Mesoscale Hydrodynamic Simulations Research Articles

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

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

From local to hydrodynamic friction in Brownian motion: A multiparticle collision dynamics simulation study.

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 modeled by multiparticle collision dynamics 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 hydrodynamic friction coefficient compared to the classical result. The colloid diffusion coefficient is determined by integration of the velocity autocorrelation function, where the numerical result at shorter times is combined with the theoretical hydrodynamic expression for longer times. The suitability of this approach is confirmed by simulations of sedimenting colloids. In general, we find only minor deviations from the Stokes-Einstein relation, which even disappear for larger colloids. Importantly, for colloids with slip boundary conditions, our simulation results contradict the frequently assumed additivity of local and hydrodynamic diffusion coefficients.

Bacterial swarmer cells in confinement: a mesoscale hydrodynamic simulation study.

A wide spectrum of Peritrichous bacteria undergo considerable physiological changes when they are inoculated onto nutrition-rich surfaces and exhibit a rapid and collective migration denoted as swarming. Thereby, the length of such swarmer cells and their number of flagella increases substantially. In this article, we investigated the properties of individual E. coli-type swarmer cells confined between two parallel walls via mesoscale hydrodynamic simulations, combining molecular dynamics simulations of the swarmer cell with the multiparticle particle collision dynamics approach for the embedding fluid. E. coli-type swarmer cells are three-times longer than their planktonic counter parts, but their flagella density is comparable. By varying the wall separation, we analyze the confinement effect on the flagella arrangement, on the distribution of cells in the gap between the walls, and on the cell dynamics. We find only a weak dependence of confinement on the bundle structure and dynamics. The distribution of cells in the gap changes from a geometry-dominated behavior for very narrow to fluid-dominated behavior for wider gaps, where cells are preferentially located in the gap center for narrower gaps and stay preferentially next to one of the walls for wider gaps. Dynamically, the cells exhibit a wide spectrum of migration behaviors, depending on their flagella bundle arrangement, and ranges from straight swimming to wall rolling.

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.

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.

Physical Sensing of Surface Properties by Microswimmers--Directing Bacterial Motion via Wall Slip.

Bacteria such as Escherichia coli swim along circular trajectories adjacent to surfaces. Thereby, the orientation (clockwise, counterclockwise) and the curvature depend on the surface properties. We employ mesoscale hydrodynamic simulations of a mechano-elastic model of E. coli, with a spherocylindrical body propelled by a bundle of rotating helical flagella, to study quantitatively the curvature of the appearing circular trajectories. We demonstrate that the cell is sensitive to nanoscale changes in the surface slip length. The results are employed to propose a novel approach to directing bacterial motion on striped surfaces with different slip lengths, which implies a transformation of the circular motion into a snaking motion along the stripe boundaries. The feasibility of this approach is demonstrated by a simulation of active Brownian rods, which also reveals a dependence of directional motion on the stripe width.

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.

Modelling the mechanics and hydrodynamics of swimming E. coli.

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

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

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

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

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

Mesoscale hydrodynamics simulations of particle suspensions under shear flow: From hard to ultrasoft colloids

We discuss the nonequilibrium properties of rodlike and ultrasoft, star-polymer like colloidal particles in shear flow. Conformational, dynamical, as well as rheological aspects are addressed for a broad range of concentrations. For concentrated solutions of rodlike colloids, we study the nonequilibrium properties of a phase separated system, where a disordered phase coexists with a nematic phase. For starlike polymers we consider systems of various functionality, starting from linear polymers. The individual rods, polymers, or stars exhibit an intriguing dynamical behavior, which determines their macroscopic rheological properties. Despite the diversity on the colloidal level, the various systems exhibit a qualitatively similar macroscopic behavior, e.g., shear thinning, yet with some quantitative differences.

Multiparticle collision dynamics: GPU accelerated particle-based mesoscale hydrodynamic simulations

The Compute Unified Device Architecture (CUDA) programming language on a graphics processing unit (GPU) is exploited to develop a GPU-based simulation program for the multiparticle collision dynamics (MPC) approach, a particle-based mesoscale hydrodynamic simulation technique. The coarse-grained description of the fluid dynamics in terms of ballistic motion and local stochastic interactions of particles renders MPC inherently highly parallel. We achieve a 1–2 orders of magnitude performance gain over a comparable CPU-core version of the algorithm, depending on the implementation (single threaded or OpenMP). Various aspects of the implementation are discussed in the context of an optimized performance.

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.

Dynamics and rheology of vesicle suspensions in wall-bounded shear flow

The dynamics and rheology of suspensions of fluid vesicles or red blood cells is investigated by a combination of molecular dynamics and mesoscale hydrodynamics simulations in two dimensions. The vesicle suspension is confined between two no-slip walls, which are driven externally to generate a shear flow with shear rate . The flow behavior is studied as a function of , the volume fraction of vesicles, and the viscosity contrast between inside and outside fluids. Results are obtained for the encounter and interactions of two vesicles, the intrinsic viscosity of the suspension, and the cell-free layer near the walls.

Multiparticle collision dynamics simulations of viscoelastic fluids: Shear-thinning Gaussian dumbbells

The structural, dynamical, and rheological properties are studied of a multiparticle collision dynamics (MPC) fluid composed of shear-thinning Gaussian dumbbells. MPC is a mesoscale hydrodynamic simulation technique, which has successfully been applied in simulations of a broad range of complex fluids with Newtonian solvent. The MPC particles are replaced by Gaussian dumbbells, where we enforce a constant mean square length even under nonequilibrium conditions, which leads to shear thinning. This conserves the simplicity and efficiency of the original MPC fluid dynamics, since the analytical solution is known of Newton's equations of motion of the Gaussian dumbbells. Moreover, analytically obtained nonequilibrium structural, dynamical, and rheological properties are presented of Gaussian dumbbells under shear flow within the preaveraging approximation of hydrodynamic interactions. The comparison of the analytical and simulation results shows good agreement, with small deviations only due to the preaveraging approximation. In particular, we observe shear thinning and a nonzero second normal stress coefficient.

Mesoscale Simulation of Mixed Equations of State with Application to Shocked Platinum-doped PMP Foams

Hydrocarbon polymers and foams are utilized in high energy-density physics (HEDP) and inertial confinement fusion (ICF) experiments as tampers, energy conversion and radiation pulse shaping layers in dynamic hohlraum Z-pinches, and ablators in ICF capsule implosions. Shocked foams frequently are found to be mixed with other materials either by intentional doping with high-Z elements or by instabilities and turbulent mixing with surrounding materials. In this paper we present one-dimensional and three-dimensional mesoscale hydrodynamic simulations of high-Z doped poly-(4-methyl-1-pentene) (PMP or TPX) foams in order to examine the validity of various equation of state (EOS) mixing rules available in two state-of-the-art simulation codes. Platinum-doped PMP foam experiments conducted at Sandia's Z facility provide data that can be used to test EOS mixing rules. We apply Sandia's ALEGRA-MHD code and the joint LLNL/SNL KULL HEDP code to model these doped foam experiments and exercise the available EOS mixing methods. One- dimensional simulations homogenize the foam with platinum dopant and show which EOS mixing methods produce results that are consistent with measured Hugoniot states. These simulations produce sharp shock fronts that are well described by traditional Hugoniot relations. Three-dimensional mesoscale simulations explicitly model the foam structure embedded with discrete platinum particles. The heterogeneous structure of the foam results in diffuse shock fronts and an unsteady post-shock state with large fluctuations about an average state. We compare shock propagation through pure foam and Pt-doped foams (50-50 mixture by weight) at equal average initial density, and examine how well the results compare to the experimentally measured Hugoniot states.

Flow-Induced Helical Coiling of Semiflexible Polymers in Structured Microchannels

The conformations of semiflexible (bio)polymers are studied in flow-through geometrically structured microchannels. Using mesoscale hydrodynamics simulations, we show that the polymer undergoes a rod-to-helix transition as it moves from the narrow high-velocity region into the wide low-velocity region of the channel. The transient helix formation is the result of a nonequilibrium and nonstationary buckling transition of the semiflexible polymer, which is subjected to a compressive force originating from the fluid-velocity variation in the channel. The helix properties depend on the diameter ratio of the channel, the polymer bending rigidity, and the flow strength.

Non-equilibrium relaxation and tumbling times of polymers in semidilute solution

The end-over-end tumbling dynamics of individual polymers in dilute and semidilute solutions is studied under shear flow by large-scale mesoscale hydrodynamic simulations. End-to-end vector relaxation times are determined along the flow, gradient, and vorticity directions. Along the flow and gradient directions, the correlation functions decay exponentially with sinusoidal modulations at short times. In dilute solution, the decay times of the various directions are very similar. However, in semidilute solutions, the relaxation behaviors are rather different along the various directions, with the longest relaxation time in the vorticity direction and the shortest time in the flow direction. The various relaxation times exhibit a power-law shear-rate dependence with the exponent − 2/3 at high shear rates. Quantitatively, the relaxation times are equal to the tumbling times extracted from cross-correlation functions of fluctuations of radius-of-gyration components along the flow and gradient direction.

Synchronization and bundling of anchored bacterial flagella

The synchronization and bundling process of bacterial flagella is investigated by mesoscale hydrodynamic simulations. Systems with two to six flagella are considered, which are anchored at one end, and are driven by a constant torque. A flagellum is modelled as a linear helical structure composed of mass points with their elastic shape maintained by bonds, bending, and torsional potentials. The characteristic times for synchronization and bundling are analyzed in terms of motor torque, separation, and number of flagella. We find that hydrodynamic interactions determine the bundling behavior. The synchronization time is smaller than the bundling time, but their ratio depends strongly on the initial separation. The bundling time decreases with increasing number of flagella at a fixed radius in a circular arrangement due to multi-helix hydrodynamics.

Dynamic self-assembly and directed flow of rotating colloids in microchannels

Nonequilibrium structure formation and dynamics in suspensions of superparamagnetic colloids driven by an external rotating magnetic field are studied by particle-based mesoscale hydrodynamics simulations in confined geometry. We address the fundamental question how the rotation of the colloids about their own axes can be converted into a translational motion by breaking the symmetry of the confining geometry. We study a two-dimensional system of colloids with short-range repulsive interactions, which mimics flow in shallow microchannels. In straight channels, we observe a two-way traffic but--for symmetry reasons--no net transport. However, by keeping some colloids fixed near one of the two walls, net transport can be achieved. This approach allows the control and switchability of the flow in complex microchannel networks. A minimal geometry that fulfills the requirement of broken symmetry are ring channels. We determine the translational velocity of the spinning colloids and study its dependence on the channel width for various median radii. We conclude that spinning colloids present a promising alternative for flow generation and control in microfluidic devices.