averaged and surface-averaged quantities are considered. Comparisons between theory and computations using direct simulation Monte Carlo for dilute gases, and molecular dynamics for dense fluids, show that the use of equilibrium theory provides accurate results.Comment: 24 pages postscript (including 16 figures

An investigation of the dynamics of phase transitions in Lennard-Jones fluids

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Physics, 1998.Includes bibliographical references (leaves 73-76).This thesis reports the development, validation and application of a method to simulate external heat addition in molecular dynamics simulations of Lennard-Jones fluids. This simulation capability is very important for both purely theoretical and practical applications. Here we examine one theoretical application, namely the evaporation of clusters of liquid Argon under constant pressure. The algorithm is based on modified equations of motion derived from Newton's equations with the use of what is known in the literature as Gauss' least constraint principle. The modified equations of motion satisfy the constraint of linear (in time) energy addition to all the system molecules. The first part of the thesis presents the validation of the heat addition algorithm: the method is useful only if it does not adversely affect the properties of the simulated material. The validation consists of a series of simulations of a Lennard-Jones fluid in a two-dimensional channel bounded between two parallel (molecular) walls. The walls are kept at constant temperature, while the fluid is externally heated using the new simulation method. The temperature profile solution for this problem is, according to (the exact) continuum theory, parabolic. Given the heat addition rate, estimates for the value of the thermal conductivity can be obtained from the curvature of the temperature profile. The estimates for the thermal conductivity are compared to experimental data for the fluid, and simulation data based on the Newtonian (exact) equations of motion for the same fluid. We find that the thermal conductivity estimates obtained from our simulations are in agreement with the baseline results utilizing the Newtonian equations of motion. The second part of the thesis reports on the investigation of the phase change of fluid clusters at constant pressure in real time using the heat addition algorithm. This has not been attempted before; results exist in the literature only for quasistatic simulations whereby the phase change behavior of a Lennard-Jones fluid is recovered by performing a series of equilibrium simulations at varying temperatures. The results obtained through the newly proposed, developed, and validated time dependent method are in agreement with the results of the quasistatic simulations as linear response theory predicts. We conclude with the interpretation of our results using homogeneous nucleation theory. We find that our results are consistent with homogeneous nucleation which predicts that phase separation starts at the nanoscopic level with critical radii of the order of a few nanometers for both evaporation and condensation. The critical nuclei for evaporation, which are gaseous, are predictably larger than the nuclei for condensation, which are in the liquid state. Our results are in good agreement with experimental data. This work can form the basis for the investigation of open problems related to nucleation theory and nucleation kinetics, such as metastable cluster lifetimes, and nucleation frequencies. Alternative phase change mechanisms, such as spinodal decomposition, can also be investigated.by Nicolas Hadjiconstantinou.S.M

Statistical Error in Particle Simulations of Fluid Flow and Heat Transfer

We present predictions for the statistical error due to finite sampling in the presence of thermal fluctuations in molecular simulation algorithms. Specifically, we present predictions for the error dependence on hydrodynamic parameters and the number of samples taken. Expressions for the common hydrodynamic variables of interest such as flow velocity, temperature, density, pressure, shear stress and heat flux are derived using equilibrium statistical mechanics. Both volume-averaged and surface-averaged quantities are considered. Comparisons between theory and computations using direct simulation Monte Carlo for dilute gases, and molecular dynamics for dense fluids, show that the use of equilibrium theory provides accurate results.Singapore-MIT Alliance (SMA