Standard Dissipative Particle Dynamics Research Articles

An improved dissipative particle dynamics method for the liquid-particle two-phase flow in microchannels

Liquid-particle two-phase flow in microchannel widely exists in the fields of biomedical and environmental monitoring, such as the lab-chip device for disease diagnosis. The standard dissipative particle dynamics (DPD) method has been previously employed to study the liquid-particle two-phase flow in microchannel, but it cannot accurately simulate the real process because of the unsuitable DPD parameters. In the present study, an improved DPD method was developed by changing the system energy and fitting the characteristic curve between the random force coefficient and the Schmidt number. In addition, a new logarithmic relationship between the conservative force coefficient and the particle size was found. The result demonstrated that the improved DPD method enabled more accurate simulation on the liquid-particle two-phase flow in microchannels than the standard DPD method. For instance, in the simulation of particle sedimentation, the relative deviation between the value obtained by the improved DPD method and the theoretical value was less than 6% while the relative deviation was more than 20% for the standard DPD method. The simulated result of the particle migration in microchannel was in good agreement with the result obtained by Matas et al, and the relative deviation was less than 1.5%. Therefore, the improved DPD method would have great potentials in the study on the liquid-particle two-phase flow in microchannels.

Application of dissipative particle dynamics to interfacial systems: Parameterization and scaling

Dissipative Particle Dynamics (DPD) is a stochastic particle model that is able to simulate larger systems over longer time scales than atomistic modeling approaches by including the concept of coarse-graining. Whether standard DPD can cover the whole mesoscale by changing the level of coarse-graining is still an open issue. A scaling scheme originally developed by Füchslin et al. (2009) was here applied to interfacial systems as one of the most successful uses of the classical DPD method. In particular, equilibrium properties such as the interfacial tension were analyzed at different levels of coarse-graining for planar oil–water interfaces with and without surfactant. A scaling factor for the interfacial tension was found due to the combined effect of the scaling scheme and the coarse-graining parameterization. Although the level of molecular description was largely decreased, promising results showed that it is possible to conserve the interfacial tension trend at increasing surfactant concentrations, remarkably reducing modeling complexity. The same approach was also employed to simulate a droplet configuration. Both planar and droplet conformations were maintained, showing that typical domain formations of multi-component systems can be performed in DPD by means of the scaling procedure. Therefore, we explored the possibility of describing oil–water and oil–water–surfactant systems in standard DPD using a scaling scheme with the aim of highlighting its advantages and limitations.

EH-DPD: a dissipative particle dynamics approach to electrohydrodynamics

Electrohydrodynamics is crucial in many nanofluidic and biotechnological applications. In such small scales, the complexity due to the coupling of fluid dynamics with the dynamics of ions is increased by the relevance of thermal fluctuations. Here, we present a mesoscale method based on the Dissipative Particle Dynamics (DPD) model of the fluid. Two scalar quantities, corresponding to the number of positive and negative ions carried by each DPD particle, are added to the standard DPD formulation. We introduced a general framework that, given the definition of the free-energy of the DPD particle, allows to derive a fluctuation-dissipation relation and the expression for ionic fluxes between the DPD particles. This provides a link between the dynamics of the system and its equilibrium properties. The model is then validated simulating a planar electroosmotic flow for the cases of overlapping and non overlapping electric double layers. It is shown that using a Van der Waals equation of state the effect of ionic finite size can be accounted, leading to significant effects on the concentration and velocity profiles with respect to the ideal solution case.Graphic abstract

Effect of transverse dissipative particle dynamics on dynamic properties of nanometer-thick liquid films on solid surfaces

ABSTRACT To ascertain the effect of transverse dissipative particle dynamics (DPD), which includes lateral dissipative forces in addition to the central ones in the standard DPD, on dynamics of systems involving interfaces, we compare dynamic properties derived from coarse-grained (CG) molecular dynamics simulations with the standard and transverse DPD for nanometer-thick liquid films on solid surfaces. The dynamic properties include relaxation times of the film thickness distribution and molecular rotational motion, and transport properties associated with molecular translational motion. Our results show that these dynamic properties are tuneable by changing friction coefficients in the transverse DPD, whereas this is not the case in the standard DPD. We also confirm that the transverse DPD applied to liquid–solid CG bead pairs can tune dynamic properties of nanometer-thick liquid films on solid surfaces, though it is less effective than when applied to liquid–liquid CG bead pairs. Moreover, we reveal that the dissipative forces are isotropic in transverse DPD, whereas the liquid–solid dissipative forces are highly anisotropic and nearly along the direction perpendicular to solid surfaces in standard DPD. This suggests that the transverse liquid–solid DPD might be crucial for modelling the in-plane energy dissipation at liquid–solid interfaces.

Scaling and Interactions of Linear and Ring Polymer Brushes via DPD Simulations.

Single and double layers of polymer coated surfaces are investigated by means of Dissipative Particle Dynamics (DPD), focusing on the difference between grafted ring and linear chains. Several different surface coverages , as well as chain lengths N and brush separations D, are analyzed for athermal, i.e., good solvent, conditions. The size in the form of the radius of gyration , the shape as asphericity , and orientation , as well as density profiles as functions of distance from grafting plane , are studied. The effect of an added bond repulsion potential to suppress bond crossing in DPD is analyzed. Scaling laws of and its components and are investigated. We find for surface coverages below the overlap surface concentration . For we find and of ring brushes with the standard DPD model and with added bond repulsion. The dependence of the radius of gyration was found to be with for surface coverages grater than . The perpendicular component scales independent of the bond repulsion potential as , whereas the scaling of the parallel component exhibits a topological repulsion dependence for standard DPD and for bond repulsion.

Invariance of experimental observables with respect to coarse-graining in standard and many-body dissipative particle dynamics.

Dissipative particle dynamics (DPD) is a well-established mesoscale simulation method. However, there have been long-standing ambiguities regarding the dependence of its (purely repulsive) force field parameter on temperature as well as the variation of the resulting experimental observables, such as diffusivity or surface tension, with coarse-graining (CG) degree. Here, we rederive the temperature dependence of DPD interaction parameter and revisit the role of the CG degree in standard DPD simulations. Consequently, we derive a scaling of the input variables that renders the system properties invariant with respect to CG degree and illustrate the versatility of the method by computing the surface tensions of binary solvent mixtures. We then extend this procedure to many-body dissipative particle dynamics and, by computing surface tensions of the same mixtures at a range of CG degrees, demonstrate that this newer method, which has not been widely applied so far, is also capable of simulating complex fluids of practical interest.

Improvement of Dissipative Particle Dynamics method by taking into account the particle size

In this paper, flow past a single Dissipative Particle Dynamics (DPD) particle with low Reynolds number is investigated and it is inquired that whether a single DPD particle immersed in a fluid, has an intrinsic size. Then a minimum length scale is determined such that the hydrodynamic behavior based on standard DPD formulation is modeled correctly. Almost all of the previous studies assume the DPD particles as point centers of repulsion with no intrinsic size. Hence to prescribe the size of a simulating sphere, a structure of frozen DPD particles is created. In this paper two effective radii, Stokes-Einstein radius and a radius based on the Stokes law, for DPD particles are introduced. For small Reynolds numbers; it is proved that the two radii approach each other. Finally in spite of the typical simulations which assume DPD particles as point centers of repulsion, it is concluded that each of the individual DPD particles interact with other particles as a sphere with non-zero radius. It results the reduction of the required number of particles and eventuates more economical simulations. Moreover contemplating the radius of the particles is necessary for the new Low-Dimensional model which is derived based on the DPD method.

Mesoscopic modelling of microbubble in liquid with finite density ratio of gas to liquid

A microbubble model is developed with the mesoscopic simulation tool, dissipative particle dynamics (DPD) and many-body dissipative particle dynamics (MDPD). Standard DPD particles are employed to represent bubble phase at low density, and MDPD particles are for the liquid phase. The microbubble can be stable in liquid, in contrast to the vacuum bubble model. Gas-liquid interface is well presented with density and pressure jumps. The density ratio of gas to liquid can be lower than 0.1 by increasing the cut-off radius of bubble particles. Oscillating behavior of the microbubble model is investigated and validated by comparing with the Rayleigh-Plesset equation. The current model shows correct dynamic response, and the fluctuating behavior is captured as well. The lower the density ratio of the microbubble model, the closer the oscillating frequency to that of continuum theory.

Hydrodynamic relaxations in dissipative particle dynamics.

This paper studies the dynamics of relaxation phenomena in the standard dissipative particle dynamics (DPD) model [R. D. Groot and P. B. Warren, J. Chem. Phys. 107, 4423 (1997)]. Using fluctuating hydrodynamics as the framework of the investigation, we focus on the collective transverse and longitudinal dynamics. It is shown that classical hydrodynamic theory predicts the transverse dynamics at relatively low temperatures very well when compared to simulation data; however, the theory predictions are, on the same length scale, less accurate for higher temperatures. The agreement with hydrodynamics depends on the definition of the viscosity, and here we find that the transverse dynamics are independent of the dissipative and random shear force contributions to the stress. For high temperatures, the spectrum for the longitudinal dynamics is dominated by the Brillouin peak for large length scales and the relaxation is therefore governed by sound wave propagation and is athermal. This contrasts the results at lower temperatures and small length scale, where the thermal process is clearly present in the spectra. The DPD model, at least qualitatively, re-captures the underlying hydrodynamical mechanisms, and quantitative agreement is excellent at intermediate temperatures for the transverse dynamics.

Adaptive resolution simulations coupling atomistic water to dissipative particle dynamics.

Multiscale methods are the most efficient way to address the interlinked spatiotemporal scales encountered in soft matter and molecular liquids. In the literature reported hybrid approaches span from quantum to atomistic, coarse-grained, and continuum length scales. In this article, we present the hybrid coupling of the molecular dynamics (MD) and dissipative particle dynamics (DPD) methods, bridging the micro- and mesoscopic descriptions. The interfacing is performed within the adaptive resolution scheme (AdResS), which is a linear momentum conserving coupling technique. Our methodology is hence suitable to simulate fluids on the micro/mesoscopic scale, where hydrodynamics plays an important role. The presented approach is showcased for water at ambient conditions. The supramolecular coupling is enabled by a recently developed clustering algorithm SWINGER that assembles, disassembles, and reassembles clusters as needed during the course of the simulation. This allows for a seamless coupling between standard atomistic MD and DPD models. The developed framework can be readily applied to various applications in the fields of materials and life sciences, e.g., simulations of phospholipids and polymer melts, or to study the red blood cells behavior in normal and disease states.

Application of Berendsen barostat in dissipative particle dynamics for nonequilibrium dynamic simulation.

The Berendsen barostat from molecular dynamics simulation is applied in both standard dissipative particle dynamics (DPD) and many-body dissipative particle dynamics (MDPD) simulations. The original Berendsen barostat works well in (M)DPD simulation of a single-component system under constant pressure condition and in nonequilibrium dynamic processes. The partial Berendsen barostat is proposed for multi-component system simulation with (M)DPD. The displacement rescaling process of the Berendsen barostat is only applied on the particles outside the center region, acting as a pressure "boundary condition." The center part forms the free zone, in which the interface shape and nonequilibrium dynamic behavior between different phases can be captured properly. An immiscible bubble in the second fluid under constant pressure condition is studied, and the oscillation of the bubble radius and fluctuation of systempressure can be obtained by the current barostat. Preliminary models for bubble growing and collapsing under square pressure wave and bubble oscillation under harmonic pressure wave are also reported in the current simulation. It shows that the partial Berendsen barostat is suitable for the modeling of nonequilibrium process of single or few droplets/bubbles in multi-component systems.

Application of the dissipative particle dynamics method to the instability problem of a liquid thread.

We investigate the application of the dissipative particle dynamics method to the instability problem of a long liquid thread surrounded by another fluid. The dispersion curves obtained from simulations are compared with classic theoretical predictions. The results from standard dissipative particle dynamics (DPD) simulations at first have a tendency of gradually approaching to Tomotika's Stokes flow prediction when the Reynolds number is decreased. But they then abnormally deviate again when the viscosity is very large. The same phenomenon is also confirmed in droplet retraction simulations when also compared with theoretical Stokes flow results. On the other hand, when a hard-core DPD model is used, with the decrease of the Reynolds number the simulation results did finally approach Tomotika's predictions when Re≈0.1. A combined presentation of the hard-core DPD results and the standard DPD results, excluding the abnormal ones, demonstrates that they are approximately on a continuum when labeled with Reynolds number. These results suggest that the standard DPD method is a suitable method for investigation of the instability problem of immersed liquid thread in the inertioviscous regime (0.1<Re<10), which is relevant for microfluidics applications but there is currently no theory. It cannot reach the Re≈0.1 regime because of some irregular properties of highly viscous DPD fluid, while the hard-core DPD is suitable to overcome this inferiority with standard DPD.

Developing coarse-grained potentials for the prediction of multi-properties of trans-1,4-polybutadiene melt

In this paper, we combined structure-based and thermodynamic quantities-based coarse-graining (CG) approaches and adopted the bulk density, local conformational distributions and radial distribution function of the underlying atomistic model system as the target properties to derive the CG force field (FF) for the polymer system of trans-1,4-polybutadiene. The resultant CG FF exhibits good observable representability. In addition to the overall chain size, the extracted bulk modulus, isothermal compressibility, storage and loss moduli from CG model systems are of the same level of magnitude as the atomistic results, suggesting that this hybrid CG approach improves the reproduction capability of the CG model on mechanical property, pressure-dependent density fluctuations, and viscoelasticity. Upon the introduction of a standard dissipative particle dynamics (DPD) thermostat to remedy the removed degrees of freedom and reduced friction during CG, the CG model can completely mimic the dynamics of the atomistic model. Furthermore, we found that the standard DPD thermostat approach is applicable to the steady shear flow simulation at low and moderate rates and the relevant dissipative factor derived by matching diffusion coefficients can only quantitatively reproduce the shear viscosity at low shear rates. Overall, these findings demonstrate the ability of combined CG methods in optimizing CG FF to reproduce multi-properties of polymers.

Studies on liquid–liquid interfacial tension with standard dissipative particle dynamics method

The interfacial tension of immiscible liquid–liquid interface is studied with a standard dissipative particle dynamics (DPD) method, in which two different interfacial tension measuring approaches, i.e. the Irving–Kirkwood approach and droplet retraction approach, are employed. The droplet retraction approach predicts a lower interfacial tension than that predicted by the Irving–Kirkwood approach. With the origin standard DPD method, the conservative parameter between different species () plays an important role in the prediction of the interfacial tension. The smaller the , the more accurate results are obtained. A low-density gap is found around the interface of the standard DPD simulation with a large . For simulating droplet deformation in elongation flow, the large density gap found on the interface between the droplet and its surrounding fluid is believed to be the reason of the overestimation of the interfacial tension. By reducing the compressibility of origin DPD fluid, a better agreement of the interfacial tensions found between these two approaches to be obtained. It also permits a close agreement with the experimental work for droplet deformation in an elongation flow.

Parallel implementation of isothermal and isoenergetic Dissipative Particle Dynamics using Shardlow-like splitting algorithms

A parallel implementation of the Shardlow splitting algorithm (SSA) for Dissipative Particle Dynamics (DPD) simulations is presented. The isothermal and isoenergetic SSA implementations are compared to the DPD version of the velocity-Verlet integrator in terms of numerical stability and performance. The integrator stability is assessed by monitoring temperature, pressure and total energy for both the standard and ideal DPD fluid models. The SSA requires special consideration due to its recursive nature resulting in more inter-processor communication as compared to traditional DPD integrators. Nevertheless, this work demonstrates that the SSA exhibits stability over longer time steps that justify its regular use in parallel, multi-core applications. For the computer architecture used in this study, a factor of 10–100 speedup is achieved in the overall time-to-solution for isoenergetic DPD simulations and a 15–34 speedup is achieved for the isothermal DPD simulations.

The Lowe-Andersen thermostat as an alternative to the dissipative particle dynamics in the mesoscopic simulation of entangled polymers

Dissipative Particle Dynamics (DPD) has shown a great potential in studying the dynamics and rheological properties of soft matter; however, it is associated with deficiencies in describing the characteristics of entangled polymer melts. DPD deficiencies are usually correlated to the time integrating method and the unphysical bond crossings due to utilization of soft potentials. One shortcoming of DPD thermostat is the inability to produce real values of Schmidt number for fluids. In order to overcome this, an alternative Lowe-Anderson (LA) method, which successfully stabilizes the temperature, is used in the present work. Additionally, a segmental repulsive potential was introduced to avoid unphysical bond crossings. The performance of the method in simulating polymer systems is discussed by monitoring the static and dynamic characteristics of polymer chains and the results from the LA method are compared to standard DPD simulations. The performance of the model is evaluated on capturing the main shear flow properties of entangled polymer systems. Finally the linear and nonlinear viscoelastic properties of such systems are discussed.

An enhanced entangled polymer model for dissipative particle dynamics

We develop an alternative polymer model to capture entanglements within the dissipative particle dynamics (DPD) framework by using simplified bond-bond repulsive interactions to prevent bond crossings. We show that structural and thermodynamic properties can be improved by applying a segmental repulsive potential (SRP) that is a function of the distance between the midpoints of the segments, rather than the minimum distance between segments. The alternative approach, termed the modified segmental repulsive potential (mSRP), is shown to produce chain structures and thermodynamic properties that are similar to the softly repulsive, flexible chains of standard DPD. Parameters for the mSRP are determined from topological, structural, and thermodynamic considerations. The effectiveness of the mSRP in capturing entanglements is demonstrated by calculating the diffusion and mechanical properties of an entangled polymer melt.

Dissipative particle dynamics at isothermal, isobaric, isoenergetic, and isoenthalpic conditions using Shardlow-like splitting algorithms

Numerical integration schemes based upon the Shardlow-splitting algorithm (SSA) are presented for dissipative particle dynamics (DPD) approaches at various fixed conditions, including a constant-enthalpy (DPD-H) method that is developed by combining the equations-of-motion for a barostat with the equations-of-motion for the constant-energy (DPD-E) method. The DPD-H variant is developed for both a deterministic (Hoover) and stochastic (Langevin) barostat, where a barostat temperature is defined to satisfy the fluctuation-dissipation theorem for the Langevin barostat. For each variant, the Shardlow-splitting algorithm is formulated for both a velocity-Verlet scheme and an implicit scheme, where the velocity-Verlet scheme consistently performed better. The application of the Shardlow-splitting algorithm is particularly critical for the DPD-E and DPD-H variants, since it allows more temporally practical simulations to be carried out. The equivalence of the DPD variants is verified using both a standard DPD fluid model and a coarse-grain solid model. For both models, the DPD-E and DPD-H variants are further verified by instantaneously heating a slab of particles in the simulation cell, and subsequent monitoring of the evolution of the corresponding thermodynamic variables as the system approaches an equilibrated state while maintaining their respective constant-energy and constant-enthalpy conditions. The original SSA formulated for systems of equal-mass particles has been extended to systems of unequal-mass particles. The Fokker-Planck equation and derivations of the fluctuation-dissipation theorem for each DPD variant are also included for completeness.

Integration of rotational algorithms into dissipative particle dynamics: modeling polyaromatic hydrocarbons on the meso-scale

Heavy crude oil consists of thousands of compounds, a significant fraction of which have fairly large molecular weights and complex structures. Our work aims at constructing a meso-scale platform to explore this complex fluid in terms of microstructure, phase behavior, stability and rheology. In the present study, we focus on the treatment of the structures of fused aromatic rings as rigid body fragments in fractions such as asphaltenes and resins. To derive the rotational motion of rigid bodies in a non-conservative force field, we conduct a comparison of three rigid body rotational algorithms integrated into a standard dissipative particle dynamics (DPD) simulation. The simulation results confirm the superiority of the Quaternion method. To ease any doubt concerning the introduction of rigid bodies into DPD, the performance of the Quaternion method was tested carefully. Finally, the aggregation dynamics of asphaltene in very diluted toluene was investigated. The nanoaggregates are found to experience forming, breaking up and reforming. The sizes of the asphaltene monomer and nanoaggregate are identified. The diffusion coefficient of diluted asphaltene in toluene is similar to that found experimentally. All these results verify the rotational algorithm and encourage us to extend this platform to study the rheological and colloidal characteristics of heavy crude oils in the future.

Nonequilibrium simulations of filled polymer networks: Searching for the origins of reinforcement and nonlinearity

We present nonequilibrium dissipative particle dynamics (DPD) simulations of cross-linked elastomers containing solid filler particles at 30% volume fraction. We study systematically the effect of the morphology (dispersed or aggregated particles) and of the effective particle-particle interactions. In addition, we have experimented by replacing the standard harmonic DPD bonds with other potential functions, conceived to deal with the finite extensibility of the polymer chains and the possibility of a slow equilibrium between strongly and weakly adsorbed chains at the rubber-filler interface. The simulation results shed some light on the basic mechanisms of rubber reinforcement, including the nonlinearity and history dependence commonly known as "Payne effect" and "Mullins effect."