Simulation of heat conduction in nanocomposite using energy-conserving dissipative particle dynamics

Generalized Energy-Conserving Dissipative Particle Dynamics with Mass Transfer. Part 1: Theoretical Foundation and Algorithm

An extension of the generalized energy-conserving dissipative particle dynamics method (GenDPDE) that allows mass transfer between mesoparticles via a diffusion process is presented. By considering the concept of the mesoparticles as property carriers, the complexity and flexibility of the GenDPDE framework were enhanced to allow for interparticle mass transfer under isoenergetic conditions, notated here as GenDPDE-M. In the formulation, diffusion is described via the theory of mesoscale irreversible processes based on linear relationships between the fluxes and thermodynamic forces, where their fluctuations are described by Langevin-like equations. The mass exchange between mesoparticles is such that the mass of the mesoparticle remains unchanged after the transfer process and requires additional considerations regarding the coupling with other system properties such as the particle internal energy. The proof-of-concept work presented in this article is the first part of a two-part article series. In Part 1, the development of the GenDPDE-M theoretical framework and the derivation of the algorithm are presented in detail. Part 2 of this article series is targeted for practitioners, where applications, demonstrations, and practical considerations for implementing the GenDPDE-M method are presented and discussed.

Dissipative particle dynamics simulations in colloid and Interface science: a review

Dissipative particle dynamics (DPD) is one of the most efficient mesoscale coarse-grained methodologies for modeling soft matter systems. Here, we comprehensively review the progress in theoretical formulations, parametrization strategies, and applications of DPD over the last two decades. DPD bridges the gap between the microscopic atomistic and macroscopic continuum length and time scales. Numerous efforts have been performed to improve the computational efficiency and to develop advanced versions and modifications of the original DPD framework. The progress in the parametrization techniques that can reproduce the engineering properties of experimental systems attracted a lot of interest from the industrial community longing to use DPD to characterize, help design and optimize the practical products. While there are still areas for improvements, DPD has been efficiently applied to numerous colloidal and interfacial phenomena involving phase separations, self-assembly, and transport in polymeric, surfactant, nanoparticle, and biomolecules systems.

Mesoscopic Dynamical Model of Ice Crystal Nucleation Leading to Droplet Freezing

We present a numerical model to study the dynamic behaviors and heat conduction of freezing liquid droplets based on the MDPDE method (many-body dissipative particle dynamics with energy conservation configurations). In this model, the freezing processes involved in cooling, recalescence, and nucleation are considered. A new scaling method was developed to connect the mesoscopic MDPDE coefficients and macrothermal conductivity. The freezing of water droplets on cold surfaces with different wettabilities was simulated. Both the evolution of temperature and ice-liquid interface movement showed close agreement with the experimental data. We discuss the formation of a pointy tip on the top of an ice-drop and nucleation and growth during the recalescence stage. The rapid expansion of the recalescence region and the growth of the solid-phase region were calculated numerically, and this showed that the nuclei distribution of the two processes were completely different. The MDPDE model can not only predict the freezing time and shape deformation of ice-drops but also the nuclei formation and crystal growth during solidification. This study provides a useful tool for deicing material design.

Dissipative particle dynamics with energy conservation: Isoenergetic integration and transport properties

Simulations of nano- to micro-meter scale fluidic systems under thermal gradients require consistent mesoscopic methods accounting for both hydrodynamic interactions and proper transport of energy. One such method is dissipative particle dynamics with energy conservation (DPDE), which has been used for various fluid systems with non-uniform temperature distributions. We propose an easily parallelizable modification of the velocity-Verlet algorithm based on local energy redistribution for each DPDE particle such that the total energy in a simulated system is conserved up to machine precision. Furthermore, transport properties of a DPDE fluid are analyzed in detail. In particular, an analytical approximation for the thermal conductivity coefficient is derived, which allows its a priori estimation for a given parameter set. Finally, we provide approximate expressions for the dimensionless Prandtl and Schmidt numbers, which characterize fluid transport properties and can be adjusted independently by a proper selection of model parameters. In conclusion, our results strengthen the DPDE method as a very robust approach for the investigation of mesoscopic systems with temperature inhomogeneities.

Generalised dissipative particle dynamics with energy conservation: density- and temperature-dependent potentials

We present a generalised, energy-conserving dissipative particle dynamics (DPDE) method appropriate for the non-isothermal simulation of particle interaction force fields that are both density- and temperature-dependent. A detailed derivation is formulated in a bottom-up manner by considering the thermodynamics of small systems with the appropriate consideration of the fluctuations. Connected to the local volume is a local density and corresponding local pressure, which is determined from an equation-of-state based force field that depends also on a particle temperature. Compared to the original DPDE method, the formulation of the generalised DPDE method requires a change in the independent variable from the particle internal energy to the particle entropy. As part of the re-formulation, the terms dressed particle entropy and the corresponding dressed particle temperature are introduced, which depict the many-body contributions in the local volume. The generalised DPDE method has similarities to the energy form of the smoothed dissipative particle dynamics method, yet fundamental differences exist, which are described in the manuscript. The basic dynamic equations are presented along with practical considerations for implementing the generalised DPDE method, including a numerical integration scheme based on the Shardlow-like splitting algorithm. Demonstrations and validation tests are performed using analytical equation-of-states for the van der Waals and Lennard-Jones fluids. Particle probability distributions are analysed, where excellent agreement with theoretical estimates is demonstrated. As further validation of the generalised DPDE method, both equilibrium and non-equilibrium simulation scenarios are considered, including adiabatic flash heating response and vapour-liquid phase separation.

Refined energy-conserving dissipative particle dynamics model with temperature-dependent properties and its application in solidification problem

It has been observed previously that the physical behaviors of Schmidt number (Sc) and Prandtl number (Pr) of an energy-conserving dissipative particle dynamics (eDPD) fluid can be reproduced by the temperature-dependent weight function appearing in the dissipative force term. In this paper, we proposed a simple and systematic method to develop the temperature-dependent weight function in order to better reproduce the physical fluid properties. The method was then used to study a variety of phase-change problems involving solidification. The concept of the "mushy" eDPD particle was introduced in order to better capture the temperature profile in the vicinity of the solid-liquid interface, particularly for the case involving high thermal conductivity ratio. Meanwhile, a way to implement the constant temperature boundary condition at the wall was presented. The numerical solutions of one- and two-dimensional solidification problems were then compared with the analytical solutions and/or experimental results and the agreements were promising.

Natural convection heat transfer simulation using energy conservative dissipative particle dynamics

Dissipative particle dynamics with energy conservation (eDPD) was used to study natural convection via Rayleigh-Bénard (RB) problem and a differentially heated enclosure problem (DHE). The current eDPD model implemented the Boussinesq approximation to model the buoyancy forces. The eDPD results were compared to the finite volume solutions and it was found that the eDPD method predict the temperature and flow fields throughout the natural convection domains properly. The eDPD model recovered the basic features of natural convection, such as development of plumes, development of thermal boundary layers, and development of natural convection circulation cells (rolls). The eDPD results were presented via temperature isotherms, streamlines, velocity contours, velocity vector plots, and temperature and velocity profiles. Further useful quantities, such as Nusselt number was calculated from the eDPD results and found to be in good agreement with the finite volume calculations.