Generalized Energy-Conserving Dissipative Particle Dynamics with Mass Transfer. Part 2: Applications and Demonstrations

Abstract

We present the second part of a two-part paper series intended to address a gap in computational capability for coarse-grain particle modeling and simulation, namely, the simulation of phenomena in which diffusion via mass transfer is a contributing mechanism. In part 1, we presented a formulation of a dissipative particle dynamics method to simulate interparticle mass transfer, termed generalized energy-conserving dissipative particle dynamics with mass transfer (GenDPDE-M). In the GenDPDE-M method, the mass of each mesoparticle remains constant following the interparticle mass exchange. In part 2 of this series, further verification and demonstrations of the GenDPDE-M method are presented for mesoparticles with embedded binary mixtures using the ideal gas (IG) and van der Waals (vdW) equation-of-state (EoS). The targeted readership of part 2 is toward practitioners, where applications and practical considerations for implementing the GenDPDE-M method are presented and discussed, including a numerical discretisztion algorithm for the equations-of-motion. The GenDPDE-M method is verified by reproducing the particle distributions predicted by Monte Carlo simulations for the IG and vdW fluids, along with several demonstrations under both equilibrium and non-equilibrium conditions. GenDPDE-M can be generally applied to multi-component mixtures and to other fundamental EoS, such as the Lennard-Jones or Exponential-6 models, as well as to more advanced EoS models such as Statistical Associating Fluid Theory.

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

“…A comparison of two simulations with different transport coefficients κ and D̵ verifies the independence of the equilibrium properties on the transport coefficients and the correctness of the FDTs. The EoM were solved using the Shardlow splitting algorithm, , where all details regarding the numerical integration can be found in Part 2 of this article series …”

“…V 0 2 (62) where the first term is inspired by the ideal gas model, while the second term corresponds to an "elastic spring" for the particle mass with a spring constant, β, and an equilibrium mass, m 0 . Note that f in eq 62 is not an extensive function of m, which poses no conceptual issues in the following analysis.…”

“…The EoM were solved using the Shardlow splitting algorithm, 29,41 where all details regarding the numerical integration can be found in Part 2 of this article series. 62 In Figure 1 we compare the MC particle distributions with those obtained from simulation, where the dynamics are given by the EoM of eqs 58 and 59. We consider distributions for the particle mass, particle internal energy, and particle temperature.…”

Green–Kubo expressions for transport coefficients from dissipative particle dynamics simulations revisited

“…30, is general and can be used in other cases where stochastic dynamic equations are present, which include generalised DPD methods, e.g., a recent extension of generalised energy-conserving DPD with inter-particle mass transfer. 39,40 These cases will be addressed elsewhere.…”

“…Pairwise, many-body or any other type of potential forces are included because our results are independent of their explicit form. Furthermore, the analysis of the stress tensor used for demonstration in this work also applies to DPDE methods, 13,14,37,38 as well as to GenDPDE methods, 20,21 and their variants, including the inter-particle mass transfer (GenDPDE-M), 39,40 since the dynamics of the momentum is represented by the same equation and is independent of other properties exchanged by the mesoparticles. DPD is a particulate Lagrangian method developed to simulate hydrodynamic behaviour at the mesoscopic level.…”