Dynamic correlations in stochastic rotation dynamics

Morphology-Tailored Dynamic State Transition in Active-Passive Colloidal Assemblies

Mixtures of active self-propelled and passive colloidal particles promise rich assembly and dynamic states that are beyond reach via equilibrium routes. Yet, controllable transition between different dynamic states remains rare. Here, we reveal a plethora of dynamic behaviors emerging in assemblies of chemically propelled snowman-like active colloids and passive spherical particles as the particle shape, size, and composition are tuned. For example, assembles of one or more active colloids with one passive particle exhibit distinct translating or orbiting states while those composed of one active colloid with 2 passive particles display persistent "8"-like cyclic motion or hopping between circling states around one passive particle in the plane and around the waist of 2 passive ones out of the plane, controlled by the shape of the active colloid and the size of the passive particles, respectively. These morphology-tailored dynamic transitions are in excellent agreement with state diagrams predicted by mesoscale dynamics simulations. Our work discloses new dynamic states and corresponding transition strategies, which promise new applications of active systems such as micromachines with functions that are otherwise impossible.

Clustering of self-thermophilic asymmetric dimers: the relevance of hydrodynamics

Self-thermophilic dimers are characterized by a net phoretic attraction which, in combination with hydrodynamic interactions, results in the formation of crystalline-like aggregates. To distinguish the effect of the different contributions is frequently an important challenge. We present a simulation investigation done in parallel in the presence and the absence of hydrodynamic interactions for the case of asymmetric self-thermophoretic dimers. In the absence of hydrodynamics, the clusters have the standard heads-in configurations. In contrast, in the presence of hydrodynamics, clusters with heads-in conformation are being formed, in which dimers with their propulsion velocity pointing out of the cluster are assembled and stabilized by strong hydrodynamic osmotic flows. Significant variation in the material properties is to be expected from such differences in the collective behavior, whose understanding and control is of great relevance for the development of new synthetic active materials.

Hydrodynamic effects on the liquid-hexatic transition of active colloids

We study numerically the role of hydrodynamics in the liquid-hexatic transition of active colloids at intermediate activity, where motility induced phase separation (MIPS) does not occur. We show that in the case of active Brownian particles (ABP), the critical density of the transition decreases upon increasing the particle's mass, enhancing ordering, while self-propulsion has the opposite effect in the activity regime considered. Active hydrodynamic particles (AHP), instead, undergo the liquid-hexatic transition at higher values of packing fraction [Formula: see text] than the corresponding ABP, suggesting that hydrodynamics have the net effect of disordering the system. At increasing densities, close to the hexatic-liquid transition, we found in the case of AHP the appearance of self-sustained organized motion with clusters of particles moving coherently.

Self-phoretic Brownian dynamics simulations

A realistic and effective model to simulate phoretic Brownian dynamics swimmers based on the general form of the thermophoretic force is here presented. The collective behavior of self-phoretic dimers is investigated with this model and compared with two simpler versions, allowing the understanding of the subtle interplay of steric interactions, propulsion, and phoretic effects. The phoretic Brownian dynamics method has control parameters which can be tuned to closely map the properties of experiments or simulations with explicit solvent, in particular those performed with multiparticle collision dynamics. The combination of the phoretic Brownian method and multiparticle collision dynamics is a powerful tool to precisely identify the importance of hydrodynamic interactions in systems of self-phoretic swimmers.

Real-time temperature measurement in stochastic rotation dynamics

Many physical and chemical processes involve energy change with rates that depend sensitively on local temperature. Important examples include heterogeneously catalyzed reactions and activated desorption. Because of the multiscale nature of such systems, it is desirable to connect the macroscopic world of continuous hydrodynamic and temperature fields to mesoscopic particle-based simulations with discrete particle events. In this work we show how to achieve real-time measurement of the local temperature in stochastic rotation dynamics (SRD), a mesoscale method particularly well suited for problems involving hydrodynamic flows with thermal fluctuations. We employ ensemble averaging to achieve local temperature measurement in dynamically changing environments. After validation by heat diffusion between two isothermal plates, heating of walls by a hot strip, and by temperature programed desorption, we apply the method to a case of a model flow reactor with temperature-sensitive heterogeneously catalyzed reactions on solid spherical catalysts. In this model, adsorption, chemical reactions, and desorption are explicitly tracked on the catalyst surface. This work opens the door for future projects where SRD is used to couple hydrodynamic flows and thermal fluctuations to solids with complex temperature-dependent surface mechanisms.

Hydrodynamics of immiscible binary fluids with viscosity contrast: a multiparticle collision dynamics approach

We present a multiparticle collision dynamics (MPC) implementation of layered immiscible fluids A and B of different shear viscosities separated by planar interfaces. The simulated flow profile for imposed steady shear motion and the time-dependent shear stress functions are in excellent agreement with our continuum hydrodynamics results for the composite fluid. The wave-vector dependent transverse velocity auto-correlation functions (TVAF) in the bulk-fluid regions of the layers decay exponentially, and agree with those of single-phase isotropic MPC fluids. In addition, we determine the hydrodynamic mobilities of an embedded colloidal sphere moving steadily parallel or transverse to a fluid-fluid interface, as functions of the distance from the interface. The obtained mobilities are in good agreement with hydrodynamic force multipoles calculations, for a no-slip sphere moving under creeping flow conditions near a clean, ideally flat interface. The proposed MPC fluid-layer model can be straightforwardly implemented, and it is computationally very efficient. Yet, owing to the spatial discretization inherent to the MPC method, the model can not reproduce all hydrodynamic features of an ideally flat interface between immiscible fluids.

Collective behavior of thermophoretic dimeric active colloids in three-dimensional bulk

Colloids driven by phoresis constitute one of the main avenues for the design of synthetic microswimmers. For these swimmers, the specific form of the phoretic and hydrodynamic interactions dramatically influences their dynamics. Explicit solvent simulations allow the investigation of the different behaviors of dimeric Janus active colloids. The phoretic character is modified from thermophilic to thermophobic, and this, together with the relative size of the beads, strongly influences the resulting solvent velocity fields. Hydrodynamic flows can change from puller-type to pusher-type, although the actual flows significantly differ from these standard flows. Such hydrodynamic interactions combined with phoretic interactions between dimers result in several interesting phenomena in three-dimensional bulk conditions. Thermophilic dimeric swimmers are attracted to each other and form large and stable aggregates. Repulsive phoretic interactions among thermophobic dimeric swimmers hinder such clustering and lead, together with long- and short-ranged attractive hydrodynamic interactions, to short-lived, aligned swarming structures.

Large Fluctuations in Nonideal Coarse-Grained Systems

Using the recently introduced molecular dynamics lattice gas approach, we test fluctuations of coarse-grained quantities. We show that as soon as the system can no longer be considered an ideal gas fluctuations fail to diminish upon coarse graining as is usually expected. These results suggest that current approaches to simulating fluctuating hydrodynamics may have to be augmented to achieve quantitative results for systems with a nonideal equation of state. The molecular dynamics lattice gas method gives a guidance to the exact nature of the fluctuation in such systems.

Hydrodynamic correlations of viscoelastic fluids by multiparticle collision dynamics simulations

The emergent fluctuating hydrodynamics of a viscoelastic fluid modeled by the multiparticle collision dynamics (MPC) approach is studied. The fluid is composed of flexible, Gaussian phantom polymers that interact by local momentum-conserving stochastic MPCs. For comparison, the analytical solution of the linearized Navier-Stokes equation is calculated, where viscoelasticity is taken into account by a time-dependent shear relaxation modulus. The fluid properties are characterized by the transverse velocity autocorrelation function in Fourier space as well as in real space. Various polymer lengths are considered-from dumbbells to (near-)continuous polymers. Viscoelasticity affects the fluid properties and leads to strong correlations, which overall decay exponentially in Fourier space. In real space, the center-of-mass velocity autocorrelation function of individual polymers exhibits a long-time tail, independent of the polymer length, which decays as t^-3/2, similar to a Newtonian fluid, in the asymptotic limit t → ∞. Moreover, for long polymers, an additional power-law decay appears at time scales shorter than the longest polymer relaxation time with the same time dependence, but negative correlations, and the polymer length dependence L^-1/2. Good agreement is found between the analytical and simulation results.

Phototaxis of active colloids by self-thermophoresis

Phototaxis usually refers to the ability of a motile micoorganism to move directionally within a light gradient, which is important for microorganisms to gain energy or avoid damage. Here, we show that an active Janus particle driven by self-thermophoresis from light heating is able to exhibit significant phototactic motion by means of mesoscale dynamics simulation. Depending on the particle-fluid interactions, the active particle can move along or against the light gradient, corresponding to positive or negative phototaxis, respectively. We find that the phototaxis of the active colloid is determined by various mechanisms, including alignment (polarization) of the particle to the light gradient, orientation-dependent motility and spatially inhomogeneous motility. Our results shed light on the phototactic behavior of artificial active colloids and open up a new possibility to design photo-responsive micromachines.

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.

Guidance and Self-Sorting of Active Swimmers: 3D Periodic Arrays Increase Persistence Length of Human Sperm Selecting for the Fittest

Male infertility is a reproductive disease, and existing clinical solutions for this condition often involve long and cumbersome sperm sorting methods, including preprocessing and centrifugation-based steps. These methods also fall short when sorting for sperm free of reactive oxygen species, DNA damage, and epigenetic aberrations. Although several microfluidic platforms exist, they suffer from structural complexities, i.e., pumps or chemoattractants, setting insurmountable barriers to clinical adoption. Inspired by the natural filter-like capabilities of the female reproductive tract for sperm selection, a model-driven design, featuring pillar arrays that efficiently and noninvasively isolate highly motile and morphologically normal sperm, with lower epigenetic global methylation, from raw semen, is presented. The Simple Periodic ARray for Trapping And isolatioN (SPARTAN) created here modulates the directional persistence of sperm, increasing the spatial separation between progressive and nonprogressive motile sperm populations within an unprecedentedly short 10 min assay time. With over 99% motility of sorted sperm, a 5-fold improvement in morphology, 3-fold increase in nuclear maturity, and 2-4-fold enhancement in DNA integrity, SPARTAN offers to standardize sperm selection while eliminating operator-to-operator variations, centrifugation, and flow. SPARTAN can also be applied in other areas, including conservation ecology, breeding of farm animals, and design of flagellar microrobots for diagnostics.

Spatial correlations of hydrodynamic fluctuations in simple fluids under shear flow: A mesoscale simulation study

Hydrodynamic fluctuations in simple fluids under shear flow are demonstrated to be spatially correlated, in contrast to the fluctuations at equilibrium, using mesoscopic hydrodynamic simulations. The simulation results for the equal-time hydrodynamic correlations in a multiparticle collision dynamics (MPC) fluid in shear flow are compared with the explicit expressions obtained from fluctuating hydrodynamics calculations. For large wave vectors k, the nonequilibrium contributions to transverse and longitudinal velocity correlations decay as k^{-4} for wave vectors along the flow direction and as k^{-2} for the off-flow directions. For small wave vectors, a crossover to a slower decay occurs, indicating long-range correlations in real space. The coupling between the transverse velocity components, which vanishes at equilibrium, also exhibits a k^{-2} dependence on the wave vector. In addition, we observe a quadratic dependency on the shear rate of the nonequilibrium contribution to pressure.

Anisotropic thermophoresis

Colloidal migration in a temperature gradient is referred to as thermophoresis. In contrast to particles with a spherical shape, we show that elongated colloids may have a thermophoretic response that varies with the colloid orientation. Remarkably, this can translate into a non-vanishing thermophoretic force in the direction perpendicular to the temperature gradient. Opposite to the friction force, the thermophoretic force of a rod oriented with the temperature gradient can be larger or smaller than when oriented perpendicular to it. The precise anisotropic thermophoretic behavior clearly depends on the colloidal rod aspect ratio, and also on its surface details, which provides an interesting tunability to the devices constructed based on this principle. By means of mesoscale hydrodynamic simulations, we characterize this effect for different types of rod-like colloids.

Particle-based modeling of heterogeneous chemical kinetics including mass transfer

Connecting the macroscopic world of continuous fields to the microscopic world of discrete molecular events is important for understanding several phenomena occurring at physical boundaries of systems. An important example is heterogeneous catalysis, where reactions take place at active surfaces, but the effective reaction rates are determined by transport limitations in the bulk fluid and reaction limitations on the catalyst surface. In this work we study the macro-micro connection in a model heterogeneous catalytic reactor by means of stochastic rotation dynamics. The model is able to resolve the convective and diffusive interplay between participating species, while including adsorption, desorption, and reaction processes on the catalytic surface. Here we apply the simulation methodology to a simple straight microchannel with a catalytic strip. Dimensionless Damkohler numbers are used to comment on the spatial concentration profiles of reactants and products near the catalyst strip and in the bulk. We end the discussion with an outlook on more complicated geometries and increasingly complex reactions.

Mesoscale simulation of phoretically osmotic boundary conditions

Boundary walls can drive the tangential flow of fluids by phoretic osmosis when exposed to a gradient field, including chemical, thermal or electric potential gradient. At the microscale, such boundary driving mechanisms become quite pronounced. Here, we propose a mesoscale strategy to simulate the phoretically osmotic boundaries, in which the microscopic fluid-wall interactions are coarse-grained into the bounce-back or specular reflection, and the phoretically osmotic force is generated by selectively reversing the tangential velocity of specific fluid particles near the boundary wall. With this scheme, the phoretically osmotic boundary can be realized with a minimal modification to the widely used mesoscopic no-slip/slip hydrodynamic boundary condition. Its implementation is quite efficient and the resulting phoretically osmotic flow is flexibly tunable. Its validity is verified by performing extensive mesoscale simulations for both the diffusioosmotic and thermoosmotic boundaries. In particular, we use the proposed scheme to investigate fluid transport driven by the phoretic osmosis in microfluidic systems and the effects of the diffusioosmosis on the dynamics of active catalytic colloidal particles. Our work thus offers new possibilities to study the phoretically osmotic effect in active complex fluids and microfluidic systems by simulation, where the gradient fields are ubiquitous.

Thermoosmotic microfluidics

Microchannels with asymmetrically ratcheted walls are here shown to behave as effective and versatile microfluidic pumps if locally heated. When the boundary walls have different temperatures, the confined liquid experiences a temperature gradient along the sawtooth edges, which can induce a thermoosmotic flow. A mesoscale molecular simulation approach is here employed to investigate the flows which are contrasted using an analytical approach. Microchannels can be composed by one or two ratcheted walls which can be straight or cylindrical. Varying the channel geometry can not only change the overall fluid flux, but also vary the flow patters from shear to capillary type, or even to extensional type flows. This scheme does not require multiphase fluids or any movable channel parts, although they are possible to be implemented. The proposed principle is then very versatile to locally manipulate complex fluids, and a promising tool to recover waste heat, to facilitate cooling of microchips, and to manufacture portable lab-on-a-chip devices.

Modeling a spheroidal microswimmer and cooperative swimming in a narrow slit

We propose a hydrodynamic model for a spheroidal microswimmer with two tangential surface velocity modes. This model is analytically solvable and reduces to Lighthill's and Blake's spherical squirmer model in the limit of equal major and minor semi-axes. Furthermore, we present an implementation of such a spheroidal squirmer by means of particle-based mesoscale hydrodynamics simulations using the multiparticle collision dynamics approach. We investigate its properties as well as the scattering of two spheroidal squirmers in a slit geometry. Thereby we find a stable fixed point, where two pullers swim cooperatively forming a wedge-like conformation with a small constant angle.

Catalytic microrotor driven by geometrical asymmetry

An asymmetric gear with homogeneous surface properties is, here, presented as a prototype to fabricate catalytic microrotors. The driving torque arises from the diffusiophoretic effect induced by the concentration gradients generated by catalytic chemical reactions at the gear surface. This torque produces a spontaneous and unidirectional rotation of the asymmetric gear. By means of mesoscopic simulations, we prove and characterize this scenario. The gear rotational velocity is determined by the gear-solvent interactions, the gear geometry, the solvent viscosity, and the catalytic reaction ratio. Our work presents a simple way to design self-propelled microrotors, alternative to existing catalytic bi-component, or thermophoretic ones.

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.

Effect of hydrodynamic correlations on the dynamics of polymers in dilute solution

We analyze the effect of time-dependent hydrodynamic interactions on the dynamics of flexible polymers in dilute solution. In analytical calculations, the fluctuating hydrodynamics approach is adopted to describe the fluid, and a Gaussian model to represented the polymer. Simulations are performed exploiting the multiparticle collision dynamics approach, a mesoscale hydrodynamic simulation technique, to explicitly describe the fluid. Polymer center-of-mass velocity correlation functions are calculated for various polymer lengths. Similarly, segment mean square displacements are discussed and polymer diffusion coefficients are determined. Particular attention is paid to the influence of sound propagation on the various properties. The simulations reveal a strong effect of hydrodynamic interactions. Specifically, the time dependence of the center-of-mass velocity correlation functions is determined by polymer properties over a length-dependent time window, but are asymptotically solely governed by fluid correlations, with a long-time tail decaying as t(-3/2). The correlation functions are heavily influenced by sound modes for short polymers, an effect which gradually disappears with increasing polymer length. We find excellent agreement between analytical and simulation results. This allows us to provide a theory-based asymptotic value for the polymer diffusion coefficient in the limit of large system sizes, which is based on a single finite-system-size simulation.

Bulk viscosity of multiparticle collision dynamics fluids

We determine the viscosity parameters of the multiparticle collision dynamics (MPC) approach, a particle-based mesoscale hydrodynamic simulation method for fluids. We perform analytical calculations and verify our results by simulations. The stochastic rotation dynamics and the Andersen thermostat variant of MPC are considered, both with and without angular momentum conservation. As an important result, we find a nonzero bulk viscosity for every MPC version. The explicit calculation shows that the bulk viscosity is determined solely by the collisional interactions of MPC.

Thermostat for nonequilibrium multiparticle-collision-dynamics simulations

Multiparticle collision dynamics (MPC), a particle-based mesoscale simulation technique for complex fluid, is widely employed in nonequilibrium simulations of soft matter systems. To maintain a defined thermodynamic state, thermalization of the fluid is often required for certain MPC variants. We investigate the influence of three thermostats on the nonequilibrium properties of a MPC fluid under shear or in Poiseuille flow. In all cases, the local velocities are scaled by a factor, which is either determined via a local simple scaling approach (LSS), a Monte Carlo-like procedure (MCS), or by the Maxwell-Boltzmann distribution of kinetic energy (MBS). We find that the various scaling schemes leave the flow profile unchanged and maintain the local temperature well. The fluid viscosities extracted from the various simulations are in close agreement. Moreover, the numerically determined viscosities are in remarkably good agreement with the respective theoretically predicted values. At equilibrium, the calculation of the dynamic structure factor reveals that the MBS method closely resembles an isothermal ensemble, whereas the MCS procedure exhibits signatures of an adiabatic system at larger collision-time steps. Since the velocity distribution of the LSS approach is non-Gaussian, we recommend to apply the MBS thermostat, which has been shown to produce the correct velocity distribution even under nonequilibrium conditions.

Hydrodynamic simulations of self-phoretic microswimmers

A mesoscopic hydrodynamic model to simulate synthetic self-propelled Janus particles which is thermophoretically or diffusiophoretically driven is here developed. We first propose a model for a passive colloidal sphere which reproduces the correct rotational dynamics together with strong phoretic effect. This colloid solution model employs a multiparticle collision dynamics description of the solvent, and combines stick boundary conditions with colloid-solvent potential interactions. Asymmetric and specific colloidal surface is introduced to produce the properties of self-phoretic Janus particles. A comparative study of Janus and microdimer phoretic swimmers is performed in terms of their swimming velocities and induced flow behavior. Self-phoretic microdimers display long range hydrodynamic interactions with a decay of 1/r(2), which is similar to the decay of gradient fields generated by self-phoretic particle, and can be characterized as pullers or pushers. In contrast, Janus particles are characterized by short range hydrodynamic interactions with a decay of 1/r(3) and behave as neutral swimmers.

Hydrodynamics of discrete-particle models of spherical colloids: a multiparticle collision dynamics simulation study

We investigate the hydrodynamic properties of a spherical colloid model, which is composed of a shell of point particles by hybrid mesoscale simulations, which combine molecular dynamics simulations for the sphere with the multiparticle collision dynamics approach for the fluid. Results are presented for the center-of-mass and angular velocity correlation functions. The simulation results are compared with theoretical results for a rigid colloid obtained as a solution of the Stokes equation with no-slip boundary conditions. Similarly, analytical results of a point-particle model are presented, which account for the finite size of the simulated system. The simulation results agree well with both approaches on appropriative time scales; specifically, the long-time correlations are quantitatively reproduced. Moreover, a procedure is proposed to obtain the infinite-system-size diffusion coefficient based on a combination of simulation results and analytical predictions. In addition, we present the velocity field in the vicinity of the colloid and demonstrate its close agreement with the theoretical prediction. Our studies show that a point-particle model of a sphere is very well suited to describe the hydrodynamic properties of spherical colloids, with a significantly reduced numerical effort.

Effects of thermal fluctuations and fluid compressibility on hydrodynamic synchronization of microrotors at finite oscillatory Reynolds number: a multiparticle collision dynamics simulation study

We investigate the emergent dynamical behavior of hydrodynamically coupled microrotors by means of multiparticle collision dynamics (MPC) simulations. The two rotors are confined in a plane and move along circles driven by active forces. Comparing simulations to theoretical results based on linearized hydrodynamics, we demonstrate that time-dependent hydrodynamic interactions lead to synchronization of the rotational motion. Thermal noise implies large fluctuations of the phase-angle difference between the rotors, but synchronization prevails and the ensemble-averaged time dependence of the phase-angle difference agrees well with analytical predictions. Moreover, we demonstrate that compressibility effects lead to longer synchronization times. In addition, the relevance of the inertia terms of the Navier-Stokes equation are discussed, specifically the linear unsteady acceleration term characterized by the oscillatory Reynolds number ReT. We illustrate the continuous breakdown of synchronization with the Reynolds number ReT, in analogy to the continuous breakdown of the scallop theorem with decreasing Reynolds number.

A self-propelled thermophoretic microgear

An asymmetric microgear will spontaneously and unidirectionally rotate if it is heated in a cool surrounding solvent. The resulting temperature gradient along the edges of the gear teeth translates in a directed thermophoretic force, which will exert a net torque on the gear. By means of computer simulations, the validity of this scenario is proved. The rotational direction and speed are dependent on gear–solvent interactions, and can be analytically related to system parameters like the thermal diffusion factor, the solvent viscosity, or the temperature difference. This microgear provides a simple way to extract net work from non-isothermal solutions, and can become a valuable tool in microfluids.

No-slip boundary conditions and forced flow in multiparticle collision dynamics

Multiparticle collision dynamics (MPCD) is a particle-based fluid simulation technique that is becoming increasingly popular for mesoscale fluid modeling. However, some confusion and conflicting results persist in literature regarding several important methodological details, in particular the enforcement of the no-slip condition and thermostatting in forced flow. These issues persist in simple flows past stationary boundaries, which we exclusively focus on here. We discuss the parametrization of MPCD fluids and its consequences for fluid-solid boundaries in great detail, and show that the method of virtual particles proposed by Lamura et al. and adopted by many others is required only for parameter choices that lead to viscosities dominated by collisional contributions. We test several implementations of the virtual particle method and discuss how to completely eliminate slip at stationary boundaries. We also show that stochastic boundary reflection rules are inherently problematic for forced flow and suggest a possible remedy. Finally, we discuss the most robust way to achieve forced flow and evaluate several thermostatting methods in the process. All discussion is limited to solid objects that do not move as a result of collisions with MPCD particles (i.e., walls). However, the results can be extended to solutes that experience forces and torques due to interactions with MPCD particles (e.g., colloids). The detailed analysis presented for this simple case provides the level of rigor and accuracy to the MPCD method required for the study of more complex systems.

Hydrodynamic correlations in multiparticle collision dynamics fluids

The emergent fluctuating hydrodynamics of the multiparticle collision dynamics (MPC) approach, a particle-based mesoscale simulation technique for fluid dynamics, is analyzed theoretically and numerically. We focus on the stochastic rotation dynamics implementation of the MPC method. The fluid is characterized by its longitudinal and transverse velocity correlation functions in Fourier space and velocity autocorrelation functions in real space. Particular attention is paid to the role of sound, which leads to piecewise negative correlation functions. Moreover, finite system-size effects are addressed with an emphasis on the role of sound. Analytical expressions are provided for the transverse and longitudinal velocity correlations, which are derived from the linearized Landau-Lifshitz Navier-Stokes equation adopted for an isothermal MPC fluid. The comparison of the analytical results with simulations shows excellent agreement above a minimal length scale. The simulations indicate a breakdown in hydrodynamics on length scales smaller than this minimal length. This demonstrates that we have an excellent analytical description and understanding of the MPC method and its limitations in terms of time and length scales.

Drift velocity in non-isothermal inhomogeneous systems

Drift velocity and driving force are not directly proportional in the case of inhomogeneous suspensions, where a space dependent mobility induces an additional contribution to the drift velocity. Similarly, particle flux and drift velocity are related not only by the gradient of density but also by an additional contribution given by the gradient of the self-diffusion coefficient. We provide quantitative support to this scenario in a non-equilibrium system by means of computer simulations with a temperature gradient. Moreover, our simulation results demonstrate that the temperature gradient-induced mass transport coefficient, namely thermal diffusion coefficient, is not directly proportional to the drift velocity so that the well-accepted relation of proportionality is just an approximation.

Thermophoresis of colloids by mesoscale simulations

The motion of a colloid induced by a temperature gradient is simulated by means of multiparticle collision dynamics, a mesoscale simulation technique. Two algorithms to quantify the thermophoretic behavior are employed and contrasted. The validity of the methods is verified as a function of the temperature gradient, system size, and algorithm parameters. The variation of the solvent-colloid interaction from attractive to purely repulsive interestingly results in the change of the colloid behavior from thermophobic to thermophilic.

Simulations of thermophoretic nanoswimmers

We consider a nanodimer in solution with asymmetric thermal properties that shows self-propelled motion. One monomer of the nanodimer can be heated to a fixed temperature producing a radially symmetric temperature gradient. The thermophoretic properties of the second monomer produce then a propulsion against or toward the heated particle, such that the nanodimer becomes a puller or pusher nanoswimmer. We combine our simulation measurements with a theoretical analysis that satisfactorily characterizes the self-propelled velocity with the temperature gradient, and the thermophoretic properties of the bead.

Hydrodynamic fluctuations in thermostatted multiparticle collision dynamics

In this work we study the behavior of mesoscopic fluctuations of a fluid simulated by Multiparticle Collision Dynamics when this is applied together with a local thermostatting procedure that constrains the strength of temperature fluctuations. We consider procedures in which the thermostat interacts with the fluid at every simulation step as well as cases in which the thermostat is applied only at regular time intervals. Due to the application of the thermostat temperature fluctuations are forced to relax to equilibrium faster than they do in the nonthermostatted, constant-energy case. Depending on the interval of application of the thermostat, it is demonstrated that the thermodynamic state changes gradually from isothermal to adiabatic conditions. In order to exhibit this effect we compute from simulations diverse correlation functions of the hydrodynamic fluctuating fields. These correlation functions are compared with those predicted by a linearized hydrodynamic theory of a simple fluid in which a thermostat is applied locally. We find a good agreement between the model and the numerical results, which confirms that hydrodynamic fluctuations in Multiparticle Collision Dynamics in the presence of the thermostat have the properties expected for spontaneous fluctuations in fluids in contact with a heat reservoir.

Transport coefficients of off-lattice mesoscale-hydrodynamics simulation techniques

The viscosity and self-diffusion constant of particle-based mesoscale hydrodynamic methods, multiparticle collision dynamics (MPC), and dissipative particle dynamics, are investigated, both with and without angular-momentum conservation. Analytical results are derived for fluids with an ideal-gas equation of state and a finite-time-step dynamics, and compared with simulation data. In particular, the viscosity is derived in a general form for all variants of the MPC method. In general, very good agreement between theory and simulations is obtained.

Transport coefficients of multi-particle collision algorithms with velocity-dependent collision rules

Detailed calculations of the transport coefficients of a recently introduced particle-based model for fluid dynamics with a non-ideal equation of state are presented. Excluded volume interactions are modeled by means of biased stochastic multi-particle collisions which depend on the local velocities and densities. Momentum and energy are exactly conserved locally. A general scheme to derive transport coefficients for such biased, velocity-dependent collision rules is developed. Analytic expressions for the self-diffusion coefficient and the shear viscosity are obtained, and very good agreement is found with numerical results at small and large mean free paths. The viscosity turns out to be proportional to the square root of temperature, as in a real gas. In addition, the theoretical framework is applied to a two-component version of the model, and expressions for the viscosity and the difference in diffusion of the two species are given.