Multiparticle Collision Dynamics Method Research Articles

Availability of multi-particle collision dynamics method for magnetic particle suspensions

Availability of multi-particle collision dynamics method for magnetic particle suspensions

Self-Organized Velocity Pulses of Dense Colloidal Suspensions in Microchannel Flow.

We present a numerical study of dense colloidal suspensions in a pressure-driven microchannel flow in two dimensions. The colloids are modeled as elastic and frictional spheres suspended in a Newtonian fluid, which we simulate using the method of multiparticle collision dynamics. The model reproduces periodic velocity and density pulse trains, traveling upstream in the microchannel, which are found in experiments conducted by Isa etal. [Phys. Rev. Lett. 102, 058302 (2009)PRLTAO0031-900710.1103/PhysRevLett.102.058302]. We show that colloid-wall friction and the resultant force chains are crucial for the formation of these pulses. With an increasing colloid density, first solitary jams occur, which become periodic pulse trains at intermediate densities and unstable solitary pulses at high densities. We formulate a phenomenological continuum model and show how these spatiotemporal flow and density profiles can be understood as homoclinic and periodic orbits in traveling-wave equations.

Collective sedimentation of squirmers under gravity.

Active particles, which interact hydrodynamically, display a remarkable variety of emergent collective phenomena. We use squirmers to model spherical microswimmers and explore the collective behavior of thousands of them under the influence of strong gravity using the method of multi-particle collision dynamics for simulating fluid flow. The sedimentation profile depends on the ratio of swimming to sedimentation velocity as well as on the squirmer type. It shows closely packed squirmer layers at the bottom and a highly dynamic region with exponential density dependence towards the top. The mean vertical orientation of the squirmers strongly depends on height. For swimming velocities larger than the sedimentation velocity, squirmers show strong convection in the exponential region. We quantify the strength of convection and the extent of convection cells by the vertical current density and its current dipole, which are large for neutral squirmers as well as for weak pushers and pullers.

Diffusion of Nanoparticles in Semidilute Polymer Solutions: A Multiparticle Collision Dynamics Study

The diffusion of nanoparticles immersed in semidilute polymer solutions is investigated by a hybrid mesoscopic multiparticle collision dynamics method. Effects of polymer concentration and hydrodynamic interactions among polymer monomers are focused. Extensive simulations show that the dependence of diffusion coefficient D on the polymer concentration c agrees with Phillies equation D-exp (−αcδ) with a scaling exponent δ≈0.97 which coincides with the experimental one in literature. For increasing nanoparticle size, the scaling prefactor α increases monotonically while the scaling exponent always keeps fixed. Moreover, we also study the diffusion of nanoparticle without hydrodynamic interactions and find that mobility of the nanoparticle slows down, and the scaling exponent is obviously different from the one in experiments, implying that hydrodynamic interactions play a crucial role in the diffusion of a nanoparticle in semidilute polymer solutions.

Comparison of different coupling schemes between counterions and charged nanoparticles in multiparticle collision dynamics.

We applied the multiparticle collision dynamics (MPC) simulation technique to highly asymmetric electrolytes in solution, i.e., charged nanoparticles and their counterions in a solvent. These systems belong to a domain of solute size which ranges between the electrolyte and the colloidal domains, where most analytical theories are expected to fail, and efficient simulation techniques are still missing. MPC is a mesoscopic simulation method which mimics hydrodynamics properties of a fluid, includes thermal fluctuations, and can be coupled to a molecular dynamics of solutes. We took advantage of the size asymmetry between nanoparticles and counterions to treat the coupling between solutes and the solvent bath within the MPC method. Counterions were coupled to the solvent bath during the collision step and nanoparticles either through a direct interaction force or with stochastic rotation rules which mimic stick boundary conditions. Moreover, we adapted the simulation procedure to address the issue of the strong electrostatic interactions between solutes of opposite charges. We show that the short-ranged repulsion between counterions and nanoparticles can be modeled by stochastic reflection rules. This simulation scheme is very efficient from a computational point of view. We have also computed the transport coefficients for various densities. The diffusion of counterions was found in one case to increase slightly with the volume fraction of nanoparticles. The deviation of the electric conductivity from the ideal behavior (solutes at infinite dilution without any direct interactions) is found to be strong.

Hydrodynamics in adaptive resolution particle simulations: Multiparticle collision dynamics

A new adaptive resolution technique for particle-based multi-level simulations of fluids is presented. In the approach, the representation of fluid and solvent particles is changed on the fly between an atomistic and a coarse-grained description. The present approach is based on a hybrid coupling of the multiparticle collision dynamics (MPC) method and molecular dynamics (MD), thereby coupling stochastic and deterministic particle-based methods. Hydrodynamics is examined by calculating velocity and current correlation functions for various mixed and coupled systems. We demonstrate that hydrodynamic properties of the mixed fluid are conserved by a suitable coupling of the two particle methods, and that the simulation results agree well with theoretical expectations.

Dynamic Structure Factor of Core–Shell Microgels: A Neutron Scattering and Mesoscale Hydrodynamic Simulation Study

Polymeric microgels with core–shell morphology provide promising properties for many applications such as controlled uptake and release of guest nanoparticles. In this work we investigated how the structure and dynamics of the core and the shell in the microgel are coupled using both experimental and computer simulation approaches. The studied core–shell model systems which consist of a collapsed core and a swollen shell (CCSS) and a swollen core and collapsed shell (SCCS) show a different behavior in both structure and dynamics. The intermediate scattering profiles obtained from neutron spin echo (NSE) spectroscopy of CCSS microgels show an initial fast decay similar to that of bare swollen microgels followed by a slow decay similar to that of a purely collapsed microgel. This is also reflected in mesoscale hydrodynamic simulations using the multiparticle collision dynamics method. In the case of CCSS microgels, the decay rate of the intermediate scattering functions shows a crossover from collective diffusive dynamics at low wavenumbers to a Zimm-type dynamics at larger wavenumbers. This is similar to the behavior of a purely swollen microgels. In the case of SCCS microgels, the intermediate scattering profiles from experiment and simulations show a slow dynamics at small as well as large wavenumbers. Studying the dynamics of the individual compartments in the simulated structures suggests that the slower dynamics in SCCS microgels can be attributed to the collective motion of collapsed and aggregated shell parts which form in the periphery of the microgel. Additionally, in both CCSS and SCCS microgels, a slowdown of the dynamics is observed in the swollen compartment compared to the bare swollen microgel, which is a result of the interplay between core and shell compartments.

Taylor line swimming in microchannels and cubic lattices of obstacles.

Microorganisms naturally move in microstructured fluids. Using the simulation method of multi-particle collision dynamics, we study in two dimensions an undulatory Taylor line swimming in a microchannel and in a cubic lattice of obstacles, which represent simple forms of a microstructured environment. In the microchannel the Taylor line swims at an acute angle along a channel wall with a clearly enhanced swimming speed due to hydrodynamic interactions with the bounding wall. While in a dilute obstacle lattice swimming speed is also enhanced, a dense obstacle lattice gives rise to geometric swimming. This new type of swimming is characterized by a drastically increased swimming speed. Since the Taylor line has to fit into the free space of the obstacle lattice, the swimming speed is close to the phase velocity of the bending wave traveling along the Taylor line. While adjusting its swimming motion within the lattice, the Taylor line chooses a specific swimming direction, which we classify by a lattice vector. When plotting the swimming velocity versus the magnitude of the lattice vector, all our data collapse on a single master curve. Finally, we also report more complex trajectories within the obstacle lattice.

Phase separation and coexistence of hydrodynamically interacting microswimmers.

A striking feature of the collective behavior of spherical microswimmers is that for sufficiently strong self-propulsion they phase-separate into a dense cluster coexisting with a low-density disordered surrounding. Extending our previous work, we use the squirmer as a model swimmer and the particle-based simulation method of multi-particle collision dynamics to explore the influence of hydrodynamics on their phase behavior in a quasi-two-dimensional geometry. The coarsening dynamics towards the phase-separated state is diffusive in an intermediate time regime followed by a final ballistic compactification of the dense cluster. We determine the binodal lines in a phase diagram of Péclet number versus density. Interestingly, the gas binodals are shifted to smaller densities for increasing mean density or dense-cluster size, which we explain using a recently introduced pressure balance [S. C. Takatori, et al., Phys. Rev. Lett. 2014, 113, 028103] extended by a hydrodynamic contribution. Furthermore, we find that for pushers and pullers the binodal line is shifted to larger Péclet numbers compared to neutral squirmers. Finally, when lowering the Péclet number, the dense phase transforms from a hexagonal "solid" to a disordered "fluid" state.

Hydrostatic Simulation of Earth's Atmospheric Gas Using Multi-particle Collision Dynamics

Multi-particle collision dynamics (MPCD) is a mesoscopic simulation method to simulate fluid particle-like flows. MPCD has been widely used to simulate various problems in condensed matter. In this study, hydrostatic behavior of gas in the Earth's atmospheric layer is simulated by using MPCD method. The simulation is carried out by assuming the system under ideal state and is affected only by gravitational force. Gas particles are homogeneous and placed in 2D box. Interaction of the particles with the box is applied through implementation of boundary conditions (BC). Periodic BC is applied on the left and the right side, specular reflection on the top side, while bounce-back on the bottom side. Simulation program is executed in Arch Linux and running in notebook with processor Intel i5 @2700 MHz with 10 GB DDR3 RAM. The results show behaviors of the particles obey kinetic theory for ideal gas when gravitational acceleration value is proportional to the particle mass. Density distribution as a function of altitude also meets atmosphere's hydrostatic theory.

Self-organization in suspensions of end-functionalized semiflexible polymers under shear flow.

The nonequilibrium dynamical behavior and structure formation of end-functionalized semiflexible polymer suspensions under flow are investigated by mesoscale hydrodynamic simulations. The hybrid simulation approach combines the multiparticle collision dynamics method for the fluid, which accounts for hydrodynamic interactions, with molecular dynamics simulations for the semiflexible polymers. In equilibrium, various kinds of scaffold-like network structures are observed, depending on polymer flexibility and end-attraction strength. We investigate the flow behavior of the polymer networks under shear and analyze their nonequilibrium structural and rheological properties. The scaffold structure breaks up and densified aggregates are formed at low shear rates, while the structural integrity is completely lost at high shear rates. We provide a detailed analysis of the shear- rate-dependent flow-induced structures. The studies provide a deeper understanding of the formation and deformation of network structures in complex materials.

Effect of angular momentum conservation on hydrodynamic simulations of colloids.

In contrast to most real fluids, angular momentum is not a locally conserved quantity in some mesoscopic simulation methods. Here we quantify the importance of this conservation in the flow fields associated with different colloidal systems. The flow field is analytically calculated with and without angular momentum conservation for the multiparticle collision dynamics (MPC) method, and simulations are performed to verify the predictions. The flow field generated around a colloidal particle moving under an external force with slip boundary conditions depends on the conservation of angular momentum, and the amplitude of the friction force is substantially affected. Interestingly, no dependence on the angular momentum conservation is found for the flow fields generated around colloids under the influence of phoretic forces. Moreover, circular Couette flow between a no-slip and a slip cylinder is investigated, which allows us to validate one of the two existing expressions for the MPC stress tensor.

Modelling the mechanics and hydrodynamics of swimming E. coli.

The swimming properties of an E. coli-type model bacterium are investigated by mesoscale hydrodynamic simulations, combining molecular dynamics simulations of the bacterium with the multiparticle particle collision dynamics method for the embedding fluid. The bacterium is composed of a spherocylindrical body with attached helical flagella, built up from discrete particles for an efficient coupling with the fluid. We measure the hydrodynamic friction coefficients of the bacterium and find quantitative agreement with experimental results of swimming E. coli. The flow field of the bacterium shows a force-dipole-like pattern in the swimming plane and two vortices perpendicular to its swimming direction arising from counterrotation of the cell body and the flagella. By comparison with the flow field of a force dipole and rotlet dipole, we extract the force-dipole and rotlet-dipole strengths for the bacterium and find that counterrotation of the cell body and the flagella is essential for describing the near-field hydrodynamics of the bacterium.

Numerical simulation of star polymers under shear flow using a coupling method of multi-particle collision dynamics and molecular dynamics

The numerical simulation of flow-induced structures is important for the flow analysis of complex fluids. Several schemes have been proposed for coupling the macro-flow computation and the microsimulation of the inner structure of complex fluids. In the present study, the flow-induced structure of star polymers was numerically simulated using a coupling method of multi-particle collision dynamics (MPCD) and coarse-grained molecular dynamics (MD). The polymers were modeled as elastic dumbbells, which consist of finitely extensible nonlinear elastic springs and beads. The motion of the beads was computed by MD. The MPCD was applied to model the effect of Brownian motion and hydrodynamic interactions among the beads. In the present study, the MPC-AT+a algorithm was employed for the collision steps in MPCD computations. The behavior of linear polymers in a shear flow was numerically analyzed to confirm the validity of the present simulation scheme. The numerical results agree well with both experimental results and predictions by other numerical methods. Furthermore, the simulation of star polymers under shear flow was carried out. The present simulation captured characteristic behaviors such as the configuration of the star polymers, which was more compact for polymers with more arms due to extruded volume effects, polymers tumbling at high Weissenberg numbers, and the fluctuation in expansions in the direction of flow decreasing for polymers with more arms.

Scaffold Structures by Telechelic Rodlike Polymers: Nonequilibrium Structural and Rheological Properties under Shear Flow

The nonequilibrium structural and rheological properties of suspension of rodlike polymers with attractive ends are investigated by mesoscale hydrodynamic simulations. The hybrid simulation approach combines the multiparticle collision dynamics method for the fluid with molecular dynamics simulations for the polymers. In equilibrium, the rodlike polymers self-organize into scaffold-like network structures above a critical density and attraction strength. Shear flow induces significant structural changes. We identify three major regimes. At low Weissenberg numbers, the scaffold structure is compactified accompanied by a phase separation into a fluid domain and a dense scaffold-like structure. The shear viscosity shows a Newtonian plateau, which is determined by the fluid layer. At intermediated shear rates, shear bands appear with bundles of polymers. Again, we observe a nearly Newtonian viscosity regime governed by the fluid bands. At high shear rates, any structure is dissolved and a paranematic phase appears, with rods well aligned with the flow, and shear thinning appears.

Electrophoretic mobilities of counterions and a polymer in cylindrical pores.

We have simulated the transport properties of a uniformly charged flexible polymer chain and its counterions confined inside cylindrical nanopores under an external electric field. The hydrodynamic interaction is treated by describing the solvent molecules explicitly with the multiparticle collision dynamics method. The chain consisting of charged monomers and the counterions interact electrostatically with themselves and with the external electric field. We find rich behavior of the counterions around the polymer under confinement in the presence of the external electric field. The mobility of the counterions is heterogeneous depending on their location relative to the polymer. The adsorption isotherm of the counterions on the polymer depends nonlinearly on the electric field. As a result, the effective charge of the polymer exhibits a sigmoidal dependence on the electric field. This in turn leads to a nascent nonlinearity in the chain stretching and electrophoretic mobility of the polymer in terms of their dependence on the electric field. The product of the electric field and the effective polymer charge is found to be the key variable to unify our simulation data for various polymer lengths. Chain extension and the electrophoretic mobility show sigmoidal dependence on the electric field, with crossovers from the linear response regime to the nonlinear regime and then to the saturation regime. The mobility of adsorbed counterions is nonmonotonic with the electric field. For weaker and moderate fields, the adsorbed counterions move with the polymer and at higher fields they move opposite to the polymer's direction. We find that the effective charge and the mobility of the polymer decrease with a decrease in the pore radius.

Self-Organized Structures of Attractive End-Functionalized Semiflexible Polymer Suspensions

The equilibrium structural properties of suspensions of semiflexible polymers with attractive ends are investigated by mesoscale hydrodynamic simulations. The hybrid simulation approach combines the multiparticle collision dynamics method for the fluid with molecular dynamics simulations for the semiflexible polymers. In equilibrium, the linear polymers self-organize into scaffold-like network structures, which are governed by polymer flexibility and end-attraction strength. We investigate the appearing structures for various adhesive strengths and polymer stiffnesses. The morphology of the suspension changes abruptly when the end-attraction strength exceeds a critical value, and stiff polymers assemble more easily into scaffold-like networks than flexible polymers. These studies provide a deeper understanding of the network structure formation in complex materials.

Controlling inertial focussing using rotational motion.

In inertial microfluidics lift forces cause a particle to migrate across streamlines to specific positions in the cross section of a microchannel. We control the rotational motion of a particle and demonstrate that this allows to manipulate the lift-force profile and thereby the particle's equilibrium positions. We perform two-dimensional simulation studies using the method of multi-particle collision dynamics. Particles with unconstrained rotational motion occupy stable equilibrium positions in both halfs of the channel while the center is unstable. When an external torque is applied to the particle, two equilibrium positions annihilate by passing a saddle-node bifurcation and only one stable fixpoint remains so that all particles move to one side of the channel. In contrast, non-rotating particles accumulate in the center and are pushed into one half of the channel when the angular velocity is fixed to a non-zero value.

Hydrodynamics Determines Collective Motion and Phase Behavior of Active Colloids in Quasi-Two-Dimensional Confinement

We study the collective motion of confined spherical microswimmers such as active colloids which we model by so-called squirmers. To simulate hydrodynamic flow fields including thermal noise, we use the method of multiparticle collision dynamics. We demonstrate that hydrodynamic near fields acting between squirmers as well as between squirmers and bounding walls crucially determine their collective motion. In particular, with increasing density we observe a clear phase separation into a gaslike and cluster phase for neutral squirmers whereas strong pushers and pullers more gradually approach the hexagonal cluster state.

Thermoelectric efficiency in momentum-conserving systems

We show that for a two-dimensional gas of elastically interacting particles the thermoelectric efficiency reaches the Carnot efficiency in the thermodynamic limit. Numerical simulations, by means of the multi-particle collision dynamics method, show that this result is robust under perturbations. That is, the thermoelectric figure of merit remains large when momentum conservation is broken by weak noise.