Sutapa Roy

Transport phenomena in fluids: Finite-size scaling for critical behavior

Results for transport properties, in conjunction with phase behavior and thermodynamics, are presented to understand the critical behavior of a binary Lennard-Jones fluid, on the basis of Monte Carlo and molecular dynamics simulations. Evidence for much stronger finite-size effects in dynamics compared to statics has been demonstrated. Results for bulk viscosity are the first in the literature where the critical divergence is quantified via a novel application of finite-size scaling. Our results are in accordance with the theoretical predictions of mode-coupling and dynamic renormalization group calculations.

Nucleation and growth of droplets in vapor-liquid transitions.

Results for the kinetics of vapor-liquid transitions, following temperature quenches with different densities, are presented from molecular dynamics simulations of a Lennard-Jones system. For a critical density, bicontinuous liquid and vapor domains are observed which grow with time, obeying the predictions for the hydrodynamic mechanism. On the other hand, for quenches with density significantly below the critical one, phase separation progresses via nucleation and growth of liquid droplets. In the latter case, the Brownian diffusion and collision mechanism for the droplet growth is confirmed. We also discuss the possibility of interdroplet interaction leading to a different amplitude in the growth law. Arguments for faster growth, observed at early times, are also provided.

Finite-size scaling study of shear viscosity anomaly at liquid-liquid criticality

We study the equilibrium dynamics of a symmetrical binary Lennard-Jones fluid mixture near its consolute criticality. Molecular dynamics simulation results for the shear viscosity, η, from a microcanonical ensemble are compared with those from a canonical ensemble with various thermostats. It is observed that the Nosé-Hoover thermostat is a good candidate for this purpose, and is therefore adopted for the quantification of the critical singularity of η, to avoid the temperature fluctuations (or even drifts) that are often encountered in microcanonical simulations. Via a finite-size scaling analysis of our simulation data we have been able to confirm that the shear viscosity exhibits a weak critical singularity in agreement with the theoretical predictions.

Finite-size effects in dynamics: Critical vs. coarsening phenomena

Finite-size effects in systems with diverging characteristic length scale have been addressed via state-of-the-art Monte Carlo and molecular-dynamics simulations of various models exhibiting solid-solid, liquid-liquid and vapor-liquid transitions. Our simulations, combined with the appropriate application of the finite-size scaling theory, confirm various non-trivial singularities in equilibrium dynamic critical phenomena and non-equilibrium domain coarsening phenomena, as predicted by analytical theories. We convincingly demonstrate that the finite-size effects in the domain growth problems, with conserved order parameter dynamics, is weak and universal, irrespective of the transport mechanism. This result is strikingly different from the corresponding effects in critical dynamics. In critical phenomena, the difference in finite-size effects between statics and dynamics is also discussed.

Effects of domain morphology on kinetics of fluid phase separation.

Kinetics of phase separation in a three-dimensional single-component Lennard-Jones fluid, that exhibits vapor-liquid transition, is studied via molecular dynamics simulations after quenching homogeneous systems, of different overall densities, inside the coexistence region. For densities close to the vapor branch of the coexistence curve, phase separation progresses via nucleation of liquid droplets and collisions among them. This is different from the evaporation-condensation mechanism proposed by Lifshitz and Slyozov, even though both lead to power-law growth of average domain size, as a function of time, with an exponent α = 1∕3. Beyond a certain threshold value of the overall density, we observe elongated, percolating domain morphology which suddenly enhances the value of α. These results are consistent with some existing theoretical expectations.

Dynamics and growth of droplets close to the two-phase coexistence curve in fluids

Results from state-of-the-art molecular dynamics simulations are presented for both equilibrium and nonequilibrium dynamics following a vapor–liquid transition in a single component Lennard-Jones system. We have fixed the overall density close to the vapor branch of the coexistence curve so that the liquid phase forms droplet structures in the background of the vapor phase. In the equilibrium case, the motion of a single droplet is studied in both microcanonical and canonical ensembles, in the latter case a hydrodynamics preserving Nose–Hoover thermostat was used to control the temperature. The droplet nucleation, motion, collision and coalescence dynamics in the nonequilibrium case were studied in the canonical ensemble with the Nose–Hoover thermostat. There it was observed that the average droplet volume grows linearly with time. Between two successive collisions, the size of the droplets remains the same even though all the constituent particles do not move with the droplets – some leave, others join. It is seen that the number of original particles in a droplet decays exponentially fast. Results from a liquid–liquid transition are also presented in the equilibrium context. Dynamics of droplets in equilibrium appears to be at variance with the nonequilibrium case.

Simulation of transport around the coexistence region of a binary fluid

We use Monte Carlo and molecular dynamics simulations to study phase behavior and transport properties in a symmetric binary fluid where particles interact via Lennard-Jones potential. Our results for the critical behavior of collective transport properties, with particular emphasis on bulk viscosity, is understood via appropriate application of finite-size scaling technique. It appears that the critical enhancements in these quantities are visible far above the critical point. This result is consistent with an earlier report from computer simulations where, however, the authors do not quantify the critical singularity.

Coarsening in fluid phase transitions

We review understanding of kinetics of fluid phase separation in various space dimensions. Morphological differences, percolating or disconnected, based on overall composition in a binary liquid or density in a vapor-liquid system, have been pointed out. Depending upon the morphology, various possible mechanisms and corresponding theoretical predictions for domain growth are discussed. On computational front, useful models and simulation methodologies have been presented. Theoretically predicted growth laws have been tested via molecular dynamics simulations of vapor-liquid transitions. In case of disconnected structure, the mechanism has been confirmed directly. This is a brief review on the topic for a special issue on coarsening dynamics, expected to appear in Comptes Rendus Physique.

Study of critical dynamics in fluids via molecular dynamics in canonical ensemble

Abstract.With the objective of understanding the usefulness of thermostats in the study of dynamic critical phenomena in fluids, we present results for transport properties in a binary Lennard-Jones fluid that exhibits liquid-liquid phase transition. Various collective transport properties, calculated from the molecular dynamics (MD) simulations in canonical ensemble, with different thermostats, are compared with those obtained from MD simulations in microcanonical ensemble. It is observed that the Nosé-Hoover and dissipative particle dynamics thermostats are useful for the calculations of mutual diffusivity and shear viscosity. The Nosé-Hoover thermostat, however, as opposed to the latter, appears inadequate for the study of bulk viscosity.Graphical abstract