Dissipative Particle Dynamics System Research Articles

Development of an automated reliable method to compute transport properties from DPD equilibrium simulations: Application to simple fluids

Dissipative particle dynamics (DPD) is a promising candidate technique for modeling rheological properties of soft matter systems. However, several methodological issues inhibit its exploitation as a computational rheology tool. In this work, we focus on the development of an automated method to compute transport properties from equilibrium simulation with particular attention to the assessment of the Green-Kubo approach reliability and computational feasibility for a large set of simple DPD systems with increasing Schmidt number. Furthermore, we investigate the time step size dependency of dynamic properties and the role of different time integration schemes. In particular, we assess the performance of the Shardlow-splitting algorithm against the most popular modified velocity-Verlet algorithm. We consider, for the first time, application of the Shardlow-splitting algorithm to the transverse DPD thermostat in different friction regimes relying on systematic numerical experiments. In addition, we make use of these findings to perform a multi-parametric study aiming to investigate the Schmidt number relationship with the effective friction coefficient.

Morse potential parameters of dissipative particle dynamics force fields for non-polarizable water models

The Morse potential parameters compatible with dissipative particle dynamics (DPD) for water are determined by the Ornstein-Zernike (OZ) equation with the hyper-netted chain (HNC) closure. The present study verifies that the HNC approximation is accurate for a DPD system described by the soft repulsive and Morse potentials. Firstly, we demonstrate that the modified form of the Morse potential is necessary for the numerical solution of the OZ/HNC equations. Subsequently, the Morse potential parameters for mimicking SPCE, TIP3P, TIP4P, and TIP5P water models within the DPD framework are determined by mapping the radial distribution function (RDF) in the HNC approximation to those of all-atom simulations. The first-peak positions and heights of the center-of-mass RDFs for all-atom water models are successfully reproduced by DPD simulations using the determined parameters. The OZ/HNC results for the RDFs and pressures, calculated for the obtained water models, are in satisfactory agreement with the DPD results. Moreover, we investigate how the addition of the Morse potential term to the solute-solvent interaction manifests itself in the solution properties. Major effects of the Morse potential are found in the solute-solvent RDF and the potential of mean force (PMF) between a pair of solutes. We discuss the molecular mechanism underlying the effects induced by the Morse potential in detail.

Molecular modeling of the interface of an egg yolk protein-based emulsion

Many food emulsions are stabilized by functional egg yolk biomolecules, which act as surfactants at the oil/water interface. Detailed experimental studies on egg yolk emulsifying properties have been largely hindered due to the difficulty in isolating individual chemical species. Therefore, this work presents a molecular model of an oil/water interfacial system where the emulsifier is one of the most surface-active proteins from the egg yolk low-density lipoproteins (LDL), the so-called Apovitellenin I. Dissipative particle dynamics (DPD) was here adopted in order to simulate large systems over long time scales, when compared with full-atom molecular dynamics (MD). Instead of a manual assignment of the DPD simulation parameters, a fully automated coarse-graining procedure was employed. The molecular interactions used in the DPD system were determined by means of a parameter calibration based on matching structural data from atomistic MD simulations. Despite the little availability of experimental data, the model was designed to test the most relevant physical properties of the protein investigated. Protein structural and dynamics properties obtained via MD and DPD were compared highlighting advantages and limits of each molecular technique. Promising results were achieved from DPD simulations of the oil/water interface. The proposed model was able to properly describe the protein surfactant behavior in terms of interfacial tension decrease at increasing protein surface concentration. Moreover, the adsorption time of a free protein molecule was estimated and, finally, an LDL-like particle adsorption mechanism was qualitatively reproduced.

Active- and transfer-learning applied to microscale-macroscale coupling to simulate viscoelastic flows

Active- and transfer-learning are applied to microscale dynamics of polymer flows for the multiscale discovery of effective constitutive approximations required in viscoelastic flow simulation. The result is macroscopic rheology directly connected to a microstructural model. Micro and macroscale simulations are adaptively coupled by means of Gaussian process regression (GPR) to run the expensive microscale computations only as necessary. This multiscale method is demonstrated with flows of a polymer solution as a model system. At the microscale level dissipative particle dynamics (DPD) is employed to model the fluid as a suspension of bead-spring micro-structures subjected to steady shear flow. The results yield the non-Newtonian viscosity and the first normal stress difference at strain rates as training data used in a GPR model. DPD parameters are calibrated with respect to experimental data for a real polymer solution. Compliance with these data requires adjustment of the DPD model's cutoff radius, which then becomes a function of the second invariant of the strain rate tensor. The FENE-P model is chosen for the macroscale description using the spectral element method (SEM) to simulate channel flow and flow past a circular cylinder. The DPD results at the lowest possible shear strain rate yield an estimate of the zero-shear rate viscosity, which allows the initiation of the macroscale flow by SEM as a Newtonian fluid. The resulting strain-rate field is surveyed to determine additional shear strain rate sampling points for the DPD system. This new information allows an initial fitting of parameters of the constitutive equation followed by new SEM simulations at the macroscale. Guided by active-learning GPR to select new sampling points, this process continues until convergence is achieved.The effectiveness of this new simulation paradigm for viscoelastic flows is tested with different macroscale operating conditions. The effective closure learned in the channel simulation is then transferred directly to the flow past a circular cylinder at low Reynolds number, where the results show that only two additional DPD simulations are required to achieve a satisfactory constitutive model. With an increase of the Reynolds number, the active-learning scheme automatically detects the inaccuracy of the learned constitutive model, and initiates additional DPD simulations for the extra data needed to once again close the microscale-macroscale coupled system. This new paradigm of active- and transfer-learning for multiscale modeling is readily applicable to other microscale-macroscale coupled simulations of complex fluids and other materials. Furthermore, the coupling between microscale and macroscale solvers can be seamlessly implemented with our open source multiscale universal interface (MUI) library.

Controlling particle penetration and depletion at the wall using Dissipative Particle Dynamics

First presented in 1993, Dissipative Particle Dynamics(DPD) has gained increasingly popularity in the scientific community due to its extensive potential to be employed in a broad range of mesoscale systems, such as polymers, colloids, surfactants and many other multi-phase systems. Although much research has been done in DPD systems, a challenge still persists when physical boundaries, such as the presence of walls, are present. One of the main issues is to achieve the non-slip condition while avoiding density distortions at the wall. In this work, particle penetration and depletion, calculated respectively as the fraction of particles in the first and second layer of the simulation box, are tracked and controlled in a wall-bounded DPD model by tuning two parameters: the wall–particle interactions and wall density. A similar response in terms of wall penetration and depletion was observed when different ratios wall/fluid for both interactions and density were employed, although increasing the wall density was found to have a slightly stronger influence in keeping the particles away from the wall region. By quantifying the fraction of particles in each layer the present authors were able to track their distribution across the channel as well as determine the combinations wall-density/interactions capable of avoiding wall penetration while depletion is controlled.

A note on dissipative particle dynamics (DPD) modelling of simple fluids

In this paper, we show that a dissipative particle dynamics (DPD) model of a viscous Newtonian fluid may actually produce a linear viscoelastic fluid. We demonstrate that a single set of DPD particles can be used to model a linear viscoelastic fluid with its physical parameters, namely the dynamical viscosity and the relaxation time in its memory kernel, determined from the DPD system at equilibrium. The emphasis of this study is placed on (i) the estimation of the linear viscoelastic effect from the standard parameter choice; and (ii) the investigation of the dependence of the DPD transport properties on the length and time scales, which are introduced from the physical phenomenon under examination. Transverse-current auto-correlation functions (TCAF) in Fourier space are employed to study the effects of the length scale, while analytic expressions of the shear stress in a simple small amplitude oscillatory shear flow are utilised to study the effects of the time scale. A direct mechanism for imposing the particle diffusion time and fluid viscosity in the hydrodynamic limit on the DPD system is also proposed.

An easy-to-use boundary condition in dissipative particle dynamics system

Boundary condition in dissipative particle dynamics system is a challenging problem since the emergence of this promising numerical method. Here, we present a quite simple boundary condition which takes the distribution of solid particles, minimal distance between fluid and solid particles, and the velocity of fluid particle into consider. By generating an attempered velocity, the approaching fluid particles are forced back into fluid area softly. This boundary condition is good at preventing penetration and keeping the interfacial properties and meanwhile easy to implement. Three representative cases are studied to show its advantages in simulating solid/fluid systems.

A dissipative particle dynamics method for arbitrarily complex geometries

Dissipative particle dynamics (DPD) is an effective Lagrangian method for modeling complex fluids in the mesoscale regime but so far it has been limited to relatively simple geometries. Here, we formulate a local detection method for DPD involving arbitrarily shaped geometric three-dimensional domains. By introducing an indicator variable of boundary volume fraction (BVF) for each fluid particle, the boundary of arbitrary-shape objects is detected on-the-fly for the moving fluid particles using only the local particle configuration. Therefore, this approach eliminates the need of an analytical description of the boundary and geometry of objects in DPD simulations and makes it possible to load the geometry of a system directly from experimental images or computer-aided designs/drawings. More specifically, the BVF of a fluid particle is defined by the weighted summation over its neighboring particles within a cutoff distance. Wall penetration is inferred from the value of the BVF and prevented by a predictor–corrector algorithm. The no-slip boundary condition is achieved by employing effective dissipative coefficients for liquid–solid interactions. Quantitative evaluations of the new method are performed for the plane Poiseuille flow, the plane Couette flow and the Wannier flow in a cylindrical domain and compared with their corresponding analytical solutions and (high-order) spectral element solution of the Navier–Stokes equations. We verify that the proposed method yields correct no-slip boundary conditions for velocity and generates negligible fluctuations of density and temperature in the vicinity of the wall surface. Moreover, we construct a very complex 3D geometry – the “Brown Pacman” microfluidic device – to explicitly demonstrate how to construct a DPD system with complex geometry directly from loading a graphical image. Subsequently, we simulate the flow of a surfactant solution through this complex microfluidic device using the new method. Its effectiveness is demonstrated by examining the rich dynamics of surfactant micelles, which are flowing around multiple small cylinders and stenotic regions in the microfluidic device without wall penetration. In addition to stationary arbitrary-shape objects, the new method is particularly useful for problems involving moving and deformable boundaries, because it only uses local information of neighboring particles and satisfies the desired boundary conditions on-the-fly.

Influence of the conservative force on transport coefficients in the DPD method

The transport coefficients of a dissipative particle dynamics system are investigated numerically taking into account the conservative force. The influence of the conservative force parameter on kinetic and dissipative viscosity is considered and compared with theoretical predictions. The analytical solution of the potential term that arises from the conservative force is generally very complicated; therefore, this term has been ignored in most previous work and deemed negligible. In the present work, an expression for the effect of the conservative force on potential viscosity is semi-empirically obtained revealing the dependence of the latter on various parameters such as conservative force strength, density number and temperature. This relation offers a proper approximation of conservative force impact on potential viscosity.

Computing the non-Markovian coarse-grained interactions derived from the Mori-Zwanzig formalism in molecular systems: Application to polymer melts.

Memory effects are often introduced during coarse-graining of a complex dynamical system. In particular, a generalized Langevin equation (GLE) for the coarse-grained (CG) system arises in the context of Mori-Zwanzig formalism. Upon a pairwise decomposition, GLE can be reformulated into its pairwise version, i.e., non-Markovian dissipative particle dynamics (DPD). GLE models the dynamics of a single coarse particle, while DPD considers the dynamics of many interacting CG particles, with both CG systems governed by non-Markovian interactions. We compare two different methods for the practical implementation of the non-Markovian interactions in GLE and DPD systems. More specifically, a direct evaluation of the non-Markovian (NM) terms is performed in LE-NM and DPD-NM models, which requires the storage of historical information that significantly increases computational complexity. Alternatively, we use a few auxiliary variables in LE-AUX and DPD-AUX models to replace the non-Markovian dynamics with a Markovian dynamics in a higher dimensional space, leading to a much reduced memory footprint and computational cost. In our numerical benchmarks, the GLE and non-Markovian DPD models are constructed from molecular dynamics (MD) simulations of star-polymer melts. Results show that a Markovian dynamics with auxiliary variables successfully generates equivalent non-Markovian dynamics consistent with the reference MD system, while maintaining a tractable computational cost. Also, transient subdiffusion of the star-polymers observed in the MD system can be reproduced by the coarse-grained models. The non-interacting particle models, LE-NM/AUX, are computationally much cheaper than the interacting particle models, DPD-NM/AUX. However, the pairwise models with momentum conservation are more appropriate for correctly reproducing the long-time hydrodynamics characterised by an algebraic decay in the velocity autocorrelation function.

Modeling Self-Assembly of the Surfactants into Biological Bilayer Membranes with Special Chemical Structure Using Dissipative Particle Dynamics Method

The aim of this study is to simulate the self-assembly of the surfactant molecules with special chemical structure and bending stiffness into bilayer membranes using a mesoscopic Dissipative Particle Dynamics (DPD) method. Thesurfactants are modeled with special chemical structure and bending stiffness. To confirm that the novel model is physical, we determine the interaction parameters based on matching the compressibility and solubility of the DPD system with real physics of the fluid. To match the mutual solubility for binary fluids, we use the relation between DPD parameters and -parameters in Flory-Huggins-type models. Unsaturated bonds can change the stiffness of a lipid membrane which is modeled by introducing a bond bending potential. To verify our model we investigate the effect of surfactant structure like chain length and stiffness of those molecules on the properties of the modeled membrane as area per surfactant. To validate our results, we also compare them with the theoretical calculations as well as with the experimental and other existing simulations results. We show that there is a good coincidence between all of the results.

Fluctuating hydrodynamics in periodic domains and heterogeneous adjacent multidomains: Thermal equilibrium.

We first study fluctuating hydrodynamics (FH) at equilibrium in periodic domains by use of the smoothed dissipative particle dynamics (SDPD) method. We examine the performance of SDPD by comparing it with the theory of FH. We find that the spatial correlation of particle velocity is always the Dirac δ function, irrespective of numerical resolution, in agreement with the theory. However, the spatial correlation of particle density has a finite range of r(c), which is due to the kernel smoothing procedure for the density. Nevertheless, this finite range of correlation can be reduced to an arbitrarily small value by increasing the resolution, that is, reducing r(c), similarly to how the smoothing kernel converges to the Dirac δ function. Moreover, we consider temporal correlation functions (CFs) of random field variables in Fourier space. For sufficient resolution, the CFs of SDPD simulations agree very well with analytical solutions of the linearized FH equations. This confirms that both the shear and sound modes are modeled accurately and that fluctuations are generated, transported, and dissipated in both thermodynamically and hydrodynamically consistent ways in SDPD. We also show that the CFs of the classical dissipative particle dynamics (DPD) method with proper parameters can recover very well the linearized solutions. As a reverse implication, the measurement of CFs provides an effective means of extracting viscosities and sound speed of a DPD system with a new set of input parameters. Subsequently, we study the FH in truncated domains in the context of multiscale coupling via the domain decomposition method, where a SDPD simulation in one subdomain is coupled with a Navier-Stokes (NS) solver in an adjacent subdomain with an overlapping region. At equilibrium, the mean values of the NS solution are known a priori and do not need to be extracted from actual simulations. To this end, we model a buffer region as an equilibrium boundary condition (EBC) at the truncated side of the SDPD simulation. In the EBC buffer, the velocity of particles is drawn from a known Gaussian distribution, that is, the Maxwell-Boltzmann distribution. Due to the finite range of spatial correlation, the density of particles in the EBC buffer must be drawn from a conditional Gaussian distribution, which takes into account the available density distribution of neighboring interior particles. We introduce a Kriging method to provide such a conditional distribution and hence preserve the spatial correlation of density. Spatial and temporal correlations of SDPD simulations in the truncated domain are compared to that in a single complete domain. We find that a gap region between the buffer and interior is important to reduce the extra dissipation generated by the artificial buffer at equilibrium, rendering more investigations necessary for thermal fluctuations in the multiscale coupling of nonequilibrium flows.

Dissipative particle dynamics simulation for the effect of interaction on the self-assembly behaviours of heterogemini surfactant in aqueous solution

ABSTRACTSelf-assembly behaviours of heterogemini surfactant in aqueous solution have been explored by means of dissipative particle dynamics simulation. Five kinds of heterogemini molecules are involved and a variety of novel morphologies have been obtained. Results based on detailed analyses show that head–tail and tail–water interactions play different roles in the formation of six kinds of self-assembly morphologies. The key factors are tail–water and head–tail repulsions separately for morphology with small (sphere) and relatively large scales (rod, planar grid, lamella and tunnels). Besides, the appearance of network in only one system can be regarded as a particular type of intermediate state. Coexistence of several sphere micelles in an amplified dissipative particle dynamics system gives us a better understanding of interactions inside the soft matter. Our simulation results can provide a theoretical guide to further research towards self-assembly behaviours of heterogemini surfactants and practical applications of these matters.

Exponential-time differencing schemes for low-mass DPD systems

Several exponential-time differencing (ETD) schemes are introduced into the method of dissipative particle dynamics (DPD) to solve the resulting stiff stochastic differential equations in the limit of small mass, where emphasis is placed on the handling of the fluctuating terms (i.e., those involving random forces). Their performances are investigated numerically in some test viscometric flows. Results obtained show that the present schemes outperform the velocity-Verlet algorithm regarding both the satisfaction of equipartition and the maximum allowable time step.

A numerical study of strongly overdamped Dissipative Particle Dynamics (DPD) systems

In this paper, we investigate the behaviour of a Dissipative Particle Dynamics (DPD) system in the overdamped limit where the particles approach zero mass limit. In this limit, the DPD system becomes singular. We propose two numerical schemes to deal with this system - one results in a fully-populated but well-conditioned matrix system, while the other employs a deflation technique to handle the system in an iterative manner, where the eigenvalue of −1 corresponding to a rigid-body motion is mapped to zero. The latter iterative scheme is to be preferred, with the possibility of parallel implementations. Some numerical results are presented to verify the two proposed schemes.

J053031 Lennard-Jones流体の粗視化に基づく散逸粒子動力学相互作用モデルの構築 : 気液界面を含む系に関する検討

The application of molecular dynamics (MD) simulation to mesoscale (10-100 nm) flow analysis is computationally expensive at present. Dissipative particle dynamics (DPD) simulation is the powerful candidate for the alternative method. Larger scale and longer time simulation is possible by using DPD since a single dissipative particle represents multi-particles. In DPD interaction models, the force contains three parts, each of which is pairwise additive: conservative, dissipative and random forces, respectively. In the conventional DPD framework, the parameters of these three forces are determined so that macroscopic properties such as diffusivity or compressibility are recovered. In our study, we investigate the method of bottom-up construction of DPD models by means of MD simulations. We focus on the center of mass of the cluster containing Lennard-Jones (LJ) particles and extract the effective forces exerted on the clusters. In our simulations, the DPD model can roughly reproduce the surface tension of the MD system while the temperature and diffusivity are underestimated due to the overestimation of friction coefficients. The diffusivity of the DPD system can be improved by scaling the friction coefficients so that the temperature of the DPD system matches that of the MD system.

Simulation of dilute solutions of linear and star-branched polymers by dissipative particle dynamics

A most promising off-lattice technique in order to simulate not only static but in addition dynamic behavior of linear and star-branched chains is the dissipative particle dynamics (DPD) method. In this model the atomistic representation of polymer molecules is replaced by a (coarse-grained) equivalent chain consisting of beads which are repulsive for each other in order to mimic the excluded volume effect (successive beads in addition are linked by springs). Likewise solvent molecules are combined to beads which in turn are repulsive for each other as well as for the polymer segments. The system is relaxed by molecular dynamics solving Newton's laws under the influence of short ranged conservative forces (i.e., repulsion between nonbonded beads and a proper balance of repulsion and attraction between bonded segments) and dissipative forces due to friction between particles, the latter representing the thermostat in conjunction with proper random forces. A variation of the strength of the repulsion between different types of beads allows the simulation of any desired thermodynamic situation. Static and dynamic properties of isolated linear and star-branched chains embedded in athermal, exothermal, and endothermal solvent are presented and theta conditions are examined. The generally accepted scaling concept for athermal systems is fairly well reproduced by linear and star-branched DPD chains and theta conditions appear for a unique parameter independent of functionality as in the case of Monte Carlo simulations. Furthermore, the correspondence between DPD and Monte Carlo data referring to the shape of chains and stars is fairly well, too. For dilute solutions the Zimm behavior is expected for dynamic properties which is indeed realized in DPD systems.

Triple-decker: Interfacing atomistic–mesoscopic–continuum flow regimes

Multiscale flow phenomena in microfluidic and biomedical applications require the use of heterogeneous modeling approaches. In this paper we present a hybrid method based on coupling the Molecular Dynamics (MD) method, the Dissipative Particle Dynamics (DPD) method, and the incompressible Navier–Stokes (NS) equations. MD, DPD, and NS are formulated in separate subdomains and are coupled via an overlapping region by communicating state information at the subdomain boundaries. Imposition of boundary conditions in the MD and DPD systems involves particle insertion and deletion, specular wall reflection and body force terms. The latter includes a boundary pressure force in order to minimize near-boundary density fluctuations, and an adaptive shear force which enforces the tangential velocity component of boundary conditions. The triple-decker algorithm is verified for prototype flows, including simple and multi-layer fluids (Couette, Poiseuille, and lid-driven cavity), using highly accurate reference solutions. A zero-thickness interface is also possible if it is aligned with the flow streamlines.

Simulating flow of DNA suspension using dissipative particle dynamics

We simulate DNA suspension microchannel flows using the dissipative particle dynamics (DPD) method. Two developments make this simulation more realistic. One is to improve the dynamic characteristics of a DPD system by modifying the weighting function of the dissipative force and increasing its cutoff radius, so that the Schmidt number can be increased to a practical level. Another is to set up a wormlike chain model in the DPD framework, according to the measured extension properties of a DNA molecule in uniform flows. This chain model is then used to study flows of a DNA suspension through microchannels. Interesting results on the conformation evolution of DNA molecules passing through the microchannels, including periodic contraction-diffusion microchannels, are reported.

Controlling Density Fluctuations in Wall-Bounded Dissipative Particle Dynamics Systems

Dissipative Particle Dynamics (DPD) simulations of wall-bounded flows exhibit density fluctuations that depend strongly on the no-slip boundary condition and increase with the level of coarse graining. We develop an adaptive model for wall-particle interactions that eliminates such oscillations and can target prescribed density profiles. Comparisons are made with ideal no-slip boundary conditions and molecular dynamics simulations. The new model is general and can be used in other coarse-grained particle methods.