Dissipative Particle Dynamics Fluid Research Articles

Dissipative particle dynamics simulation of proposed artificial filament contraction mechanism using variable external force inspired by nature

ABSTRACT In this numerical research, the proposed mechanism of contraction of an artificial muscle filament with regard to the performance of a natural filament and the possibility of industrial production is presented using the Dissipative Particle Dynamics (DPD) method. First, an artificial myosin component has been simulated, which includes a micro-nozzle with a thin fixed two-end polymer membrane in the middle. The swelling of the limited permeable membrane from one side results from moving the DPD fluid and, consequently, the fluid force will be transferred. Also, by changing the direction of the movement of the fluid, the swelling of the polymer membrane is reversed. It has been shown that the amount of swelling is directly dependent on the amount and direction of external force implementation ( F e = ± 0.001, ± 0.003, ± 0.005 and ± 0.007) and there is a delay (almost one DPD unit) in the amount of displacement when the direction of the flow is changed due to the inertia force effect. The proposed mechanism includes six double artificial myosins, whose myosin movement causes that actin to take contraction in a wave motion considering both forward and backward movements of the limited permeable thin membrane. Also, more artificial myosins may provide smoother contraction.

Self-assembly of rod-coil diblock copolymer-nanoparticle composites in thin films: dissipative particle dynamics.

In this study, the assembled structures of rod-coil diblock copolymer and nanoparticle blends were studied via dissipative particle dynamics (DPD). Thin films were composed of soft confinement DPD fluid beads and the fluctuating film structure was maintained during the simulation process. Analysis of the position of nanoparticles was done in the smectic lamellar phase of the rod-coil polymer matrix, and density distributions of rods, coils, and nanoparticles were obtained as functions of the size of the nanoparticle and the DPD repulsion constant between the rod and the nanoparticle. The distribution of nanoparticles was explained by using the concept of translational entropy of nanoparticles, stretching energy of the polymer chain, relative repulsion enthalpy of nanoparticles to rods or coils, and the effect of the liquid crystalline rod.

Modeling Gas-Liquid Interfaces by Dissipative Particle Dynamics: Adsorption and Surface Tension of Cetyl Trimethyl Ammonium Bromide at the Air-Water Interface.

Adsorption of surfactants at gas-liquid interfaces that causes reduction in the surface tension is a classical problem in colloid and interface science with multiple practical applications in oil and gas recovery, separations, cosmetics, personal care, and biomedicine. Here, we develop an original coarse-grained model of the liquid-gas interface within the conventional dissipative particle dynamics (DPD) framework with the goal of quantitatively predicting the surface tension in the presence of surfactants. As a practical case-study example, we explore the adsorption of the cationic surfactant cetyl trimethyl ammonium bromide (CTAB) on the air-water interface. The gas phase is modeled as a DPD fluid composed of fictitious hard-core "gas" beads with exponentially decaying repulsive potentials to prevent penetration of the liquid phase components. A rigorous parametrization scheme is proposed based on matching the bulk and interfacial properties of water and octane taken as the reference compounds. Quantitative agreement between the simulated and experimental surface tension of CTAB solutions is found for a wide range of bulk surfactant concentrations (∼10-3 to ∼1 mmol/L) with the reduction of the surface tension from ∼72 mN/m (pure water) to the limiting value of ∼37.5 mN/m at the critical micelle concentration. The gas phase DPD model with the proposed parametrization scheme can be extended and applied to modeling various gas-liquid interfaces with surfactant and lipid monolayers, such as bubble suspensions, foams, froths, etc.

Coarse-graining, compressibility, and thermal fluctuation scaling in dissipative particle dynamics employed with pre-determined input parameters

In this study, a Dissipative Particle Dynamics (DPD) method is employed with its input parameters directly determined from the fluid properties, such as the fluid mass density, water compressibility, and viscosity. The investigation of thermal fluctuation scaling requires constant fluid properties, and this proposed DPD version meets this requirement. Its numerical verifications in simple or complex fluids under viscometric or non-viscometric flows indicate that (i) the level of thermal fluctuations in the DPD model for both types of fluids is consistently reduced with an increase in the coarse-graining level and (ii) viscometric or non-viscometric flows of a model fluid at different coarse-graining levels have a similar behavior. Furthermore, to reduce the compressibility effect of the DPD fluid in simulating incompressible flows, a new simple treatment is presented and shown to be very effective.

Temperature Error Reduction of DPD Fluid by Using Partitioned Runge-Kutta Time Integration Scheme

This study puts emphasis on reducing the temperature error of dissipative particle dynamics (DPD) fluid by directly applying a minimal-stage third-order partitioned Runge-Kutta (PRK3) method to the time integration, which does not include any of additional governing equations and change in the DPD thermostat formulation. The error is estimated based on the average values of both kinetic and configurational temperatures. The result shows that the errors in both temperatures errors are greatly reduced by using the PRK3 scheme as comparing them to those of previous studies. Additionally, the comparison among three different PRK3 schemes demonstrates our recent findings that the symplecticity conservation of the system is important to reduce the temperature error of DPD fluid especially for large time increments. The computational efficiencies are also estimated for the PRK3 scheme as well as the existing ones. It was found from the estimation that the simulation using the PRK3 scheme is more than twice as efficient as those using the existing ones. Finally, the roles of both kinetic and configurational temperatures as error indicators are discussed by comparing them to the velocity autocorrelation function and the radial distribution function. It was found that the errors of these temperatures involve different characteristics, and thus both temperatures should be taken into account to comprehensively evaluate the numerical error of DPD.

Investigation of DPD transport properties in modeling bioparticle motion under the effect of external forces: Low Reynolds number and high Schmidt scenarios.

We have used a dissipative particle dynamics (DPD) model to study the movement of microparticles in a microfluidic device at extremely low Reynolds number (Re). The particles, immersed in a medium, are transported in the microchannel by a flow force and deflected transversely by an external force along the way. An in-house Fortran code is developed to simulate a two-dimensional fluid flow using DPD at Re ≥ 0.0005, which is two orders of magnitude less than the minimum Re value previously reported in the DPD literature. The DPD flow profile is verified by comparing it with the exact solution of Hagen-Poiseuille flow. A bioparticle based on a rigid spring-bead model is introduced in the DPD fluid, and the employed model is verified via comparing the velocity profile past a stationary infinite cylinder against the profile obtained via the finite element method. Moreover, the drag force and drag coefficient on the stationary cylinder are also computed and compared with the reported literature results. Dielectrophoresis (DEP) is investigated as a case study for the proposed DPD model to compute the trajectories of red blood cells in a microfluidic device. A mapping mechanism to scale the external deflecting force from the physical to DPD domain is performed. We designed and built our own experimental setup with the aim to compare the experimental trajectories of cells in a microfluidic device to validate our DPD model. These experimental results are used to investigate the dependence of the trajectory results on the Reynolds number and the Schmidt number. The numerical results agree well with the experiment results, and it is found that the Schmidt number is not a significant parameter for the current application; Reynolds numbers combined with the DEP-to-drag force ratio are the only important parameters influencing the behavior of particles inside the microchannel.

Imposition of physical parameters in dissipative particle dynamics

In the mesoscale simulations by the dissipative particle dynamics (DPD), the motion of a fluid is modelled by a set of particles interacting in a pairwise manner, and it has been shown to be governed by the Navier–Stokes equation, with its physical properties, such as viscosity, Schmidt number, isothermal compressibility, relaxation and inertia time scales, in fact its whole rheology resulted from the choice of the DPD model parameters. In this work, we will explore the response of a DPD fluid with respect to its parameter space, where the model input parameters can be chosen in advance so that (i) the ratio between the relaxation and inertia time scales is fixed; (ii) the isothermal compressibility of water at room temperature is enforced; and (iii) the viscosity and Schmidt number can be specified as inputs. These impositions are possible with some extra degrees of freedom in the weighting functions for the conservative and dissipative forces. Numerical experiments show an improvement in the solution quality over conventional DPD parameters/weighting functions, particularly for the number density distribution and computed stresses.

Reducing the effects of compressibility in DPD-based blood flow simulations through severe stenotic microchannels

Viscous fluid flow simulations based on dissipative particle dynamics (DPD) may bear compressible flow effects when flowing through severe stenotic geometries. This is caused by the soft repulsive potential employed in the DPD force field, which limits the particle-based fluid system ability to sustain a large degree of compression. To mitigate this problem, a Morse potential was added to the DPD force field. We studied the fluid properties of the modified fluid model (DPD–Morse) and compared it with a previously published conventional DPD based fluid model. Our DPD–Morse model demonstrated reduced compressibility while preserving other fluid properties such as the fluid density and viscosity. We further investigated the fluid flow properties for a severe 3D stenotic microchannel with a 67% stenosis, using the two models. The DPD fluid model presented a significant density gradient along the flow direction, where the fluid density increased upstream towards the stenosis and decreased downstream from the stenosis before regaining its initial value. In contrast, the DPD–Morse model demonstrated a far better uniform fluid density distribution along the flow direction. We compared both solutions with CFD simulations. The DPD–Morse fluid resembled the behavior of the continuum fluid model whereas DPD fluid deviated from it. To estimate the effect that the difference between the two DPD formulations may have on the platelet activation potential, we have further embedded a platelet model within the flow field and investigated the shear stress accumulation along the platelet transport trajectory. In the stenotic section, the DPD fluid demonstrated a larger stress gradient than the DPD–Morse fluid. The platelet transport period was shorter for the DPD fluid as it generated a larger fluid density gradient that overestimated the acceleration of the platelet through the stenosis. With reduced fluid compressibility, our modified DPD–Morse fluid model was more accurate than the DPD fluid model when computing the platelet activation potential in a severe stenosis.

A dissipative particle dynamics model for thixotropic materials exhibiting pseudo-yield stress behaviour

Many materials (e.g., gels, colloids, concentrated cohesive sediments, etc.) exhibit a stable solid form at rest, and liquify once subjected to an applied stress exceeding a critical value – a yield-stress behaviour. This can be qualitatively explained by the forming and destruction of the fluid microstructure [1], and it may be modelled as a thixotropic and yield stress material. In this paper, we propose a mesoscopic model which is able to mimic a thixotropic and yield stress behaviour using a particle-based technique known as dissipative particle dynamics (DPD). The DPD technique satisfies conservation of mass and momentum and it has been applied successfully for a number of problems involving complex-structure fluids, such as polymer solutions, suspensions of rigid particles, droplets, biological fluids, etc. In this work, an indirect linkage dissipative particle model (ILDP) is proposed based on qualitative microstructural physics, which results in a non-Newtonian fluid with observed yield stress and thixotropic properties. The model comprises of two types, or species, of DPD particles – with only repulsive conservative force between the same species, and with repulsive force at short range and attractive force at long range between different species. Numerical results show that the proposed DPD fluid can represent some observed complex behaviours, such as yield stress and thixotropic effects.

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.

Mesoscopic simulation of a thinning liquid bridge using the dissipative particle dynamics method.

In this research, the dissipative particle dynamics method was used to investigate the problem of thinning and breakup in a liquid bridge. It was found that both the inertial-force-dominated thinning process and the thermal-fluctuation-dominated thinning process can be reproduced with the dissipative particle dynamics (DPD) method by varying the simulation parameters. A highly suspect viscous thinning regime was also found, but the conclusion is not irrefutable because of the complication of the shear viscosity of DPD fluid. We show in this article that the DPD method can serve as a good candidate to elucidate crossover problem in liquid bridge thinning from being hydrodynamics dominated to being thermal fluctuation dominated.

Dissipative Particle Dynamics: Effects of Parameterization and Thermostating Schemes on Rheology

We report a sensitivity analysis for dissipative particle dynamics (DPD) method, showing that it is highly sensitive to parameterization, integration method, and thermostating schemes. Practical guidelines are presented to maintain Newtonian characteristics of DPD fluid at a possible range of shear rates over wide-ranging DPD parameters. The effects of cutoff radii and the weight functions exponent in DPD triple forces are studied on viscosity, and optimized ranges are recommended for effective temperature control. Moreover, the advantages and shortcomings of DPD method is manifested using alternative thermostats (Peters, Lowe-Andersen, and Nosé-Hoover-Lowe-Andersen) in simultaneously meeting proper temperature control and Newtonian behavior in moderate to high shear rate regimes. It was shown that improper temperature control may lead to nonphysical shear-thickening. Diverse ranges of simulation settings are identified that are capable of delivering Newtonian viscosities from 0.83 to 46.3 in DPD units. This study also aims to reduce the risk of numerical artefacts giving seemingly accurate results in single-species, suspensions, or other complex systems.

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.

Analysis of Dissipative Particle Dynamics Fluid in Sheared Regimes

The present Dissipative Particles Dynamics (DPD) simulation study aims at extracting some correlations between velocity and temperature profiles, and dynamic viscosity with externally applied shear velocity via Lees-Edwards boundary condition. System physical and rheological behaviours are studied under changes made to shear velocity, cutoff radii and weight function exponent in the definition of conservative, dissipative and random forces. Two cutoff radii are altered up to the level where system of particles shows anomalous behaviour. Radial distribution function and temperature (T) are invoked to rule out invalid cutoff radii combinations. Calculated viscosity in a range of weight functions exponents (S) is compared against theory in a variety of shear velocities, where reasonable agreement with respect to T control is achieved.

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.

Physically based wall boundary condition for dissipative particle dynamics

In this paper, we present a novel wall boundary condition model, which stands just on the physical facts, for the dissipative particle dynamics (DPD) method. After the validation of this model by means of the common benchmarks such as the Couette and the Poiseuille flows, we study the effects of this model on the diffusion coefficient in a wide variety of different coarse-graining levels. The obtained results show that the proposed model preserves the thermodynamics of the system, also eliminates the spurious effects of the wall, and consequently is able to preserve the accurate structural characteristics of the working DPD fluid in the wall’s vicinity. We also study the fluid flow through a channel with the polymer-coated walls. A comprehensive investigation into the wall–solvent–polymer interactions is presented for the solvents with different qualities. Since the working DPD fluid’s structure is heterogeneous, the working fluid’s structure, its density variations and the force field that is experienced by the working DPD fluid particles near the wall cannot be predicted before the simulation. Hence, all of these data have to be determined systematically during the simulation. We show that the force field experienced by the particles near the wall depends substantially upon the solvent quality. We also show that the force fields experienced by the particles from different types (solvent/polymer) in the wall’s vicinity are significantly different from each other except in the athermal solvent.

Numerical investigations on the compressibility of a DPD fluid

The compressibility of a dissipative particle dynamics (DPD) fluid is studied numerically through several newly developed test models, where both the density and the divergence of the velocity field are considered. In the case of zero conservative force, the DPD fluid turns out to be compressible. Effects of the compressibility are observed to be reduced as the particle mass is chosen to be smaller and the system temperature to be higher. In the case of non-zero conservative force, the condition of constant density and divergence-free of velocity can be approximately achieved at large values of the repulsion parameter (i.e., weakly compressible flow). Furthermore, the speed of sound and local Mach number are computed and found to be in good agreement with the theoretical estimation.

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.

Hydrodynamic interactions in dissipative particle dynamics

Dissipative particle dynamics (DPD) has recently attracted great interest due to its potential to simulate the dynamics of colloidal particles in fluidic devices. In this work, we explore the validity of DPD to reproduce the hydrodynamic interaction between a suspended particle and confining solid walls. We first show that a relatively large Schmidt number of the DPD fluid can be obtained by increasing the ratio between the strength of the dissipative force and the kinetic energy of the particles. We then measure the mobility and diffusion coefficient of the colloidal particles and show good agreement with the predicted results. We then focus on the particle-solid interactions and measure the force on a colloidal particle moving both parallel and perpendicular to two parallel walls. In both cases we found good agreement with the theoretical predictions based on Stokes flows for separations as small as one-tenth of the particle radius.

Tunable-slip boundaries for coarse-grained simulations of fluid flow

On the micro- and nanoscale, classical hydrodynamic boundary conditions such as the no-slip condition no longer apply. Instead, the flow profiles exhibit "slip" at the surface, which is characterized by a finite slip length (partial slip). We present a new, systematic way of implementing partial-slip boundary conditions with arbitrary slip length in coarse-grained computer simulations. The main idea is to represent the complex microscopic interface structure by a spatially varying effective viscous force. An analytical equation for the resulting slip length can be derived for planar and for curved surfaces. The comparison with computer simulations of a DPD (dissipative particle dynamics) fluid shows that this expression is valid from full slip to no slip.