Pickering emulsion transport in skeletal muscle tissue:A dissipative particle dynamics simulation approach

Lymph node targeting is a commonly used strategy for particulate vaccines,particularly for Pickering emulsions.However,extensive research on the internal delivery mechanisms of these emulsions,especially the complex intercellular interactions of deformable Pickering emulsions,has been surprisingly sparse.This gap in knowledge holds significant potential for enhancing vaccine efficacy.This study aims to address this by summarizing the process of lymph-node-targeting transport and introducing a dissipative particle dynamics simulation method to evaluate the dynamic processes within cell tissue.The transport of Pickering emulsions in skeletal muscle tissue is specifically investigated as a case study.Various factors impacting the transport process are explored,including local cellular tissue environmental factors and the properties of the Pickering emulsion itself.The simulation results primarily demonstrate that an increase in radial repulsive interaction between emulsion particles can decrease the transport efficiency.Additionally,larger intercellular gaps also diminish the transport efficiency of emulsion droplet particles due to the increased motion complexity within the intricate transport space compared to a single channel.This study sheds light on the nuanced interplay between engineered and biological systems influencing the transport dynamics of Pickering emulsions.Such insights hold valuable potential for optimizing transport processes in practical biomedical applications such as drug delivery.Importantly,the desired transport efficiency varies depending on the specific application.For instance,while a more rapid transport might be crucial for lymph-node-targeted drug delivery,certain applications requiring a slower release of active components could benefit from the reduced transport efficiency observed with increased particle repulsion or larger intercellular gaps.

Simulation of nanofluid natural convection based on single-particle hydrodynamics in energy-conserving dissipative particle dynamics(eDPD)

In the present study,the nanofliud natural convection is investigated by the energy-conserving dissipative particle dynamics(eDPD)method,where the nanoparticles are considered at the single-particle level.The thermal expansion coefficientβand the viscosityμof the simulated system containing nanoparticles are calculated and found to be in close alignment with the previous simulation results.The single-particle hydrodynamics in e DPD enables simulations of nanofluid natural convection with higher Rayleigh numbers and greater nanoparticle volume fractions.Additionally,this approach is utilized to simulate the nanoparticle distribution during the enhanced heat transfer process in the nanofluid natural convection.The localized aggregation of nanoparticles enhances the heat transfer performance of the nanofluid under specific Rayleigh numbers and nanoparticles volume fractions.

A stable implicit nodal integration-based particle finite element method(N-PFEM)for modelling saturated soil dynamics

In this study,we present a novel nodal integration-based particle finite element method(N-PFEM)designed for the dynamic analysis of saturated soils.Our approach incorporates the nodal integration technique into a generalised Hellinger-Reissner(HR)variational principle,creating an implicit PFEM formulation.To mitigate the volumetric locking issue in low-order elements,we employ a node-based strain smoothing technique.By discretising field variables at the centre of smoothing cells,we achieve nodal integration over cells,eliminating the need for sophisticated mapping operations after re-meshing in the PFEM.We express the discretised governing equations as a min-max optimisation problem,which is further reformulated as a standard second-order cone programming(SOCP)problem.Stresses,pore water pressure,and displacements are simultaneously determined using the advanced primal-dual interior point method.Consequently,our numerical model offers improved accuracy for stresses and pore water pressure compared to the displacement-based PFEM formulation.Numerical experiments demonstrate that the N-PFEM efficiently captures both transient and long-term hydro-mechanical behaviour of saturated soils with high accuracy,obviating the need for stabilisation or regularisation techniques commonly employed in other nodal integration-based PFEM approaches.This work holds significant implications for the development of robust and accurate numerical tools for studying saturated soil dynamics.

A flexible multiscale algorithm based on an improved smoothed particle hydrodynamics method for complex viscoelastic flows

Viscoelastic flows play an important role in numerous engineering fields,and the multiscale algorithms for simulating viscoelastic flows have received significant attention in order to deepen our understanding of the nonlinear dynamic behaviors of viscoelastic fluids.However,traditional grid-based multiscale methods are confined to simple viscoelastic flows with short relaxation time,and there is a lack of uniform multiscale scheme available for coupling different solvers in the simulations of viscoelastic fluids.In this paper,a universal multiscale method coupling an improved smoothed particle hydrodynamics(SPH)and multiscale universal interface(MUI)library is presented for viscoelastic flows.The proposed multiscale method builds on an improved SPH method and leverages the MUI library to facilitate the exchange of information among different solvers in the overlapping domain.We test the capability and flexibility of the presented multiscale method to deal with complex viscoelastic flows by solving different multiscale problems of viscoelastic flows.In the first example,the simulation of a viscoelastic Poiseuille flow is carried out by two coupled improved SPH methods with different spatial resolutions.The effects of exchanging different physical quantities on the numerical results in both the upper and lower domains are also investigated as well as the absolute errors in the overlapping domain.In the second example,the complex Wannier flow with different Weissenberg numbers is further simulated by two improved SPH methods and coupling the improved SPH method and the dissipative particle dynamics(DPD)method.The numerical results show that the physical quantities for viscoelastic flows obtained by the presented multiscale method are in consistence with those obtained by a single solver in the overlapping domain.Moreover,transferring different physical quantities has an important effect on the numerical results.

Structure-preserving algorithms for guiding center dynamics based on the slow manifold of classical Pauli particle

The classical Pauli particle(CPP) serves as a slow manifold, substituting the conventional guiding center dynamics. Based on the CPP, we utilize the averaged vector field(AVF) method in the computations of drift orbits. Demonstrating significantly higher efficiency, this advanced method is capable of accomplishing the simulation in less than one-third of the time of directly computing the guiding center motion. In contrast to the CPP-based Boris algorithm, this approach inherits the advantages of the AVF method, yielding stable trajectories even achieved with a tenfold time step and reducing the energy error by two orders of magnitude. By comparing these two CPP algorithms with the traditional RK4 method, the numerical results indicate a remarkable performance in terms of both the computational efficiency and error elimination. Moreover, we verify the properties of slow manifold integrators and successfully observe the bounce on both sides of the limiting slow manifold with deliberately chosen perturbed initial conditions. To evaluate the practical value of the methods, we conduct simulations in non-axisymmetric perturbation magnetic fields as part of the experiments,demonstrating that our CPP-based AVF method can handle simulations under complex magnetic field configurations with high accuracy, which the CPP-based Boris algorithm lacks. Through numerical experiments, we demonstrate that the CPP can replace guiding center dynamics in using energy-preserving algorithms for computations, providing a new, efficient, as well as stable approach for applying structure-preserving algorithms in plasma simulations.

Multi-head neural networks for simulating particle breakage dynamics

The breakage of brittle particulate materials into smaller particles under compressive or impact loads can be modelled as an instantiation of the population balance integro-differential equation.In this paper,the emerging computational science paradigm of physics-informed neural networks is studied for the first time for solving both linear and nonlinear variants of the governing dynamics.Unlike conventional methods,the proposed neural network provides rapid simulations of arbitrarily high resolution in particle size,predicting values on arbitrarily fine grids without the need for model retraining.The network is assigned a simple multi-head architecture tailored to uphold monotonicity of the modelled cumulative distribution function over particle sizes.The method is theoretically analyzed and validated against analytical results before being applied to real-world data of a batch grinding mill.The agreement between laboratory data and numerical simulation encourages the use of physics-informed neural nets for optimal planning and control of industrial comminution processes.

Microphase Separation of Star-diblock Copolymer Films： a Dissipative Particle Dynamics Simulation

The microphase-separating behaviors of two types of star-diblock copolymers （Ax）4（By）4 and （A^Bg）4 in thin films are studied using the simulation technique of dissipative particle dynamics. A variety of ordered mesostructures have been observed and the simulated phase diagrams show obvious symmetries for the （Ax）4（By）a films and asymmetries for the （AxBy）4 films, besides, it is easier for the （Ax）4（By）4 than for the （A^By）4 to carry out microphase separation under the same conditions, which has been recognized in bulk and can be ascribed to the structural difference between the two types of star copolymers. There are some correspondences between the mesostructures formed in the film and those formed in bulk at the same composition fraction. Decreasing the thickness of film and strengthening the A-B repulsion both help the mesostructures enhance the degree of order. Composition fraction dependences of the mean-square radius of gyration in the two types of star copolymer films are almost contrary, which can be attributed to the differences in their respective structures. These findings can provide a guide to designing novel microstructures involving star-diblock copolymers via geometrical confinement.

Dissipative Particle Dynamics Simulation of Microscopic Properties in Diblock Copolymer Films

Mean-square bond length, root-mean-square end-to-end distance and gyration radius in diblock copolymer films have been studied by dissipative particle dynamics simulations. Results show evident linear trends of any property separately with the thickness of film, the interaction between particles of different types, the repulsion between particle and boundary, except for the dependence of the variations of mean-square bond length on the thickness of film, which exhibits as a wave trend. What＇s more, the varying trends of mean-square bond length and root-mean-square end-to-end distance can correspond to each other. The density distribution of either component in diblock copolymer film can be controlled and adjusted effectively through its interaction with boundary.

Dissipative particle dynamics simulation of flow through periodic arrays of circular micropillar

Flow through arrays of micropillar embedded inside microfluidic chip systems is important for various microfluidic devices. It is critical to accurately predict the mass flow rate through pillar arrays based on the pillar design. This work presents a dissipative particle dynamics （DPD） model to simulate a problem of flow across periodic arrays of circular micropillar and investigates the permeability of two types of micropillar arrays. The flow fields including horizontal and vertical velocity fields, the number density field, and the streamline of the flow are analyzed. The predicted solid volumes by the presented DPD simulation of both types of arrays are quite close to the actual counterparts. These quantitative agreements show usefulness and effectiveness of the DPD model in simulating arrays of micropillar. By comparing two types of micropillar arrangement patterns, we find that the arrangement pattern of micropillar does not have significant influence on the permeability of the array.

Dissipative Particle Dynamics Simulation on Bonding Reaction Between Surface Modified Nanoparticles

A simulation study was carried out by using dissipative particle dynamics(DPD) method to explore the effects of properties of coating chains, such as length, density, rigidity of polymer chains, as well as the distance between nanoparticles on bonding reaction of coating chains grafted onto nanoparticles. The results show that bonding ratios of coated chains strongly depend on the length and density of coating chains. For nanoparticles with different coating densities, the optimum chain length for bonding reaction are varied. The rigidity of coating chains exhibits vigorous effects on bonding reaction that highly depends on chain lengths. DPD simulation can be used to study the bonding reaction between coated nanoparticles, which may help experimental synthesis of nanocomposites with excellent properties.

A note on hydrodynamics from dissipative particle dynamics

We calculate current correlation functions （CCFs） of dissipative particle dy- namics （DPD） and compare them with results of molecular dynamics （MD） and solutions of linearized hydrodynamic equations. In particular, we consider three versions of DPD, the empirical/classical DPD, coarse-grained （CG） DPD with radial-direction interactions only and full （radial, transversal, and rotational） interactions between particles. To fa- cilitate quantitative discussions, we consider specifically a star-polymer melt system at a moderate density. For bonded molecules, it is straightforward to define the CG variables and to further derive CG force fields for DPD within the framework of the Mori-Zwanzig formalism. For both transversal and longitudinal current correlation functions （TCCFs and LCCFs）, we observe that results of MD, DPD, and hydrodynamic solutions agree with each other at the continuum limit. Below the continuum limit to certain length scales, results of MD deviate significantly from hydrodynamic solutions, whereas results of both empirical and CG DPD resemble those of MD. This indicates that the DPD method with Markovian force laws possibly has a larger applicability than the continuum description of a Newtonian fluid. This is worth being explored further to represent gen- eralized hydrodynamics.

A new model for dissipative particle dynamics boundary condition of walls with different wettabilities

The implementation of solid-fluid boundary condition has been a major challenge for dissipative particle dynamics(DPD)method.Current implementations of boundary conditions usually try to approach a uniform density distribution and a velocity profile close to analytical solution.The density oscillations and slip velocity are intentionally eliminated,and different wall properties disappear in the same analytical solution.This paper develops a new wall model that combines image and frozen particles and a new strategy to emphasize different wall properties especially wettabilities.The strategy first studies the realistic wall-fluid system by molecular dynamics(MD)simulation depending on physical parameters.Then,a DPD simulation is used to match the density and velocity profiles with the new wall model.The obtained DPD parameters can simulate the systems with the same wall and fluid materials.With this method,a simulation of the Poiseuille flow of liquid argon with copper walls is presented.Other walls with super-hydrophilic,hydrophilic,and hydrophobic wettabilities are also simulated.The limitations of the analytical solution and the effect of the wall-fluid interaction are discussed.The results show that the method suggested in this paper can simulate the mesoscale behavior of the microchannel flow related to realistic systems.

Effect of shear on the symmetric diblock copolymer/nanorod mixture:A dissipative particle dynamics study

The phase behaviours of a lamellar diblock copolymer/nanorod composite under steady shear are investigated using dissipative particle dynamics. We consider a wide range of nanorod concentrations, where the nanorods each have a preferential affinity to one of the blocks. Our results suggest that shear not only aligns the orientations of the diblock eopolymer templates and nanorods towards flow direction, but also regulates the distribution of the nanorods within the polymer matrix. Meanwhile, the shear-induced reorientation and morphology transitions of the systems also significantly depend on the nanorod concentration. At certain nanorod concentrations, the competitions between shearinduced polymer thinning and nanorods dispersion behaviours determine the phase behaviours of the composites. For high nanorod concentrations, no morphology transition is observed, but reorientation is present, in which the sheared nanorods are arranged into hexagonal packing arrays. Additionally, the orientation behaviour of nanorods is determined directly by the applied shear, also interfered with by the shear-stretched copolymer molecules.

Many-body dissipative particle dynamics with energy conservation:temperature-dependent long-term attractive interaction

Heat and mass transfer during the process of liquid droplet dynamic behaviors has attracted much attention in decades.At mesoscopic scale,numerical simulations of liquid droplets motion,such as impacting,sliding,and coalescence,have been widely studied by using the particle-based method named many-body dissipative particle dynamics(MDPD).However,the detailed information on heat transfer needs further description.This paper develops a modified MDPD with energy conservation(MDPDE)by introducing a temperature-dependent long-term attractive interaction.By fitting or deriving the expressions of the strength of the attractive force,the exponent of the weight function in the dissipative force,and the mesoscopic heat friction coefficient about temperature,we calculate the viscosity,self-diffusivity,thermal conductivity,and surface tension,and obtain the Schmidt number Sc,the Prandtl number P r,and the Ohnesorge number Oh for 273 K to 373 K.The simulation data of MDPDE coincide well with the experimental data of water,indicating that our model can be used to simulate the dynamic behaviors of liquid water.Furthermore,we compare the equilibrium contact angle of droplets wetting on solid surfaces with that calculated from three interfacial tensions by MDPDE simulations.The coincident results not only stand for the validation of Young’s equation at mesoscale,but manifest the reliability of our MDPDE model and applicability to the cases with free surfaces.Our model can be extended to study the multiphase flow withcomplex heat and mass transfer.

Polymer translocation through nanopore under external electric field:dissipative particle dynamics study

The DNA sequencing technology has achieved a leapfrog development in recent years. As a new generation of the DNA sequencing technology, nanopore sequenc- ing has shown a broad application prospect and attracted vast research interests since it was proposed. In the present study, the dynamics of the electric-driven translocation of a homopolymer through a nanopore is investigated by the dissipative particle dynam- ics （DPD）, in which the homopolymer is modeled as a worm-like chain （WLC）. The DPD simulations show that the polymer chain undergoes conformation changes during the translocation process. The different structures of the polymer in the translocation process, i.e., single-file, double folded, and partially folded, and the induced current block- ades are analyzed. It is found that the current blockades have different magnitudes due to the polymer molecules traversing the pore with different folding conformations. The nanoscale vortices caused by the concentration polarization layers （CPLs） in the vicinity of the sheet are also studied. The results indicate that the translocation of the polymer has the effect of eliminating the vortices in the polyelectrolyte solution. These findings are expected to provide the theoretical guide for improving the nanopore sequencing tech- nique.

Dissipative Particle Dynamics Simulations of Domain Growth and Phase Separation in Binary Immiscible Fluids

It was investigated that the domain growth processes of spinodal decomposition with different quenching depth in two and three dimensional binary immiscible fluids by using parallel dissipative particle dynamics simulations. In two dimensions, the dynamic scaling exponent 1/2 for coalescence and 2/3 for inertial regimes in the shallow quench and strong finite size effects in the cases of deep quenching were obtained. In three dimensions, it was used that the diffusive regime with exponent n=l/3 in the shallow quench and the inertial hydrodynamic regime with n=2/3 for different quenches. The viscous effects are not clearly reflected, showing n=1/2 in both shallow and deep quenches in this time period, due to the soft nature of interaction potential adopted in dissipative particle dynamics.

Discussions on the correspondence of dissipative particle dynamics and Langevin dynamics at small scales

We investigate the behavior of dissipative particle dynamics （DPD） within different scaling regimes by numerical simulations. The paper extends earlier analytical findings of Ripoll, M., Ernst, M. H., and Espafiol, P. （Large scale and mesoscopic hy- drodynamics for dissipative particle dynamics. Journal of Chemical Physics, 115（15）, 7271-7281 （2001）） by evaluation of numerical data for the particle and collective scaling regimes and the four different subregimes. DPD simulations are performed for a range of dynamic overlapping parameters. Based on analyses of the current auto-correlation functions （CACFs）, we demonstrate that within the particle regime at scales smaller than its force cut-off radius, DPD follows Langevin dynamics. For the collective regime, we show that the small-scale behavior of DPD differs from Langevin dynamics. For the wavenumber-dependent effective shear viscosity, universal scaling regimes are observed in the microscopic and mesoscopic wavenumber ranges over the considered range of dynamic overlapping parameters.

Temperature dependence of microscopic properties in diblock copolymer films:A dissipative particle dynamics simulation

Temperature dependence of microscopic properties in diblock copolymer films has been investigated by dissipative particle dynamics simulations. Results show the relation between mean-square bond length （MSBL） and system temperature can be described as a quadratic curve. The root-mean-square radius of gyration （RMSGR） and end-end distance （RMSED） increase gradually as the temperature rises and composition fraction changes from 0.1 to 0.5, in which the effect of the former is primary. Especially, the relation between RMSGR and temperature is nearly linear in the confinement-introduced direction. Density distribution of each component in the films can be controlled and adjusted effectively by its interaction with other components and boundaries. Moreover, the changes of system temperature and composition fraction can both affect the density distributions to a certain extent.

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） con- servation, 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.

Dissipative Particle Dynamics Simulations of the Self-assembly Mechanisms of Fluorinated Ordered Mesoporous Carbon in the Aqueous Phase

To clarify the preparation mechanisms of uorinated ordered mesoporous carbon materials (FOMCs), the dissipative par- ticle dynamics method was used to simulate the self-assembly process of the amphiphilic triblock poly(ethylene oxide)- poly(propylene oxide)-poly(ethylene oxide) copolymer Pluronic F127 in the aqueous system. The self-assembly mechanisms in aqueous phase and the formation mechanisms of micropores and mesopores were investigated. It was found that the mesoporous structure of the FOMCs was formed by the hydrophobic segments of F127, while the pore wall was formed by both the hydrophilic segments and the carbon precursor in the system. The microporous structure on the pore wall was con- structed by the carbon source in the hydrophilic segments’ spaces after the template was removed. Our ndings could provide understanding and knowledge for the synthesis of mesoporous carbon by the self-assembly method on the mesoscopic scale.