Multiparticle Collision Dynamics Research Articles

Hydrodynamic correlations in isotropic fluids and liquid crystals simulated by multi-particle collision dynamics

Multi-particle collision dynamics is an appealing numerical technique aiming at simulating fluids at the mesoscopic scale. It considers molecular details in a coarse-grained fashion and reproduces hydrodynamic phenomena. Here, the implementation of multi-particle collision dynamics for isotropic fluids is analysed under the so-called Andersen-thermostatted scheme, a particular algorithm for systems in the canonical ensemble. This method gives rise to hydrodynamic fluctuations that spontaneously relax towards equilibrium. This relaxation process can be described by a linearized theory and used to calculate transport coefficients of the system. The extension of the algorithm for nematic liquid crystals is also considered. It is shown that thermal fluctuations in the average molecular orientation can be described by an extended linearized scheme. Flow fluctuations induce orientation fluctuations. However, orientational changes produce observable effects on velocity correlation functions only when simulation parameters exceed their values from those used in previous applications of the method. Otherwise, the flow can be considered to be independent of the orientation field.

Modelling the effect of particle inertia on the orientation kinematics of fibres and spheroids immersed in a simple shear flow

Simulations of flows containing non-spherical particles (fibres or ellipsoids) rely on the knowledge of the equation governing the particle motion in the flow. Most models used nowadays are based on the pioneering work of Jeffery (1922), who obtained an equation for the motion of an ellipsoidal particle immersed in a Newtonian fluid, despite the fact that this model relies on strong assumptions: negligible inertia, unconfined flow, dilute regime, flow unperturbed by the presence of the suspended particle, etc. In this work, we propose a dumbbell-based model aimed to describe the motion of an inertial fibre or ellipsoid suspended in a Newtonian fluid. We then use this model to study the orientation kinematics of such particle in a linear shear flow and compare it to the inertialess case. In the case of fibres, we observe the appearance of periodic orbits (whereas inertialess fibres just align in the flow field). For spheroids, our model predicts an orbit drift towards the flow-gradient plane, either gradually (slight inertia) or by first rotating around a moving oblique axis (heavy particles). Multi-Particle Collision Dynamics (MPCD) simulations were carried out to assess the model predictions in the case of inertial fibres and revealed similar behaviours.

State diagram for wall adhesion of red blood cells in shear flow: from crawling to flipping.

Red blood cells in shear flow show a variety of different shapes due to the complex interplay between hydrodynamics and membrane elasticity. Malaria-infected red blood cells become generally adhesive and less deformable. Adhesion to a substrate leads to a reduction in shape variability and to a flipping motion of the non-spherical shapes during the mid-stage of infection. Here, we present a complete state diagram for wall adhesion of red blood cells in shear flow obtained by simulations, using a particle-based mesoscale hydrodynamics approach, multiparticle collision dynamics. We find that cell flipping at a substrate is replaced by crawling beyond a critical shear rate, which increases with both membrane stiffness and viscosity contrast between the cytosol and suspending medium. This change in cell dynamics resembles the transition between tumbling and tank-treading for red blood cells in free shear flow. In the context of malaria infections, the flipping-crawling transition would strongly increase the adhesive interactions with the vascular endothelium, but might be suppressed by the combined effect of increased elasticity and viscosity contrast.

Stochastic simulations of the Schnakenberg model with spatial inhomogeneities using reactive multiparticle collision dynamics

A numerically efficient globally averaged number density approach is used to simulate a reaction-diffusion system using a particle-based stochastic simulation algorithm called reactive multiparticle collision (RMPC) dynamics. Constant diffusivity of the particles is achieved through a time-varying rotation angle (also called collision angle). Variation in the diffusion coefficient between two different chemical species is achieved in one of two ways: (ⅰ) using a different kBT/m value for one species compared to the other, or (ⅱ) using the same kBT/m value for both species, but using a different probability to free-stream for one species compared to another. For smaller diffusivities and larger spatial inhomogeneities, bath particles were necessary for the model to agree with the PDE solution. The latter approach was further used without a bath, and shown to be capable of producing Turing patterns after long simulation times. The significance of our work is that RMPC can serve as a feasible simulation tool for both short and long-term simulations, can handle spatial inhomogeneities, can model a fairly large range of diffusivities in a reaction-diffusion scenario, and is capable of producing Turing patterns. An advantage of this method includes more detailed system information in feasible simulation times.

Influence of polymer flexibility on nanoparticle dynamics in semidilute solutions.

The hierarchical structure and dynamics of polymer solutions control the transport of nanoparticles (NPs) through them. Here, we perform multi-particle collision dynamics simulations of solutions of semiflexible polymer chains with tunable persistence length lp to investigate the effect of chain stiffness on NP transport. The NPs exhibit two distinct dynamical regimes - subdiffusion on short time scales and diffusion on long time scales. The long-time NP diffusivities are compared with predictions from the Stokes-Einstein relation (SER), mode-coupling theory (MCT), and a recent polymer coupling theory (PCT). Increasing deviations from the SER as the polymer chains become more rigid (i.e. as lp increases) indicate that the NP motions become decoupled from the bulk viscosity of the polymer solution. Likewise, polymer stiffness leads to deviations from PCT, which was developed for fully flexible chains. Independent of lp, however, the long-time diffusion behavior is well-described by MCT, particularly at high polymer concentration. We also observed that the short-time subdiffusive dynamics are strongly dependent on polymer flexibility. As lp is increased, the NP dynamics become more subdiffusive and decouple from the dynamics of the polymer chain center-of-mass. We posit that these effects are due to differences in the segmental mobility of the semiflexible chains.

Finite-time fluctuation theorem for diffusion-influenced surface reactions on spherical and Janus catalytic particles

A finite-time fluctuation theorem for the diffusion-influenced surface reaction is investigated for spherical and Janus catalytic particles. The finite-time rates and thermodynamic force are analytically calculated by solving diffusion equations with the special boundary conditions of the finite-time fluctuation theorem. Theory is compared with numerical simulations carried out with two different methods: a random walk algorithm and multiparticle collision dynamics.

Weak Shape Anisotropy Leads to a Nonmonotonic Contribution to Crowding, Impacting Protein Dynamics under Physiologically Relevant Conditions.

The effect of a nonspherical particle shape on the dynamics in crowded solutions presents a significant challenge for a comprehensive understanding of interaction and structural relaxation in biological and soft matter. We report that small deviations from a spherical shape induce a nonmonotonic contribution to the crowding effect on the short-time cage diffusion compared with spherical systems, using molecular dynamics simulations with mesoscale hydrodynamics of a multiparticle collision dynamics fluid in semidilute systems with volume fractions smaller than 0.35. We show that the nonmonotonic effect due to anisotropy is caused by the combination of a reduced relative mobility over the entire concentration range and a looser and less homogeneous cage packing of nonspherical particles. Our finding stresses that nonsphericity induces new complexity, which cannot be accounted for in effective sphere models, and is of great interest in applications such as formulations as well as for the fundamental understanding of soft matter in general and crowding effects in living cells in particular.

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.

Field effect in the viscosity of magnetic colloids studied by multi-particle collision dynamics

Abstract Colloidal solutions of magnetic nanoparticles are usually employed when the fluidity and magnetic properties are required at the same time, either in technical or biomedical applications. However, when the magnetic size of the nanoparticles is large enough (>12–15 nm) the colloid may form an equilibrium structure with or without the external magnetic field, which can significantly influence its rheology. Using multi-particle collision dynamics we study the internal structure and viscosity of the magnetic colloids at varying magnitudes of the externally applied field. We show a generalized structural behavior across all studied regimes and an appreciable increase of flow resistance with magnetic field.

Flow Behavior of Chain and Star Polymers and Their Mixtures.

Star-shaped polymers show a continuous change of properties from flexible linear chains to soft colloids, as the number of arms is increased. To investigate the effect of macromolecular architecture on the flow properties, we employ computer simulations of single chain and star polymers as well as of their mixtures under Poiseuille flow. Hydrodynamic interactions are incorporated through the multi-particle collision dynamics (MPCD) technique, while a bead-spring model is used to describe the polymers. For the ultradilute systems at rest, the polymers are distributed uniformly in the slit channel, with a weak dependence on their number of arms. Once flow is applied, however, we find that the stars migrate much more strongly towards the channel center as the number of arms is increased. In the star-chain mixtures, we find a flow-induced separation between stars and chains, with the stars located in the channel center and the chains closer to the walls. In order to identify the origin of this flow-induced partitioning, we conduct additional simulations without hydrodynamic interactions, and find that the observed cross-stream migration originates from a combination of wall-induced hydrodynamic lift forces and viscoelastic effects. The results from our study give valuable insights for designing microfluidic devices for separating polymers based on their architecture.

Reactive multi-particle collision dynamics with reactive boundary conditions

In the present study, an off-lattice particle-based method called the reactive multi-particle collision (RMPC) dynamics is extended to model reaction-diffusion systems with reactive boundary conditions in which the a priori diffusion coefficient of the particles needs to be maintained throughout the simulation. To this end, the authors have made use of the so-called bath particles whose purpose is only to ensure proper diffusion of the main particles in the system. In order to model partial adsorption by a reactive boundary in the RMPC, the probability of a particle being adsorbed, once it hits the boundary, is calculated by drawing an analogy between the RMPC and Brownian Dynamics. The main advantages of the RMPC compared to other molecular based methods are less computational cost as well as conservation of mass, energy and momentum in the collision and free streaming steps. The proposed approach is tested on three reaction-diffusion systems and very good agreement with the solutions to their corresponding partial differential equations is observed.

Simulating squirmers with multiparticle collision dynamics

.Multiparticle collision dynamics is a modern coarse-grained simulation technique to treat the hydrodynamics of Newtonian fluids by solving the Navier-Stokes equations. Naturally, it also includes thermal noise. Initially it has been applied extensively to spherical colloids or bead-spring polymers immersed in a fluid. Here, we review and discuss the use of multiparticle collision dynamics for studying the motion of spherical model microswimmers called squirmers moving in viscous fluids.Graphical abstract

Efficient mesoscale hydrodynamics: Multiparticle collision dynamics with massively parallel GPU acceleration

We present an efficient open-source implementation of the multiparticle collision dynamics (MPCD) algorithm that scales to run on hundreds of graphics processing units (GPUs). We especially focus on optimizations for modern GPU architectures and communication patterns between multiple GPUs. We show that a mixed-precision computing model can improve performance compared to a fully double-precision model while still providing good numerical accuracy. We report weak and strong scaling benchmarks of a reference MPCD solvent and a benchmark of a polymer solution with research-relevant interactions and system size. Our MPCD software enables simulations of mesoscale hydrodynamics at length and time scales that would be otherwise challenging or impossible to access.

Steady state sedimentation of ultrasoft colloids.

The structural and dynamical properties of ultra-soft colloids-star polymers-exposed to a uniform external force field are analyzed by applying the multiparticle collision dynamics technique, a hybrid coarse-grain mesoscale simulation approach, which captures thermal fluctuations and long-range hydrodynamic interactions. In the weak-field limit, the structure of the star polymer is nearly unchanged; however, in an intermediate regime, the radius of gyration decreases, in particular transverse to the sedimentation direction. In the limit of a strong field, the radius of gyration increases with field strength. Correspondingly, the sedimentation coefficient increases with increasing field strength, passes through a maximum, and decreases again at high field strengths. The maximum value depends on the functionality of the star polymer. High field strengths lead to symmetry breaking with trailing, strongly stretched polymer arms and a compact star-polymer body. In the weak-field-linear response regime, the sedimentation coefficient follows the scaling relation of a star polymer in terms of functionality and arm length.

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.

Locomotion of a flexible one-hinge swimmer in Stokes regime

E M Purcell showed that a body has to perform non-reciprocal motion in order to propel itself in a highly viscous environment. The swimmer with one degree of freedom is bound to do reciprocal motion, whereby the center of mass of the swimmer will not be able to propel itself due to the Scallop theorem. In the present study, we are proposing a new artificial swimmer called the one-hinge swimmer. Here we will show that flexibility plays a crucial role in the breakdown of Scallop theorem in the case of one-hinge swimmer or two-dimensional scallop at low Reynolds number. To model a one-hinge artificial swimmer, we use bead spring model for two arms joined by a hinge with bending potential for the arms in order to make them semi-flexible. The fluid is simulated using a particle based mesoscopic simulation method called the multi-particle collision dynamics with Anderson thermostat. Here, we show that when our swimmer has rigid arms, the center of mass of the swimmer is not able to propel itself as expected from the Scallop theorem. When we introduce flexibility in the arms, the time reversal symmetry breaks in the case of the one-hinged swimmer without the presence of a head contrary to the one-armed super paramagnetic swimmer which required a passive head in order to swim. The reduced velocity of the swimmer is studied using a range of parameters like flexibility, beating frequency and the amplitude of the beat, where we obtain similar scaling as that of the one-armed swimmer. We also calculate the dimensionless Sperm number for the swimmer and we get the maximum velocity when the Sperm number is around ∼1.8

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.

Pair Interaction of Catalytical Sphere Dimers in Chemically Active Media.

We study the pair dynamics of two self-propelled sphere dimers in the chemically active medium in which a cubic autocatalytic chemical reaction takes place. Concentration gradient around the dimer, created by reactions occurring on the catalytic sphere surface and responsible for the self-propulsion, is greatly influenced by the chemical activities of the environment. Consequently, the pair dynamics of two dimers mediated by the concentration field are affected. In the particle-based mesoscopic simulation, we combine molecular dynamics (MD) for potential interactions and reactive multiparticle collision dynamics (RMPC) for solvent flow and bulk reactions. Our results indicate three different configurations between a pair of dimers after the collision, i.e., two possible scenarios of bound dimer pairs and one unbound dimer pair. A phase diagram is sketched as a function of the rate coefficients of the environment reactions. Since the pair interactions are the basic elements of larger scale systems, we believe the results may shed light on the understanding of the collective dynamics.

Role of non-equilibrium conformations on driven polymer translocation.

One of the major theoretical methods in understanding polymer translocation through a nanopore is the Fokker-Planck formalism based on the assumption of quasi-equilibrium of polymer conformations. The criterion for applicability of the quasi-equilibrium approximation for polymer translocation is that the average translocation time per Kuhn segment, ⟨τ⟩/NK, is longer than the relaxation time τ0 of the polymer. Toward an understanding of conditions that would satisfy this criterion, we have performed coarse-grained three dimensional Langevin dynamics and multi-particle collision dynamics simulations. We have studied the role of initial conformations of a polyelectrolyte chain (which were artificially generated with a flow field) on the kinetics of its translocation across a nanopore under the action of an externally applied transmembrane voltage V (in the absence of the initial flow field). Stretched (out-of-equilibrium) polyelectrolyte chain conformations are deliberately and systematically generated and used as initial conformations in translocation simulations. Independent simulations are performed to study the relaxation behavior of these stretched chains, and a comparison is made between the relaxation time scale and the mean translocation time (⟨τ⟩). For such artificially stretched initial states, ⟨τ⟩/NK < τ0, demonstrating the inapplicability of the quasi-equilibrium approximation. Nevertheless, we observe a scaling of ⟨τ⟩ ∼ 1/V over the entire range of chain stretching studied, in agreement with the predictions of the Fokker-Planck model. On the other hand, for realistic situations where the initial artificially imposed flow field is absent, a comparison of experimental data reported in the literature with the theory of polyelectrolyte dynamics reveals that the Zimm relaxation time (τZimm) is shorter than the mean translocation time for several polymers including single stranded DNA (ssDNA), double stranded DNA (dsDNA), and synthetic polymers. Even when these data are rescaled assuming a constant effective velocity of translocation, it is found that for flexible (ssDNA and synthetic) polymers with NK Kuhn segments, the condition ⟨τ⟩/NK < τZimm is satisfied. We predict that for flexible polymers such as ssDNA, a crossover from quasi-equilibrium to non-equilibrium behavior would occur at NK ∼ O(1000).

Thermophoretic forces on a mesoscopic scale.

We use a mesoscale-molecular simulation technique known as Multi-Particle Collision Dynamics (MPC) to study the forces acting on a stationary colloid inside a temperature gradient. We compare our measurements of the thermophoretic force to a theoretical prediction based on Onsager's reciprocal relations, assuming that the temperature gradient is constant across the colloid. We find a good agreement between our measurements and theoretical predictions over a wide range of system parameters, even when the condition of uniform gradients is not strictly fulfilled. Our measurements further suggest that the magnitude of the thermophoretic force depends on the hydrodynamic boundary condition at the colloidal surface, thus highlighting the hydrodynamic character of colloidal thermophoresis. We also investigate how fluid advection disturbs the interfacial layer around the colloid and introduce a dimensionless number to quantify the validity of local thermodynamic equilibrium.