Smoothed Dissipative Particle Dynamics Research Articles

An investigation of dynamic droplet wetting within the smoothed dissipative particle dynamics (SDPD) multi-scale modeling framework

The multi-scale numerical procedure proposed in our previous work based on smoothed dissipative particle dynamics (SDPD) is employed, and a new multi-phase interaction model based on the inter-particle force (IPF) that includes a consistent repulsion force is presented and verified. A comparative investigation utilizing smoothed particle hydrodynamics (SPH), SDPD, and our multi-scale methods is then carried out and the computational efficiency, droplet morphology, wetting flow field, and advantages of the multi-scale method are demonstrated. In addition, the droplet thickness is derived from the Navier–Stokes equations with a stochastic force, demonstrating the effect of thermal fluctuations on the mesoscopic scale. Finally, the wetting states are simulated at different surface roughness values, and the transition of states and some new mechanisms are clarified. When the roughness scale is smaller than the interaction range between particles, the wetting state may change significantly, and this effect becomes weaker when the roughness scale exceeds the interaction range. The results also show that the horizontal roughness (direction of droplet spreading) is more decisive than vertical one (perpendicular to the direction of droplet spreading), usually leading to a transition of the wetting states, while the vertical roughness usually plays a reinforcing role.

Modeling stable cavitation of coated microbubbles: A framework integrating smoothed dissipative particle dynamics and the Rayleigh-Plesset equation.

Coated microbubbles are widely used in medical applications, particularly in enhanced drug and gene delivery. One of the mechanisms underlying these applications involves the shear stress exerted on the cell membrane by acoustic microstreaming generated through cavitation bubbles. In this study, we develop a novel simulation approach that combines the smooth dissipative particle dynamics (SDPD) simulation method with numerical modeling of the Rayleigh-Plesset-like equation in an ad hoc manner to simulate stable cavitation of microbubbles at microsecond and micrometer scales. Specifically, the SDPD method is utilized to model fluid dynamics, while the Rayleigh-Plesset-like equation is employed to describe bubble dynamics. Adopting a 1.5 μm coated microbubble driven by ultrasound with a frequency of 2MHz and a pressure of 500kPa as a representative example, we observe a high-velocity microstreaming pattern emerging around the bubble on a very small scale of a few micrometers after only a few microseconds. These spatiotemporal scales may pose challenges for experimental observation. The formation of this microstreaming arises from the opposing motion of the fluid layer next to the bubble and the fluid layers further away. Furthermore, our simulations reveal high shear stress levels of thousands of Pascals exerted on a wall located a few micrometers from the bubble. This contrasts with the shear stress values of a few Pascals calculated from theoretical models in the literature, which do not incorporate radial streaming into their theories. The implications of our results for bubble cavitation-induced pore formation on the cell membrane are discussed in some details.

Generalized Lagrangian heterogeneous multiscale modelling of complex fluids

We introduce a fully Lagrangian heterogeneous multiscale method (LHMM) to model complex fluids with microscopic features that can extend over large spatio/temporal scales, such as polymeric solutions and multiphasic systems. The proposed approach discretizes the fluctuating Navier–Stokes equations in a particle-based setting using smoothed dissipative particle dynamics (SDPD). This multiscale method uses microscopic information derived on-the-fly to provide the stress tensor of the momentum balance in a macroscale problem, therefore bypassing the need for approximate constitutive relations for the stress. We exploit the intrinsic multiscale features of SDPD to account for thermal fluctuations as the characteristic size of the discretizing particles decreases. We validate the LHMM using different flow configurations (reverse Poiseuille flow, flow passing a cylinder array and flow around a square cavity) and fluid (Newtonian and non-Newtonian). We show the framework's flexibility to model complex fluids at the microscale using multiphase and polymeric systems. We also show that stresses are adequately captured and passed from micro to macro scales, leading to richer fluid response at the continuum. In general, the proposed methodology provides a natural link between variations at a macroscale, whereas accounting for memory effects of microscales.

Shear flow-driven droplet motion with smoothed dissipative particle dynamics

Droplet motion in shear flow is a typical phenomenon in nature that also plays an important role in the spread of COVID-19 when viruses like SARS-CoV-2 exist in exhalation droplets. In this paper, we adopted smoothed dissipative particle dynamics (SDPD) to simulate the Couette flow and Poiseuille flow. Then, the self-diffusion coefficient and the Schmidt number of the quiescent flow in SDPD are confirmed by comparison with those in DPD. In addition, the SDPD method with pacific coefficients is used to simulate the disintegration of droplets and the collisional aggregation and separation of droplets in shear flow. The applicability of the SDPD method is demonstrated through these simulations, which can be useful in the investigation of many complex fluid flows during the expansion of COVID-19.

A novel dimensionless number characterizing flow regimes based on smoothed dissipative particle dynamics (SDPD)

A novel dimensionless number characterizing flow regimes based on smoothed dissipative particle dynamics (SDPD)

Mesoscopic simulations of inertial drag enhancement and polymer migration in viscoelastic solutions flowing around a confined array of cylinders

We study the flow around a periodic array of cylinders using a mesoscopic viscoelastic fluid that mimics polymeric solutions. We model our fluid employing a novel mesoscopic method based on Smoothed Dissipative Particle Dynamics and FENE springs. We characterize the static and dynamic properties of our model solutions and compare the results with theoretical predictions based on the Zimm model. After rheological characterization of the modeled solutions, we simulate the flow around a confined array of cylinders. The balance between inertia and elasticity in our simulations is studied using a wide range of Reynolds (Re) and Weissenberg (Wi) numbers. We find that increasing the flow rate reduces the drag coefficient on the cylinder up to a critical Re corresponding to a minimum. Thereafter, inertia becomes dominant and we encounter drag enhancement for all the solutions studied, including the Newtonian solvent. With the use of simple model for the viscous and inertial contributions to drag, we conclude that inertial effects are driving the increase in the drag experienced by the cylinder. In our simulations, we also observe migration of polymer chains away from the channel walls and in the wake of the cylinder. We conclude that stress gradients induced by the curvature of streamlines and convection of the depleted layers at the walls as the principal mechanisms driving the migration of chains. We find the extent of the migration correlates well with the viscoelastic Mach number (Ma = Re Wi ) suggesting that both elastic and inertial effects play a role in this phenomenon. • A mesoscopic model fluid with viscoelastic behavior is presented. • The drag on a confined array of periodically spaced cylinders is investigated. • Drag enhancement is explained with a simple model combining inertial and viscous drag. • Polymeric migration at the walls and the wake of the cylinders is investigated.

Smoothed Dissipative Particle Dynamics package for LAMMPS

An isothermal implementation of Smoothed Dissipative Particle Dynamics (SDPD) for LAMMPS is presented. SDPD is useful for hydrodynamics simulations at mesoscale where the effect of thermal fluctuations are important, but a molecular dynamics simulation is prohibitively expensive. We have used this package to simulate diffusion of spherical colloids. The results (particularly the long-time behaviour of velocity autocorrelation function) are in agreement with theoretical models that take hydrodynamic interactions into account. Program summaryProgram Title: Smoothed Dissipative Particle HydrodynamicsProgram Files doi:http://dx.doi.org/10.17632/nhfp6nsr6n.1Licensing provisions: LGPLv3Programming language: C++Nature of problem: Multi-scale simulation of fluctuating hydrodynamics with consistent thermodynamics and hydrodynamic interactions in arbitrary geometry.Solution method: We have implemented an isothermal version of the Smoothed Dissipative Particle Hydrodynamics. SDPD is a multi-scale method as its input is only the resolution of particle grid used to model the fluid and macroscopic properties of fluid like viscosity and density (e.g there is no need to specify the strength of fluctuating force). SDPD respects the laws of thermodynamics and the Navier–Stokes equation by design.

Entropy stability analysis of smoothed dissipative particle dynamics

This article presents an entropy stability analysis of smoothed dissipative particle dynamics (SDPD) to review the validity of particle discretization of entropy equations. First, we consider the simplest SDPD system: a simulation of incompressible flows using an explicit time integration scheme, assuming a quasi-static scenario with constant volume, constant number of particles, and infinitesimal time shift. Next, we derive a form of entropy from the discretized entropy equation of SDPD by integrating it with respect to time. We then examine the properties of a two-particle system for a constant temperature gradient. Interestingly, our theoretical analysis suggests that there exist eight different types of entropy stability conditions, which depend on the types of kernel functions. It is found that the Lucy kernel, poly6 kernel, and spiky kernel produce the same types of entropy stability conditions, whereas the spline kernel produces different types of entropy stability conditions. Our results contribute to a deeper understanding of particle discretization.

Parallel modeling of cell suspension flow in complex micro-networks with inflow/outflow boundary conditions

We proposed a parallel framework with inflow/outflow boundary conditions for particle-based simulations of cell suspension flow through complex micro-networks that is often encountered in microcirculation and microfluidic devices. The behaviors of fluid and cells are modeled by a hybrid approach of smoothed dissipative particle dynamics (SDPD) and immersed boundary method (IBM). The simulation system is associated with two more domains, the inflow domain at the inlets and the outflow domains at the outlets, to implement the inflow/outflow boundary conditions. The inflow is duplicated into the system from a fully-developed flow generated in the inflow domain under a periodic boundary condition. The outflow is iteratively controlled by two adaptive forces to maintain mass and momentum conservation, and meanwhile, the fluid and cells leaving the outlets are removed from the system. A master-slave parallel configuration is constructed, where the master thread is responsible for dividing the simulation domain or allocating the simulation tasks to three types of slave threads, cell, inflow and hybrid slave threads. To save message communication, each cell is assigned to a separate thread by task decomposition, while the inflow/hybrid slave threads are divided by domain decomposition. Four validation studies were carried out for the fluid flows in a straight and a bifurcated tubes, the deformation of a capsule in a straight tube, as well as the rheology of many red blood cells (RBCs) in a straight tube. The results were compared with their corresponding analytical solutions or previously-published numerical results, and good agreements were observed on the velocity field, cell deformation, and rheological behaviors of cells. Moreover, two numerical experiments were conducted to demonstrate the capability of the proposed methodology. One is RBCs through a microvascular network with an inlet but four outlets, and the other is those through a serpentine microfluidic chip with several complex geometric features, including bifurcations, sharp corners, sudden expansion and multiple outlets. Both of these experiments not only demonstrated the capability of the new methodology, but also suggested a potential to simulate real-world biomedical problems, such as thrombus formation, tumor metastasis, drug delivery, and so on.

Implicit atomistic viscosities in smoothed dissipative particle dynamics.

We apply a standard nonequilibrium dynamics microscopic analysis of transport coefficients to the smoothed dissipative particle dynamics (SDPD) method of steady-shear flow conditions. Extending the research of Ellero etal. [Phys. Rev. E 82, 046702 (2010)PRESCM1539-375510.1103/PhysRevE.82.046702] for smoothed particle hydrodynamics (SPH), we focus, in particular, on velocity and acceleration statistics and on mean-density phenomena. Implicit and explicit fluctuations affect non-Gaussian statistics and effective viscosities whereas only explicit fluctuations affect large-scale dissipation through the fluctuation-dissipation relation. SDPD facilitates the simulation of mesoscopic systems as the resolution scale is defined by the scaling of the random fluctuations. In the kinetic regime, SDPD recovers the behavior of SPH. In the diffusive regime, non-Gaussian behavior occurs, in contrast to SPH. We observe the formation of isotropic randomly oriented structures with high density which are related to the magnitude of thermal fluctuations. It is demonstrated that SDPD produces non-Gaussian acceleration PDF corresponding to that of a turbulent flow field.

A Smooth Dissipative Particle Dynamics method for nonisothermal liquid and gas flows in bounded domains

A Smoothed Dissipative Particle Dynamics formulation with dynamic virtual particle allocation (SDPD-DV) is developed for the simulation of mesoscale nonisothermal flows with non-slip, constant temperature and constant heat flux boundary conditions. For liquids, the particle internal energy is evaluated through a first-order expansion from an initial volume and entropy state. For liquids, the particle pressure and temperature are evaluated using the coefficients of adiabatic compressibility, volumetric thermal expansion and heat capacity. For monatomic and diatomic gases, the fluid particle internal energy is evaluated through a Sackur-Tetrode type of equation. For both liquids and gases, the viscosity and thermal conductivity are modeled by a power law. Integration of position and momentum equations is performed with a velocity-Verlet method and bounce-forward reflection. Integration of the entropy equation is performed with a Runge-Kutta method. Verification of SDPD-DV is performed for planar isothermal Couette, planar Fourier, and planar nonisothermal Couette flows of liquid H2O and gaseous N2, and for a nonisothermal planar Poiseuille flow of a fluid with an exponential temperature-depended viscosity. SDPD-DV simulations for liquid H2O, gaseous Ar and N2 systems under thermal equilibrium assess the impact of the ratio of particle mass (mi) over the real molecular mass and the size of smoothing length (h) on fluid properties, hydrodynamic fluctuations and transport coefficients. For liquid systems the density fluctuations exhibit scatter about the analytical estimates and the temperature fluctuations follow the analytical estimates for mass ratios smaller than 10,000. The velocity fluctuations are in excellent agreement with theoretical estimates. For gases, the density fluctuations exhibit scatter about the analytical estimates and the pressure fluctuations agree with the analytical estimates for mass ratios smaller than 10,000. The temperature and velocity fluctuations are in excellent agreement with the analytical estimates. The self-diffusivity evaluated from SDPD-DV simulations for liquid and gases is shown to increase with smoothing length for a given mass ratio, scales with h2/mi and is in excellent agreement with analytical estimates. The shear viscosity evaluated from SDPD-DV simulations for liquid and gases exhibits scatter around the experimental values and is shown to be scale free.

An integrated boundary approach for colloidal suspensions simulated using smoothed dissipative particle dynamics

In particle-based continuum solvers such as smoothed particle hydrodynamics (SPH) and smoothed dissipative particle dynamics (SDPD), one of the most significant challenges is the treatment of solid boundaries like walls and colloidal particles, whose presence leads to a truncation of the integral approximation, and hence, error in the numerical solution. In this work, we describe an integrated boundary framework for modeling colloidal suspensions composed of rigid spherical particles. The integral corresponding to the colloid's contribution is analytically evaluated, giving a simple and computationally inexpensive approach relative to conventional boundary particle techniques. We formulate a thermodynamically-consistent version of this top-down method for mesoscale simulations, in which the fluid exchanges momentum with the suspended particles due to thermal fluctuations, giving a framework for modeling the dynamics of colloids at arbitrary Reynolds and Péclet numbers. The resulting evolution equations are validated for a single colloidal particle in a fluid at constant temperature. This simple approach requires ∼Nc(ρ/m)Rc2 fewer pair force calculations relative to traditional boundary particle strategies, where Nc is the number of colloids in the system, Rc is the colloid radius, ρ is the colloid mass density, and m is the mass of the SDPD particles. In addition, the use of integrated boundaries removes the need for rigidbody constraint dynamics, giving an elegant and efficient basis for large-scale simulations of colloidal suspensions that is general and does not make any physical assumptions about the flow.

A hybrid smoothed dissipative particle dynamics (SDPD) spatial stochastic simulation algorithm (sSSA) for advection–diffusion–reaction problems

We have developed a new algorithm which merges discrete stochastic simulation, using the spatial stochastic simulation algorithm (sSSA), with the particle based fluid dynamics simulation framework of smoothed dissipative particle dynamics (SDPD). This hybrid algorithm enables discrete stochastic simulation of spatially resolved chemically reacting systems on a mesh-free dynamic domain with a Lagrangian frame of reference. SDPD combines two popular mesoscopic techniques: smoothed particle hydrodynamics and dissipative particle dynamics (DPD), linking the macroscopic and mesoscopic hydrodynamics effects of these two methods. We have implemented discrete stochastic simulation using the reaction–diffusion master equations (RDME) formalism, and deterministic reaction–diffusion equations based on the SDPD method. We validate the new method by comparing our results to four canonical models, and demonstrate the versatility of our method by simulating a flow containing a chemical gradient past a yeast cell in a microfluidics chamber.

A Comparative Review of Smoothed Particle Hydrodynamics, Dissipative Particle Dynamics and Smoothed Dissipative Particle Dynamics

Smoothed particle hydrodynamics (SPH), dissipative particle dynamics (DPD) and smoothed dissipative particle dynamics (SDPD) are three typical and related particle-based methods. They have been increasingly attractive for solving fluid flow problems, especially for the biofluid flow, because of their advantages of ease and flexibility in modeling complex structure fluids. This work aims to review what the exact similarities and differences are among them, by studying four simple fluid flows: (i) self-diffusion of quiescent flow, (ii) time-dependent Coutte flow, (iii) time-dependent Poiseuille flow, and (iv) lid-driven cavity flow. The simulations show that SPH, DPD and SDPD can give the similar results. SPH generates quite smooth results and has zero system temperature due to the absence of thermal fluctuations, suitable for macroscale problems. However, DPD and SDPD have fluctuating results around the reference results and nonzero system temperature with considerable thermal fluctuations, suitable for mesoscale problems. SDPD is more convenient than DPD to some extent, because it is not required to pre-define the force coefficients. SDPD can adopt more diverse equation of state (EOS) than DPD, because its EOS is user-defined unlike the EOS of DPD, inbuilt in the formulations.

Hydrodynamically Coupled Brownian Dynamics: A coarse-grain particle-based Brownian dynamics technique with hydrodynamic interactions for modeling self-developing flow of polymer solutions.

We present a novel coarse-grain particle-based simulation technique for modeling self-developing flow of dilute and semi-dilute polymer solutions. The central idea in this paper is the two-way coupling between a mesoscopic polymer model and a phenomenological fluid model. As our polymer model, we choose Responsive Particle Dynamics (RaPiD), a Brownian dynamics method, which formulates the so-called "conservative" and "transient" pair-potentials through which the polymers interact besides experiencing random forces in accordance with the fluctuation dissipation theorem. In addition to these interactions, our polymer blobs are also influenced by the background solvent velocity field, which we calculate by solving the Navier-Stokes equation discretized on a moving grid of fluid blobs using the Smoothed Particle Hydrodynamics (SPH) technique. While the polymers experience this frictional force opposing their motion relative to the background flow field, our fluid blobs also in turn are influenced by the motion of the polymers through an interaction term. This makes our technique a two-way coupling algorithm. We have constructed this interaction term in such a way that momentum is conserved locally, thereby preserving long range hydrodynamics. Furthermore, we have derived pairwise fluctuation terms for the velocities of the fluid blobs using the Fokker-Planck equation, which have been alternatively derived using the General Equation for the Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) approach in Smoothed Dissipative Particle Dynamics (SDPD) literature. These velocity fluctuations for the fluid may be incorporated into the velocity updates for our fluid blobs to obtain a thermodynamically consistent distribution of velocities. In cases where these fluctuations are insignificant, however, these additional terms may well be dropped out as they are in a standard SPH simulation. We have applied our technique to study the rheology of two different concentrations of our model linear polymer solutions. The results show that the polymers and the fluid are coupled very well with each other, showing no lag between their velocities. Furthermore, our results show non-Newtonian shear thinning and the characteristic flattening of the Poiseuille flow profile typically observed for polymer solutions.

Relationship between transit time and mechanical properties of a cell through a stenosed microchannel.

The changes in the mechanical properties of a cell are not only the cause of some diseases, but can also be a biomarker for some disease states. In recent times, microfluidic devices with built-in constrictions have been widely used to measure these changes. The transit time in such devices, defined as the time that a cell takes to pass through a constriction, has been found to be a crucial factor associated with the cell mechanical properties. Here, we use smoothed dissipative particle dynamics (SDPD), a particle-based numerical method, to explore the relationship between the transit time and mechanical properties of a cell. Three expressions of the transit time are developed from our simulation data, with respect to the stenosed size of constrictions, the shear modulus and bending modulus of cells, respectively. We show that a convergent constriction (the inlet is wider than the outlet), and a sharp-corner constriction (the constriction outlet is narrow) are better in identifying the differences in the transit time of cells. Moreover, the transit time increases and gradually approaches a constant as the shear modulus of cells increases, but increases first and then decreases as the bending modulus increases. These results suggest that the mechanical properties of cells can indeed be measured by analyzing their transit time, based on the recommended microfluidic device.

Stable and accurate schemes for smoothed dissipative particle dynamics

Smoothed dissipative particle dynamics (SDPD) is a mesoscopic particle method that allows to select the level of resolution at which a fluid is simulated. The numerical integration of its equations of motion still suffers from the lack of numerical schemes satisfying all the desired properties such as energy conservation and stability. Similarities between SDPD and dissipative particle dynamics with energy (DPDE) conservation, which is another coarse-grained model, enable adaptation of recent numerical schemes developed for DPDE to the SDPD setting. In this article, a Metropolis step in the integration of the fluctuation/dissipation part of SDPD is introduced to improve its stability.

Everything you always wanted to know about SDPD\u22c6 (\u22c6but were afraid to ask)

An overview of the smoothed dissipative particle dynamics (SDPD) method is presented in a format that tries to quickly answer questions that often arise among users and newcomers. It is hoped that the status of SDPD is clarified as a mesoscopic particle model and its potentials and limitations are highlighted, as compared with other methods.

Static and dynamic properties of smoothed dissipative particle dynamics

In this paper, static and dynamic properties of the smoothed dissipative particle dynamics (SDPD) method are investigated. We study the effect of method parameters on SDPD fluid properties, such as structure, speed of sound, and transport coefficients, and show that a proper choice of parameters leads to a well-behaved and accurate fluid model. In particular, the speed of sound, the radial distribution function (RDF), shear-thinning of viscosity, the mean-squared displacement (〈R2〉∝t), and the Schmidt number (Sc∼O(103)−O(104)) can be controlled, such that the model exhibits a fluid-like behavior for a wide range of temperatures in simulations. Furthermore, in addition to the consideration of fluid density variations for fluid compressibility, a more challenging test of incompressibility is performed by considering the Poisson ratio and divergence of velocity field in an elongational flow. Finally, as an example of complex-fluid flow, we present the applicability and validity of the SDPD method with an appropriate choice of parameters for the simulation of cellular blood flow in irregular geometries. In conclusion, the results demonstrate that the SDPD method is able to approximate well a nearly incompressible fluid behavior, which includes hydrodynamic interactions and consistent thermal fluctuations, thereby providing, a powerful approach for simulations of complex mesoscopic systems.

Red blood cell motion and deformation in a curved microvessel

The flow of cells through curved vessels is often encountered in various biomedical and bioengineering applications, such as red blood cells (RBCs) passing through the curved arteries in circulation, and cells sorting through a shear-induced migration in a curved channels. Most of past numerical studies focused on the cell deformation in small straight microvessels, or on the flow pattern in large curved vessels without considering the cell deformation. However, there have been few attempts to study the cell deformation and the associated flow pattern in a curved microvessel. In this work, a particle-based method, smoothed dissipative particle dynamics (SDPD), is used to simulate the motion and deformation of a RBC in a curved microvessel of diameter comparable to the RBC diameter. The emphasis is on the effects of the curvature, the type and the size of the curved microvessel on the RBC deformation and the flow pattern. The simulation results show that a small curved shape of the microvessel has negligible effect on the RBC behavior and the flow pattern which are similar to those in a straight microvessel. When the microvessel is high in curvature, the secondary flow comes into being with a pair of Dean vortices, and the velocity profile of the primary flow is skewed toward the inner wall of the microvessel. The RBC also loses the axisymmetric deformation, and it is stretched first and then shrinks when passing through the curved part of the microvessel with the large curvature. It is also found that a pair of Dean vortices arise only under the condition of De>1 (De is the Dean number, a ratio of centrifugal to viscous competition). The Dean vortices are more easily observed in the larger or more curved microvessels. Finally, it is observed that the velocity profile of primary flow is skewed toward the inner wall of curved microvessel, i.e., the fluid close to the inner wall flows faster than that close to the outer wall. This is contrary to the common sense in large curved vessels. This velocity skewness was found to depend on the curvature of the microvessel, as well as the viscous and inertial forces.