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

Hybrid atomistic-continuum formulations and the moving contact line problem

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1998.Includes bibliographical references (leaves 149-153).We present a formulation and numerical solution procedure for hybrid atomistic­continuum representations of fluid flows. Hybrid representations are of great im­portance because they allow the solution of problems that require modelling on the microscale without the associated cost of a fully molecular solution. This is achieved by limiting the molecular treatment to the regions where it is needed while using the inexpensive continuum description in the remainder of the computational domain. The ingredients are, from the atomistic side, non-equilibrium molecular dynamics, and from the continuum side, spectral/finite element solutions. Molecular dynamics has been chosen for its ability to capture all the underlying physics without the need for modelling assumptions. The continuum solution techniques chosen represent the best compromise between the minimum computational cost, simplicity, and appli­cability to a wide variety of problems of interest. The matching is provided by a classical procedure, the Schwarz alternating method with overlapping subdomains. This matching technique exhibits favorable convergence properties and has been pre­ferred because of its ability to bypass the problem of matching fluxes in molecular dynamics which has not been satisfactorily treated to date. Flow of a dense fluid (supercritical Argon) in a complex two-dimensional chan­nel serves as a test problem for the validation of the technique developed above. Reasonable agreement is found between the hybrid solution and the fully continuum solution which is taken to be exact. The hybrid technique is subsequently applied to the moving contact line problem. The motion of contact lines (the locus of intersection of a two-fluid interface with a bounding solid) has, due to the multitude of length scales involved, been one of the few problems that has defied theoretical analysis over the years. It has long been concluded that continuum hydrodynamics is not adequate for the description of the physics involved in the vicinity of the contact angle, which is predominantly molecular kinetic, thus making this problem a good candidate for our solution technique. The basic ingredients for the hybrid treatment of the contact line problem are the continuum solution technique, the molecular solution technique, and a modified Schwarz method required due to the existence of two fluids and a two-fluid inter­face. The continuum solution is provided by a variationally consistent finite element simulation technique we have developed for the above reason. An already developed molecular simulation technique is adapted to provide the molecular solution. Our hybrid solution is compared with the fully molecular solution which serves as an ex­act solution for comparison purposes. Good agreement is found between the two solutions.Nicolas Hadjiconstantinou.Ph.D

Model for converting spark ignition engine flame arrival signals into flame contours.

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1995.Includes bibliographical references (leaves 88-90).by Nicolas G. Hadjiconstantinou.M.S

Introduction to Modeling and Simulation

Basic concepts of computer modeling in science and engineering using discrete particle systems and continuum fields. Techniques and software for statistical sampling, simulation, data analysis and visualization. Use of statistical, quantum chemical, molecular dynamics, Monte Carlo, mesoscale and continuum methods to study fundamental physical phenomena encountered in the fields of computational physics, chemistry, mechanics, materials science, biology, and applied mathematics. Applications drawn from a range of disciplines to build a broad-based understanding of complex structures and interactions in problems where simulation is on equal-footing with theory and experiment. Term project allows development of individual interest. Student mentoring by a coordinated team of participating faculty from across the Institute

Introduction to Modeling and Simulation

Basic concepts of computer modeling in science and engineering using discrete particle systems and continuum fields. Techniques and software for statistical sampling, simulation, data analysis and visualization. Use of statistical, quantum chemical, molecular dynamics, Monte Carlo, mesoscale and continuum methods to study fundamental physical phenomena encountered in the fields of computational physics, chemistry, mechanics, materials science, biology, and applied mathematics. Applications drawn from a range of disciplines to build a broad-based understanding of complex structures and interactions in problems where simulation is on equal-footing with theory and experiment. Term project allows development of individual interest. Student mentoring by a coordinated team of participating faculty from across the Institute