Multiparticle Collision Dynamics Method Research Articles

Multiparticle collision dynamics simulations of hydrodynamic interactions in colloidal suspensions: How well does the discrete particle approach do at short range?

The multiparticle collision dynamics (MPCD) simulation method is an attractive technique for studying the effects of hydrodynamic interactions in colloidal suspensions because of its flexibility, computational efficiency, and ease of implementation. Here, we analyze an extension of the basic MPCD method in which colloidal particles are discretized with a surface mesh of sensor nodes/particles that interact with solvent particles (MPCD + Discrete Particle or MPCD + DP). We use several situations that have been described analytically to probe the impact of colloidal particle mesh resolution on the ability of the MPCD + DP method to resolve short-ranged hydrodynamic interactions, which are important in crowded suspensions and especially in self-assembling systems that create high volume fraction phases. Specifically, we consider (A) hard-sphere diffusion near a wall, (B) two-particle diffusion, (C) hard-sphere diffusion in crowded suspensions, and (D) the dynamics of aggregation in an attractive colloidal suspension. We show that in each case, the density of sensor nodes plays a significant role in the accuracy of the simulation and that a surprisingly high number of surface nodes are needed to fully capture hydrodynamic interactions.

Magneto-Permeability Effect in Ferrofluid Flow Through Porous Media Studied via Multiparticle Collision Dynamics

AbstractAs more and more promising applications of magnetic nanoparticles in complicated environments are explored, their flow properties in porous media are of increasing interest. We here propose a hybrid approach based on the multiparticle collision dynamics method extended to porous media via friction forces and coupled with Brownian dynamics simulations of the rotational motion of magnetic nanoparticles’ magnetic moment. We simulate flow in planar channels homogeneously filled with a porous medium and verify our implementation by reproducing the analytical velocity profile of the Darcy–Brinkman model in the non-magnetic case. In the presence of an externally applied magnetic field, the non-equilibrium magnetization and friction forces lead to field-dependent velocity profiles that result in effective, field-dependent permeabilities. We provide a theoretical expression for this magneto-permeability effect in analogy with the magneto-viscous effect. Finally, we study the flow through planar channels, where only the walls are covered with a porous medium. We find a smooth crossover from the Poiseuille profile in the center of the channel to Brinkman–Darcy flow in the porous layers. We propose a simple estimate of the thickness of the porous layer based on the flow rate and maximum flow velocity.

Mesoscale simulations of diffusion and sedimentation in shape-anisotropic nanoparticle suspensions.

We determine the long-time self-diffusion coefficient and sedimentation coefficient for suspensions of nanoparticles with anisotropic shapes (octahedra, cubes, tetrahedra, and spherocylinders) as a function of nanoparticle concentration using mesoscale simulations. We use a discrete particle model for the nanoparticles, and we account for solvent-mediated hydrodynamic interactions between nanoparticles using the multiparticle collision dynamics method. Our simulations are compared to theoretical predictions and experimental data from existing literature, demonstrating good agreement in the majority of cases. Further, we find that the self-diffusion coefficient of the regular polyhedral shapes can be estimated from that of a sphere whose diameter is the average of their inscribed and circumscribed sphere diameters.

What quantity of charge on the nanoparticle can result in a hybrid morphology of the nanofluid and a higher thermal conductivity?

One of the most important mechanisms for promotion of the thermal conductivity(TC) of nanofluid is aggregation of nanoparticles. In present work, a hybrid method of multi-particle collision dynamics and molecular dynamics (MPCD-MD) is employed to evaluate the aggregation morphology and TC of Cu-H2O nanofluid. Numerical simulations for various quantity of charges (QoC) on nanoparticles are conducted, and three kinds of morphology of nanoparticles distribution, whole aggregation morphology at lower QoC, hybrid morphology at moderate QoC and fully dispersed morphology at greater QoC, are obtained for the first time in microscopic simulations. For hybrid morphologies, the fractal dimension first drops and then rises with increasing QoC, since aggregates can break up into several clusters at relatively low QoC and can be fully dispersed at relatively high QoC. Instead, the TC first increases and then decreases, and the TC can reach a peak at a certain QoC. The underneath mechanism should be a balance between the effects of nanolayers and Kapitza resistance. This can provide helpful guidance to prepare nanofluids with higher TC.

Simulating the flow of interacting ferrofluids with multiparticle collision dynamics.

Ferrofluid flow is fascinating since its fluid properties can conveniently be manipulated by external magnetic fields. Novel applications in micro- and nanofluidics as well as in biomedicine have renewed the interest in the flow of colloidal magnetic nanoparticles with a focus on small-scale behavior. Traditional flow simulations of ferrofluids, however, often use simplified constitutive models and do not include fluctuations that are relevant at small scales. Here we address these challenges by proposing a hybrid scheme that combines the multiparticle collision dynamics method for modeling hydrodynamics with Brownian dynamics simulations of a reliable kinetic model describing the microstructure, magnetization dynamics, and resulting stresses. Since both multiparticle collision dynamics and Brownian dynamics are mesoscopic methods that naturally include fluctuations, this hybrid scheme presents a promising alternative to more traditional approaches, also because of the flexibility to model different geometries and modifying the constitutive model. The scheme was tested in several ways. Poiseuille flow was simulated for various model parameters and effective viscosities were determined from the resulting flow profiles. The effective, field-dependent viscosities are found to be in very good agreement with theoretical predictions. We also study Stokes' second flow problem for ferrofluids. For weak amplitudes and low frequencies of the oscillating plate, we find that the velocity profiles are well described by the result for Newtonian fluids at the corresponding, field-dependent viscosity. Furthermore, the time-dependent profiles of the nonequilibrum magnetization component are well approximated by their steady-state values in stationary shear when evaluated with the instantaneous local shear rate. Finally, we also apply our scheme to simulate ferrofluid shear flow over a rough surface. We find characteristic differences in the nonequilibrium magnetization components when the external field is oriented in flow and in a gradient direction.

Multiparticle collision dynamics for ferrofluids.

Detailed studies of the intriguing field-dependent dynamics and transport properties of confined flowing ferrofluids require efficient mesoscopic simulation methods that account for fluctuating ferrohydrodynamics. Here, we propose such a new mesoscopic model for the dynamics and flow of ferrofluids, where we couple the multi-particle collision dynamics method as a solver for the fluctuating hydrodynamics equations to the stochastic magnetization dynamics of suspended magnetic nanoparticles. This hybrid model is validated by reproducing the magnetoviscous effect in Poiseuille flow, obtaining the rotational viscosity in quantitative agreement with theoretical predictions. We also illustrate the new method for the benchmark problem of flow around a square cylinder. Interestingly, we observe that the length of the recirculation region is increased, whereas the drag coefficient is decreased in ferrofluids when an external magnetic field is applied compared with the field-free case at the same effective Reynolds number. The presence of thermal fluctuations and the flexibility of this particle-based mesoscopic method provide a promising tool to investigate a broad range of flow phenomena of magnetic fluids, and the method could also serve as an efficient way to simulate solvent effects when colloidal particles are immersed in ferrofluids.

Gyrotactic cluster formation of bottom-heavy squirmers

Squirmers that are bottom-heavy experience a torque that aligns them along the vertical so that they swim upwards. In a suspension of many squirmers, they also interact hydrodynamically via flow fields that are initiated by their swimming motion and by gravity. Swimming under the combined action of flow field vorticity and gravitational torque is called gyrotaxis. Using the method of multi-particle collision dynamics, we perform hydrodynamic simulations of a many-squirmer system floating above the bottom surface. Due to gyrotaxis they exhibit pronounced cluster formation with increasing gravitational torque. The clusters are more volatile at low values but compactify to smaller clusters at larger torques. The mean distance between clusters is mainly controlled by the gravitational torque and not the global density. Furthermore, we observe that neutral squirmers form clusters more easily, whereas pullers require larger gravitational torques due to their additional force-dipole flow fields. We do not observe clustering for pusher squirmers. Adding a rotlet dipole to the squirmer flow field induces swirling clusters. At high gravitational strengths, the hydrodynamic interactions with the no-slip boundary create an additional vertical alignment for neutral squirmers, which also supports cluster formation.

Multi-particle collision dynamics with a non-ideal equation of state. II. Collective dynamics of elongated squirmer rods.

Simulations of flow fields around microscopic objects typically require methods that both solve the Navier-Stokes equations and also include thermal fluctuations. One such method popular in the field of soft-matter physics is the particle-based simulation method of multi-particle collision dynamics (MPCD). However, in contrast to the typically incompressible real fluid, the fluid of the traditional MPCD methods obeys the ideal-gas equation of state. This can be problematic because most fluid properties strongly depend on the fluid density. In a recent article, we proposed an extended MPCD algorithm and derived its non-ideal equation of state and an expression for the viscosity. In the present work, we demonstrate its accuracy and efficiency for the simulations of the flow fields of single squirmers and of the collective dynamics of squirmer rods. We use two exemplary squirmer-rod systems for which we compare the outcome of the extended MPCD method to the well-established MPCD version with an Andersen thermostat. First, we explicitly demonstrate the reduced compressibility of the MPCD fluid in a cluster of squirmer rods. Second, for shorter rods, we show the interesting result that in simulations with the extended MPCD method, dynamic swarms are more pronounced and have a higher polar order. Finally, we present a thorough study of the state diagram of squirmer rods moving in the center plane of a Hele-Shaw geometry. From a small to large aspect ratio and density, we observe a disordered state, dynamic swarms, a single swarm, and a jammed cluster, which we characterize accordingly.

Evaluation of the influence of aggregation morphology on thermal conductivity of nanofluid by a new MPCD-MD hybrid method

It is known the thermal conductivity can be elevated considerably by adding nanoparticles in base fluid. But the mechanisms remain unclear so far. One of the most important mechanisms to elevate the thermal conductivity is aggregation of nanoparticles. Molecular dynamics (MD) simulation can be normally employed to model the aggregation behavior in very small system due to the great computational workload. In present work, a new hybrid method of multi-particle collision dynamics and molecular dynamics (MPCD-MD) is proposed to evaluate the morphology of aggregation and thermal conductivity of Cu-H2O nanofluid for reducing the computational workload. Such a hybrid method is very competent for simulating the aggregation process and aggregation morphology of colloidal systems containing more nanoparticles, because the interactions between nanoparticles can be included in MD considering both van der Waals attraction and electrostatic repulsion. In the meanwhile, the hydrodynamic interactions of nanoparticles can be also included easily by the collision step of MPCD. Numerical simulations for various volume fractions and particle sizes at various temperatures are conducted by MPCD-MD, and the fractal dimension and thermal conductivity of Cu-H2O nanofluid are calculated. The numerical results indicate the nanofluid has greater thermal conductivity at lower fractal dimension at fixed volume fraction. The linear relationship between fractal dimension and thermal conductivity is more consistent with the published results in larger colloidal system. This is helpful for us to understand the influence of aggregation morphology of nanoparticles on the thermal conductivity of nanofluid.

Feasibility of multi-particle collision dynamics for rod-like particles and its application to a change in the orientational regime of a hematite particle suspension

We have verified that the method of multi-particle collision dynamics (MPCD) is able to activate a physically reasonable level of random motion in the medium of virtual fluid particles and activate the translational, ordinary rotational and spin rotational Brownian motion of the magnetic rod-like particles. MPCD was then applied to a quasi-2D system of rod-like hematite particles. The particle Brownian motion was found slightly over-activated, but this tendency decreased with smaller simulation time steps. The deviation from the theoretical value in the present results may be regarded to be acceptable as a first approximation since the Brownian motion was activated without the addition of any special technique. The applied magnetic field strength is found to play a significant role to enhance the order of the alignment of the raft-like clusters along the direction of the applied magnetic field. A similar orientational regime change along the applied magnetic field may be accomplished by an increase in the volumetric fraction of magnetic particles. We have therefore concluded that both an applied magnetic field and the particle volumetric fraction may be feasible parameters for inducing a regime change in the ordering of the orientation of rod-like hematite particles.

Multiparticle collision dynamics simulations of a squirmer in a nematic fluid

We study the dynamics of a squirmer in a nematic liquid crystal using the multiparticle collision dynamics (MPCD) method. A recently developed nematic MPCD method [Phys. Rev. E 99, 063319 (2019)] which employs a tensor order parameter to describe the spatial and temporal variations of the nematic order is used to simulate the suspending anisotropic fluid. Considering both nematodynamic effects (anisotropic viscosity and elasticity) and thermal fluctuations, in the present study, we couple the nematic MPCD algorithm with a molecular dynamics (MD) scheme for the squirmer. A unique feature of the proposed method is that the nematic order, the fluid, and the squirmer are all represented in a particle-based framework. To test the applicability of this nematic MPCD-MD method, we simulate the dynamics of a spherical squirmer with homeotropic surface anchoring conditions in a bulk domain. The importance of anisotropic viscosity and elasticity on the squirmer’s speed and orientation is studied for different values of self-propulsion strength and squirmer type (pusher, puller or neutral). In sharp contrast to Newtonian fluids, the speed of the squirmer in a nematic fluid depends on the squirmer type. Interestingly, the speed of a strong pusher is smaller in the nematic fluid than for the Newtonian case. The orientational dynamics of the squirmer in the nematic fluid also shows a non-trivial dependence on the squirmer type. Our results compare well with existing experimental and numerical data. The full particle-based framework could be easily extended to model the dynamics of multiple squirmers in anisotropic fluids.Graphic abstract

Multi-particle collision dynamics with a non-ideal equation of state. I.

The method of multi-particle collision dynamics (MPCD) and its different implementations are commonly used in the field of soft matter physics to simulate fluid flow at the micron scale. Typically, the coarse-grained fluid particles are described by the equation of state of an ideal gas, and the fluid is rather compressible. This is in contrast to conventional fluids, which are incompressible for velocities much below the speed of sound, and can cause inhomogeneities in density. We propose an algorithm for MPCD with a modified collision rule that results in a non-ideal equation of state and a significantly decreased compressibility. It allows simulations at less computational costs compared to conventional MPCD algorithms. We derive analytic expressions for the equation of state and the corresponding compressibility as well as shear viscosity. They show overall very good agreement with simulations, where we determine the pressure by simulating a quiet bulk fluid and the shear viscosity by simulating a linear shear flow and a Poiseuille flow.

Emergent collective dynamics of bottom-heavy squirmers under gravity

.We present the results of hydrodynamic simulations using the method of multi-particle collision dynamics for a system of squirmer microswimmers moving under the influence of gravity at low Reynolds numbers. In addition, the squirmers are bottom-heavy so that they experience a torque which aligns them along the vertical. The squirmers interact hydrodynamically by the flow fields of a stokeslet and rotlet, which are initiated by the acting gravitational force and torque, respectively, and by their own flow fields. By varying the ratio of swimming to bulk sedimentation velocity and the torque, we determine state diagrams for the emergent collective dynamics of neutral squirmers as well as strong pushers and pullers. For low swimming velocity and torque we observe conventional sedimentation, while the sedimentation profile becomes inverted when their values are increased. For neutral squirmers we discover convective rolls of circulating squirmers between both sedimentation states, which sit at the bottom of the system and are fed by plumes made of collectively sinking squirmers. At larger torques porous clusters occur that spawn single squirmers. The two latter states can also occur transiently starting from a uniform squirmer distribution and then disappear in the long-time limit. For strong pushers and pullers only weak plume formation is observed.Graphical abstract

Multiparticle collision dynamics for fluid interfaces with near-contact interactions.

We present an extension of the multiparticle collision dynamics method for flows with complex interfaces, including supramolecular near-contact interactions mimicking the effect of surfactants. The new method is demonstrated for the case of (i) short range repulsion of droplets in close contact, (ii) arrested phase separation, and (iii) different pattern formation during spinodal decomposition of binary mixtures.

Feasibility of the multi-particle collision dynamics method as a simulation technique for a magnetic particle suspension

ABSTRACTWe have elucidated the feasibility of the multi-particle collision dynamics (MPCD) method as a technique for the simulation of a magnetic particle suspension, by addressing the dependence of the translational and rotational Brownian motion of the magnetic particles on the parameters that characterise a MPCD simulation. A reasonable level of activation of the Brownian motion is indispensable for simulating the aggregate structures of the magnetic particles because their internal structure is strongly dependent on particle Brownian motion. In the present study, we have employed a diffuse reflection model for treating the interaction between the fluid and the magnetic particles. The diffuse reflection model gives rise to the tendency that the translational Brownian motion of the magnetic particles is more significantly activated than the rotational Brownian motion. If a scaling coefficient is introduced for modifying the interaction between the fluid and the magnetic particles, a more accurate solution may be obtained in regard to the aggregate structures of the magnetic particles. We may conclude that the MPCD method with the diffuse reflection model is a promising simulation technique for analysing the behaviour of magnetic particles in a suspension.

Multi-particle collision dynamics for a coarse-grained model of soft colloids.

The growing interest in the dynamical properties of colloidal suspensions, both in equilibrium and under an external drive such as shear or pressure flow, requires the development of accurate methods to correctly include hydrodynamic effects due to the suspension in a solvent. In the present work, we generalize Multiparticle Collision Dynamics (MPCD) to be able to deal with soft, polymeric colloids. Our methods build on the knowledge of the monomer density profile that can be obtained from monomer-resolved simulations without hydrodynamics or from theoretical arguments. We hereby propose two different approaches. The first one simply extends the MPCD method by including in the simulations effective monomers with a given density profile, thus neglecting monomer-monomer interactions. The second one considers the macromolecule as a single penetrable soft colloid (PSC), which is permeated by an inhomogeneous distribution of solvent particles. By defining an appropriate set of rules to control the collision events between the solvent and the soft colloid, both linear and angular momenta are exchanged. We apply these methods to the case of linear chains and star polymers for varying monomer lengths and arm number, respectively, and compare the results for the dynamical properties with those obtained within monomer-resolved simulations. We find that the effective monomer method works well for linear chains, while the PSC method provides very good results for stars. These methods pave the way to extend MPCD treatments to complex macromolecular objects such as microgels or dendrimers and to work with soft colloids at finite concentrations.

Multiparticle collision dynamics for tensorial nematodynamics.

Liquid crystals establish a nearly unique combination of thermodynamic, hydrodynamic, and topological behavior. This poses a challenge to their theoretical understanding and modeling. The arena where these effects come together is the mesoscopic (micron) scale. It is then important to develop models aimed at capturing this variety of dynamics. We have generalized the particle-based multiparticle collision dynamics (MPCD) method to model the dynamics of nematic liquid crystals. Following the Qian-Sheng theory [Phys. Rev. E 58, 7475 (1998)1063-651X10.1103/PhysRevE.58.7475] of nematics, the spatial and temporal variations of the nematic director field and order parameter are described by a tensor order parameter. The key idea is to assign tensorial degrees of freedom to each MPCD particle, whose mesoscopic average is the tensor order parameter. This nematic MPCD method includes backflow effect, velocity-orientation coupling, and thermal fluctuations. We validate the applicability of this method by testing (i) the nematic-isotropic phase transition, (ii) the flow alignment of the director in shear and Poiseuille flows, and (iii) the annihilation dynamics of a pair of line defects. We find excellent agreement with existing literature. We also investigate the flow field around a force dipole in a nematic liquid crystal, which represents the leading-order flow field around a force-free microswimmer. The anisotropy of the medium not only affects the magnitude of velocity field around the force dipole, but can also induce hydrodynamic torques depending on the orientation of dipole axis relative to director field. A force dipole experiences a hydrodynamic torque when the dipole axis is tilted with respect to the far-field director. The direction of hydrodynamic torque is such that the pusher- (or puller-) type force dipole tends to orient along (or perpendicular to) the director field. Our nematic MPCD method can have far-reaching implications not only in modeling of nematic flows, but also to study the motion of colloids and microswimmers immersed in an anisotropic medium.

Hydrodynamic interactions between solutes in multiparticle collision dynamics

Multiparticle collision dynamics (MPCD) enables to simulate fluid dynamics including both hydrodynamics and thermal fluctuations. Its main use concerns complex fluids, where the solvent interacts with concentrated solutes, may they be colloidal particles, polymers or electrolytes. A key difficulty concerns the way one couples the fluid to the solute particles, without losing the key advantages of the MPCD method in term of computational efficiency. In this paper, we investigate the dynamical properties of solutes that are coupled to the fluid within the collision step, {\em i.e.} when local momentum exchange between fluid particles occurs. We quantify how the volume where momentum exchange is performed (the size of the collision cells) constrains the hydrodynamic size of the solute. Moreover, we show that this volume should be taken smaller than the structural size of the solutes. Within these constraints, we find that the hydrodynamic properties of a 1-1 electrolyte solution are similar to the behaviour predicted by the Fuoss-Onsager theory of electrolyte dynamics, and we quantify the limitations of the theory for 2-1 and 2-2 electrolytes. However, it is also clear that mapping the diffusion time scale to that of a real system cannot be done quantitatively with this methodology.

Self-organization in a bimotility mixture of model microswimmers.

We study the cooperation and segregation dynamics in a bimotility mixture of microorganisms which swim at low Reynolds numbers via periodic deformations along the body. We employ a multiparticle collision dynamics method to simulate a two component mixture of artificial swimmers, termed as Taylor lines, which differ from each other only in the propulsion speed. The analysis reveals that a contribution of slower swimmers towards clustering, on average, is much larger as compared to the faster ones. We notice distinctive self-organizing dynamics, depending on the percentage difference in the speed of the two kinds. If this difference is large, the faster ones fragment the clusters of the slower ones in order to reach the boundary and form segregated clusters. Contrarily, when it is small, both kinds mix together at first, the faster ones usually leading the cluster and then gradually the slower ones slide out thereby also leading to segregation.

Gravity-induced dynamics of a squirmer microswimmer in wall proximity

We perform hydrodynamic simulations using the method of multi-particle collision dynamics and a theoretical analysis to study a single squirmer microswimmer at high Péclet number, which moves in a low Reynolds number fluid and under gravity. The relevant parameters are the ratio α of swimming to bulk sedimentation velocity and the squirmer type β. The combination of self-propulsion, gravitational force, hydrodynamic interactions with the wall, and thermal noise leads to a surprisingly diverse behavior. At we observe cruising states, while for the squirmer resides close to the bottom wall with the motional state determined by stable fixed points in height and orientation. They strongly depend on the squirmer type β. While neutral squirmers permanently float above the wall with upright orientation, pullers float for α larger than a threshold value and are pinned to the wall below . In contrast, pushers slide along the wall at lower heights, from which thermal orientational fluctuations drive them into a recurrent floating state with upright orientation, where they remain on the timescale of orientational persistence.