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, which interact by local momentum-conserving stochastic MPC collisions. 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 polymer length, which decays as $t^{-3/2}$, similar to a Newtonian fluid, in the asymptotic limit $t \to \infty$. 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.
The role of sound in the dynamics of mesoscale systems is typically neglected, since frequently the associated time scales are much smaller than all the other time scales of interest. However, for sufficiently small objects embedded in a solvent with a sufficiently small sound velocity, sound can play a crucial role. In particular, behavior resembling viscoelasticity has been theoretically predicted for non-viscoelastic fluids. This effect is due to the interference of the propagation of sound waves caused by the solute particle's motion and hydrodynamic vortex formation. We demonstrate this e…
Multiparticle collision dynamics (MPCD) is a flexible and robust mesoscale computational technique for simulating solvent-mediated hydrodynamic interactions in soft materials. Here, we provide a critical overview of the MPCD method and summarize its current strengths and limitations. The capabilities of the method are highlighted by reviewing its recent applications to simulate diverse phenomena, ranging from the flow of complex fluids and thermo-osmotic transport to bacterial swimming and active particle self-assembly. We also discuss outstanding challenges and emerging methodological develop…
The viscoelastic effect on the hydrodynamic relaxation in semidilute polymer solutions is investigated. From the linearized two-fluid model equations, we predict that the dynamical asymmetry coupling between the velocity fluctuations and the viscoelastic stress influences on the hydrodynamic relaxation process, resulting in a wave-number-dependent shear viscosity.
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 mo…
In this review we discuss the recent progress in the simulation of soft active matter systems and in particular the hydrodynamics of microswimmers using the method of multiparticle collision dynamics, which solves the hydrodynamic flows around active objects on a coarse-grained level. We first present a brief overview of the basic simulation method and the coupling between microswimmers and fluid. We then review the current achievements in simulating flexible and rigid microswimmers using multiparticle collision dynamics, and briefly conclude and discuss possible future directions.
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 …
We propose a theoretical model which relies on the generalized Langevin equation and may account for various dynamical features of the thermal motion of organelles, vesicles or macromolecules in viscoelastic media such as polymer networks. In particular, we consider inertial and hydrodynamic effects at short times, subdiffusive scaling at intermediate times, and eventually optical trapping at long times. Simple analytical formulas for the mean square displacement and velocity auto-correlation function are derived. The developed theory is applied to the analysis of fifty-second long trajectorie…
The friction and diffusion coefficients of rigid spherical colloidal particles dissolved in a fluid are determined from velocity and force autocorrelation functions by mesoscale hydrodynamic simulations. Colloids with both slip and no-slip boundary conditions are considered, which are embedded in fluids modelled by multiparticle collision dynamics (MPC) with and without angular momentum conservation. For no-slip boundary conditions, hydrodynamics yields the well-known Stokes law, while for slip boundary conditions the lack of angular momentum conservation leads to a reduction of the hydrodynam…
We study self-diffusion and sedimentation in colloidal suspensions of nearly-hard spheres using the multiparticle collision dynamics simulation method for the solvent with a discrete mesh model for the colloidal particles (MD+MPCD). We cover colloid volume fractions from 0.01 to 0.40 and compare the MD+MPCD simulations to Brownian dynamics simulations with free-draining hydrodynamics (BD) as well as pairwise far-field hydrodynamics described using the Rotne--Prager--Yamakawa mobility tensor (BD+RPY). The dynamics in MD+MPCD suggest that the colloidal particles are only partially coupled to the…
The nonequilibrium hydrodynamic correlations of a Multiparticle-Collision-Dynamics (MPC) fluid in shear flow are studied by analytical calculations and simulations. The Navier-Stokes equations for a MPC fluid are linearized about the shear flow and the hydrodynamic modes are evaluated as an expansion in the momentum vector. The shear-rate dependence and anisotropy of the transverse and longitudinal velocity correlations are analyzed. We demonstrate that hydrodynamic correlations in shear flow are anisotropic, specifically, the two transverse modes are no longer identical. In addition, our simu…
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 of nematics, the spatial and temporal variations of the nematic director field and or…
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 h…
We investigate the hydrodynamic properties of a fluid simulated with a mesoscopic solvent model. Two distinct regimes are identified, the `particle regime' in which the dynamics is gas-like, and the `collective regime' where the dynamics is fluid-like. This behavior can be characterized by the Schmidt number, which measures the ratio between viscous and diffusive transport. Analytical expressions for the tracer diffusion coefficient, which have been derived on the basis of a molecular-chaos assumption, are found to describe the simulation data very well in the particle regime, but important de…
We formulate the theory of nonlinear viscoelastic hydrodynamics of anisotropic crystals in terms of dynamical Goldstone scalars of spontaneously broken translational symmetries, under the assumption of homogeneous lattices and absence of plastic deformations. We reformulate classical elasticity effective field theory using surface calculus in which the Goldstone scalars naturally define the position of higher-dimensional crystal cores, covering both elastic and smectic crystal phases. We systematically incorporate all dissipative effects in viscoelastic hydrodynamics at first order in a long-w…
HTMPC: A heavily templated C++ library for large scale particle-based mesoscale hydrodynamics simulations using multiparticle collision dynamics
Peter Grünberg Institute and Jülich Centre for Neutron Science, Forschungszentrum Jülich（彼得·格林伯格研究所和朱利希中子科学中心，朱利希研究中心）；Theoretical Physics of Living Matter, Institute for Advanced Simulation, Forschungszentrum Jülich（生命物质理论物理，先进模拟研究所，朱利希研究中心）
We introduce a mesoscale method for simulating hydrodynamic transport and self assembly of inhomogeneous polymer melts in pressure driven and drag induced flows. This method extends dynamic self consistent field theory (DSCFT) into the hydrodynamic regime where bulk material transport and viscoelastic effects play a significant role. The method combines four distinct components as a single coupled system, including (1) non-equilibrium self consistent field theory describing block copolymer self-assembly, (2) multi-fluid Navier-Stokes type hydrodynamics for tracking material transport, (3) cons…
We study the capillary wave dynamics of a single viscoelastic supported film and of a double layer of immiscible viscoelastic supported films. Using both simple scaling arguments and a continuum hydrodynamic theory, we investigate the effects of viscoelasticity and interfacial slip on the relaxation dynamics of these capillary waves. Our results account for the recent observation of a wavelength-independent decay rate for capillary waves in a supported polystyrene/brominated polystyrene double layer [X. Hu {\em et al.}, Phys. Rev. E {\bf 74}, 010602 (R) (2006)].
We determine both the in-plane and out-of-plane dynamics of viscoelastic membranes separating two viscous fluids in order to understand microrheological studies of such membranes. We demonstrate the general viscoelastic signatures in the dynamics of shear, bending, and compression modes. We also find a screening of the otherwise two-dimensional character of the response to point forces due to the presence of solvent. Finally, we show that there is a linear, hydrodynamic coupling between the in-plane compression modes of the membrane and the out-of-plane bending modes in the case where the memb…
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.
Many swimming microorganisms, such as bacteria and sperm, use flexible flagella to move through viscoelastic media in their natural environments. In this paper we address the effects a viscoelastic fluid has on the motion and beating patterns of elastic filaments. We treat both a passive filament which is actuated at one end, and an active filament with bending forces arising from internal motors distributed along its length. We describe how viscoelasticity modifies the hydrodynamic forces exerted on the filaments, and how these modified forces affect the beating patterns. We show how high vis…
The progressive onset of slip at the wall, which corresponds to a slip length increasing with the solicitation time before reaching a plateau, has been investigated for model viscoelastic polymer solutions, allowing one to vary the longest relaxation time while keeping constant solid - fluid interactions. A hydrodynamic model based on a Maxwell fluid and the classical Navier's hypothesis of a linear response for the friction stress at the interface fully accounts for the data, without any adjustable parameter. No viscoelastic response needs be postulated for the friction, reflecting the local …
We show that the correct dual hydrodynamic description of homogeneous holographic models with spontaneously broken translations must include the so-called "strain pressure" -- a novel transport coefficient proposed recently. Taking this new ingredient into account, we investigate the near-equilibrium dynamics of a large class of holographic models and faithfully reproduce all the hydrodynamic modes present in the quasinormal mode spectrum. Moreover, while strain pressure is characteristic of equilibrium configurations which do not minimise the free energy, we argue and show that it also affect…
Linear Viscoelasticity of Semiflexible Polymers with Hydrodynamic Interactions
IITB-Monash Research Academy, Indian Institute of Technology Bombay（印度理工学院孟买分校 IITB-莫纳什研究院）；Department of Chemical Engineering, Indian Institute of Technology Bombay（印度理工学院孟买分校化学工程系）；Department of Chemical and Biological Engineering, Monash University（莫纳什大学化学与生物工程系）
We develop a continuum theory of linear viscoelastic response in oriented monodomain nematic elastomers. The expression for dissipation function is analogous to the Leslie-Ericksen version of anisotropic nematic viscosity; we propose the relations between the anisotropic rubber moduli and new viscous coefficients. A new dimensionless number is introduced, which describes the relative magnitude of viscous and rubber-elastic torques. In an elastic medium with an independently mobile internal degree of freedom, the nematic director with its own relaxation dynamics, the model shows a dramatic decr…
We experimentally study the dynamics of active particles (APs) in a viscoelastic fluid under various geometrical constraints such as flat walls, spherical obstacles and cylindrical cavities. We observe that the main effect of the confined viscoelastic fluid is to induce an effective repulsion on the APs when moving close to a rigid surface, which depends on the incident angle, the surface curvature and the particle activity. Additionally, the geometrical confinement imposes an asymmetry to their movement, which leads to strong hydrodynamic torques, thus resulting in detention times on the wall…
Constitutive equations for a one-dimensional, active, polar, viscoelastic liquid are derived by treating the strain field as a slow hydrodynamic variable. Taking into account the couplings between strain and polarity allowed by symmetry, the hydrodynamics of an active, polar, viscoelastic body include an evolution equation for the polarity field that generalizes the damped Kuramoto-Sivashinsky equation. Beyond thresholds of the active coupling coefficients between the polarity and the stress or the strain rate, bifurcations of the homogeneous state lead first to stationary waves, then to propa…
Linking molecular timescales to linear viscoelastic response in dilute and semidilute unentangled wormlike micelle solutions
IITB-Monash Research Academy（IITB-蒙纳士研究学院）；Department of Chemical Engineering, Indian Institute of Technology Bombay（印度理工学院孟买分校化学工程系）；Department of Chemical and Biological Engineering, Monash University（蒙纳士大学化学与生物工程系）；School of Chemistry, Monash University（蒙纳士大学化学学院）
(abridged) We present a detailed derivation of a simple hydrodynamic two-fluid model, which aims at the description of the phase separation of non-entangled polymer solutions, where viscoelastic effects play a role. It is directly based upon the coarse-graining of a well-defined molecular model, such that all degrees of freedom have a clear and unambiguous molecular interpretation. The considerations are based upon a free-energy functional, and the dynamics is split into a conservative and a dissipative part, where the latter satisfies the Onsager relations and the Second Law of thermodynamics…
Colloidal solutions posses a wide range of time and length scales, so that it is unfeasible to keep track of all of them within a single simulation. As a consequence some form of coarse-graining must be applied. In this work we use the Multi-Particle Collision Dynamics scheme. We describe a particular implementation of no-slip boundary conditions upon a solid surface, capable of providing correct force s on the solid bypassing the calculation of the velocity profile or the stre ss tensor in the fluid near the surface. As an application we measure the friction on a spherical particle, when it i…
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 potential interactions with the solvent, with stick boundary conditions. Asymmetric and specific colloidal surface is introduced to produce the properties of self-phoretic Janus part…
It is shown that the dynamics of a two-dimensional crystal with a finite concentration of dislocations, as well as vacancy and interstitial defects, is governed by the hydrodynamic equations of a viscoelastic medium. At the longest length scales the viscoelasticity is described by the simplest Maxwell model, whose shear and compressional relaxation times are obtained in terms of microscopic quantities, including the density of free dislocations. At short length scales, bond orientational order effects become important and lead to wavevector dependent corrections to the relaxation times.
The electroosmotic flow of non-Newtonian fluids in deformable microchannels is fundamentally important in the understanding of the hydrodynamics in physiological flows. The performance of these microchannels is governed by the load bearing capacity indicating the maximum amount of load that the device can withstand. While significant research efforts are aimed towards the coupling of electrokinetics with substrate deformability, the corresponding enhancement in the performances still remains elusive. Towards this, employing an intricate coupling between substrate compliance, hydrodynamic, and …
Recently, many interesting features of the hydrodynamically coupled motions of the Brownian particles in a viscous fluid have been reported which are impossible for the uncoupled motions of the similar particles. However, it is expected that those physics in a viscoelastic fluid is much more interesting due to the presence of the additional frequency dependent elasticity of the medium. Thus, a theory describing the equilibrium dynamics of two hydrodynamically coupled Brownian harmonic oscillators in a viscoelastic Maxwell fluid has been derived which appears with new and impressive aspects. In…
Extensional rheometry and Brownian Dynamics simulations of flexible polymer solutions confirm predictions based on blob concepts that coil--stretch hysteresis in extensional flows increases with concentration, reaching a maximum at the critical overlap concentration $c^\ast$ before progressively vanishing in the semidilute regime. These observations demonstrate that chain stretching strengthens intermolecular hydrodynamic screening in dilute solutions, but weakens it in semidilute solutions. Flow can thus strongly modify the concentration dependence of viscoelastic properties of polymer soluti…
We study the evaporation-induced stratification of a mixture of short and long polymer chains in a drying droplet using molecular simulations. We systematically investigate the effects of hydrodynamic interactions (HI) on this process by comparing hybrid simulations accounting for HI between polymers through the multiparticle collision dynamics technique with free-draining Langevin dynamics simulations neglecting the same. We find that the dried supraparticle morphologies are homogeneous when HI are included but are stratified in core--shell structures (with the short polymers forming the shel…
The hydrodynamics of viscoelastic materials (for example polymer melts and solutions) presents interesting and complex phenomena, for example instabilities and turbulent flow at very low Reynolds numbers due to normal stress effects and the existence of a finite stress relaxation time. This present work is motivated by renewed interest in instabilities in polymer flow. The majority of currently used numerical methods discretize a constitutive equation on a grid with finite difference or similar methods. We present work in progress in which we simulate viscoelastic flow with dissipative particl…
We investigate previously unclarified effects of fluid elasticity on shear-thickening in dilute suspensions in an Oldroyd-B viscoelastic fluid using a novel direct numerical simulation based on the smoothed profile method. Fluid elasticity is determined by the Weissenberg number Wi and by viscosity ratio $1-β=η_p/(η_s+η_p)$ which measures the coupling between the polymer stress and flow: $η_p$ and $η_s$ are the polymer and solvent viscosity, respectively.As $1-β$ increases, while the stresslet does not change significantly compared to that in the $β\to 1$ limit, the growth rate of the normaliz…
Chemical reactions inside cells are typically subject to the effects both of the cell's confining surfaces and of the viscoelastic behavior of its contents. In this paper, we show how the outcome of one particular reaction of relevance to cellular biochemistry - the diffusion-limited cyclization of long chain polymers - is influenced by such confinement and crowding effects. More specifically, starting from the Rouse model of polymer dynamics, and invoking the Wilemski-Fixman approximation, we determine the scaling relationship between the mean closure time t_{c} of a flexible chain (no exclud…
We present a hybrid lattice Boltzmann algorithm for the simulation of flow glass-forming fluids, characterized by slow structural relaxation, at the level of the Navier-Stokes equation. The fluid is described in terms of a nonlinear integral constitutive equation, relating the stress tensor locally to the history of flow. As an application, we present results for an integral nonlinear Maxwell model that combines the effects of (linear) viscoelasticity and (nonlinear) shear thinning. We discuss the transient dynamics of velocities, shear stresses, and normal stress differences in planar pressur…
In order to investigate the rheological properties of viscoelastic fluids by mesoscopic hydrodynamics methods, we develop a multi-particle collision dynamics (MPC) model for a fluid of harmonic dumbbells. The algorithm consists of alternating streaming and collision steps. The advantage of the harmonic interactions is that the integration of the equations of motion in the streaming step can be performed analytically. Therefore, the algorithm is computationally as efficient as the original MPC algorithm for Newtonian fluids. The collision step is the same as in the original MPC method. All part…
We employ a matrix-based solver for the linear rheology of fluid-immersed disordered spring networks to reveal four distinct dynamic response regimes. One regime - completely absent in the known vacuum response - exhibits coupled fluid flow and network deformation, with both components responding non-affinely. This regime contains an additional plateau (peak) in the frequency-dependent storage (loss) modulus - features which vanish without full hydrodynamic interactions. The mechanical response of immersed networks such as biopolymers and hydrogels is thus richer than previously established, a…
The RMPCDMD software package performs hybrid Molecular Dynamics simulations, coupling Multiparticle Collision Dynamics to model the solvent and Molecular Dynamics to model suspended colloids, including hydrodynamics, thermal fluctuations, and chemically active solvent particles and catalytic colloids. The main usage of RMPCDMD is the simulation of chemically powered nanomotors, but other setups are considered: colloids in the presence of a thermal gradients or forced flows. RMPCDMD is developed in Fortran 2008 with OpenMP for multithreaded operation and uses the HDF5-based H5MD file format for…
We describe a lattice Boltzmann algorithm to simulate liquid crystal hydrodynamics. The equations of motion are written in terms of a tensor order parameter. This allows both the isotropic and the nematic phases to be considered. Backflow effects and the hydrodynamics of topological defects are naturally included in the simulations, as are viscoelastic properties such as shear-thinning and shear-banding.
We present an entirely microscopic formulation of viscoleasticity of a fluid starting from the microscopic Stokes-Oldroyd B Model assuming instantaneous hydrodynamic friction, and show that linearization leads to a form for the frequency dependent viscosity that can be directly applied to the Langevin equation. Interestingly, the calculated expression of viscosity can be directly mapped to the Jeffreys' model which is essentially macroscopic in nature with the bulk viscoelasticity of the fluid being characterized by a complex elastic modulus G(ω). Further, we demonstrate that the concerned Gre…
In the limit of infinite yield time for stresses, the hydrodynamic equations for viscoelastic, Non-Newtonian liquids such as polymer melts must reduce to that for solids. This piece of information suffices to uniquely determine the nonlinear convective derivative, an ongoing point of contention in the rheology literature.
In this work, we investigate the dynamics of the number density fluctuations of a dilute suspension of active particles in a linear viscoelastic fluid. We propose a model for the frequency-dependent diffusion coefficient of the active particles, which captures the effect of rotational diffusion on the persistence of their self-propelled motion and the viscoelasticity of the medium. Using fluctuating hydrodynamics, the linearized equations for the active suspension are derived, from which we calculate its dynamic structure factor and the corresponding intermediate scattering function. For a Max…
The locomotion of microorganisms and spermatozoa in complex viscoelastic fluids is of critical importance in many biological processes such as fertilization, infection, and biofilm formation. Depending on their propulsion mechanisms, microswimmers display various responses to a complex fluid environment: increasing or decreasing their swimming speed and efficiency, modifying their propulsion kinematics and swimming gaits, and experiencing different hydrodynamic interactions with their surroundings. In this article, we review the fundamental physics of locomotion of biological and synthetic mic…
