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

Exploring the role of hydrodynamic interactions in spherically confined drying colloidal suspensions

We study the distribution of colloidal particles confined in drying spherical freestanding droplets using both dynamic density functional theory (DDFT) and particle-based simulations. In particular, we focus on the advection-dominated regime typical of aqueous droplets drying at room temperature and systematically investigate the role of hydrodynamic interactions (HIs) during this nonequilibrium process. In general, drying produces transient particle concentration gradients within the droplet in this regime, with a considerable accumulation of particles at the droplet's liquid-vapor interface. We find that these gradients become significantly larger with pairwise HIs between colloidal particles instead of a free-draining hydrodynamic approximation; however, the solvent's boundary conditions at the droplet's interface (unbounded, slip, or no-slip) do not have a significant effect on the particle distribution. DDFT calculations leveraging the radial symmetry of the drying droplet are in excellent agreement with particle-based simulations for free-draining hydrodynamics, but DDFT unexpectedly fails for pairwise HIs after the particle concentration increases during drying, manifesting as an ejection of particles from the droplet. We hypothesize that this unphysical behavior originates from an inaccurate approximation of the two-body density correlations based on the bulk pair correlation function, which we support by measuring the confined equilibrium two-body density correlations using particle-based simulations. We identify some potential strategies for addressing this issue in DDFT.

Structure and dynamics of amphiphilic patchy cubes in a nanoslit under shear

Patchy nanocubes are intriguing materials with simple shapes and space-filling and multidirectional bonding properties. Previous studies have revealed various mesoscopic structures such as colloidal crystals in the solid regime and rod-like or fractal-like aggregates in the liquid regime of the phase diagram. Recent studies have also shown that mesoscopic structural properties, such as an average cluster size M and orientational order, in amphiphilic nanocube suspensions are associated with macroscopic viscosity changes, mainly owing to differences in cluster shape among patch arrangements. Although many studies have been conducted on the self-assembled structures of nanocubes in bulk, little is known about their self-assembly in nanoscale spaces or structural changes under shear. In this study, we investigated mixtures of one- and two-patch amphiphilic nanocubes confined in two flat parallel plates at rest and under shear using molecular dynamics simulations coupled with multiparticle collision dynamics. We considered two different patch arrangements for the two-patch particles and two different slit widths H to determine the degree of confinement in constant volume fractions in the liquid regime of the phase diagram. We revealed two unique cluster morphologies that have not been previously observed under bulk conditions. At rest, the size of the rod-like aggregates increased with decreasing H, whereas that of the fractal-like aggregates remained constant. Under weak shear with strong confinement, the rod-like aggregates maintained a larger M than the fractal-like aggregates, which were more rigid and maintained a larger M than the rod-like aggregates under bulk conditions.

Decoupling of rotation and translation at the colloidal glass transition

In dense particle systems, the coupling of rotation and translation motion becomes intricate. Here, we report the results of confocal fluorescence microscopy where simultaneous recording of translational and rotational particle trajectories from a bidisperse colloidal dispersion is achieved by spiking the samples with rotational probe particles. The latter consist of colloidal particles containing two fluorescently labeled cores suited for tracking the particle's orientation. A comparison of the experimental data with event driven Brownian simulations gives insights into the system's structure and dynamics close to the glass transition and sheds new light onto the translation-rotation coupling. The data show that with increasing volume fractions, translational dynamics slows down drastically, whereas rotational dynamics changes very little. We find convincing agreement between simulation and experiments, even though the simulations neglect far-field hydrodynamic interactions. An additional analysis of the glass transition following mode coupling theory works well for the structural dynamics but indicates a decoupling of the diffusion of the smaller particle species. Shear stress correlations do not decorrelate in the simulated glass states and are not affected by rotational motion.

Molecular dynamics simulations of anisotropic particles accelerated by neural-net predicted interactions

Rigid bodies, made of smaller composite beads, are commonly used to simulate anisotropic particles with molecular dynamics or Monte Carlo methods. To accurately represent the particle shape and to obtain smooth and realistic effective pair interactions between two rigid bodies, each body may need to contain hundreds of spherical beads. Given an interacting pair of particles, traditional molecular dynamics methods calculate all the inter-body distances between the beads of the rigid bodies within a certain distance. For a system containing many anisotropic particles, these distance calculations are computationally costly and limit the attainable system size and simulation time. However, the effective interaction between two rigid particles should only depend on the distance between their center of masses and their relative orientation. Therefore, a function capable of directly mapping the center of mass distance and orientation to the interaction energy between the two rigid bodies would completely bypass inter-bead distance calculations. It is challenging to derive such a general function analytically for almost any non-spherical rigid body. In this study, we have trained neural nets, powerful tools to fit nonlinear functions to complex datasets, to achieve this task. The pair configuration (center of mass distance and relative orientation) is taken as an input, and the energy, forces, and torques between two rigid particles are predicted directly. We show that molecular dynamics simulations of cubes and cylinders performed with forces and torques obtained from the gradients of the energy neural-nets quantitatively match traditional simulations that use composite rigid bodies. Both structural quantities and dynamic measures are in agreement, while achieving up to 23 times speedup over traditional molecular dynamics, depending on hardware and system size. The method presented here can, in principle, be applied to any irregular concave or convex shape with any pair interaction, provided that sufficient training data can be obtained.

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

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

Structure Formation in Supraparticles Composed of Spherical and Elongated Particles

We studied the evaporation-induced formation of supraparticles from dispersions of elongated colloidal particles using experiments and computer simulations. Aqueous droplets containing a dispersion of ellipsoidal and spherical polystyrene particles were dried on superamphiphobic surfaces at different humidity values that led to varying evaporation rates. Supraparticles made from only ellipsoidal particles showed short-range lateral ordering at the supraparticle surface and random orientations in the interior regardless of the evaporation rate. Particle-based simulations corroborated the experimental observations in the evaporation-limited regime and showed an increase in the local nematic ordering as the diffusion-limited regime was reached. A thin shell of ellipsoids was observed at the surface when supraparticles were made from binary mixtures of ellipsoids and spheres. Image analysis revealed that the supraparticle porosity increased with an increasing aspect ratio of the ellipsoids.

Confined Dynamics in Spherical Polymer Brushes

We investigate the dynamics of polymers grafted to spherical nanoparticles in solution using hybrid molecular dynamics simulations with a coarse-grained solvent modeled via the multiparticle collision dynamics algorithm. The mean-square displacements of monomers near the surface of the nanoparticle exhibit a plateau on intermediate time scales, indicating confined dynamics reminiscent of those reported in neutron spin-echo experiments. The confined dynamics vanish beyond a specific radial distance from the nanoparticle surface that depends on the polymer grafting density. We show that this dynamical confinement transition follows theoretical predictions for the critical distance associated with the structural transition from confined to semidilute brush regimes. These findings suggest the existence of a hitherto unreported dynamic length scale connected with theoretically predicted static fluctuations in spherical polymer brushes and provide new insights into recent experimental observations.

Influence of shape on heteroaggregation of model microplastics: a simulation study

Microplastics are a growing threat, especially in aqueous habitats. For assessing the influence on the ecosystem and possible solution strategies, it is necessary to investigate the "fate" of microplastics in the environment. Microplastics are typically surrounded by natural organic matter, which can cause aggregation via favorable interactions. However, the effect of shape and flow conditions on heteroaggregation is not well understood. We perform molecular dynamics simulations of different microplastic particle shapes with smaller spherical organic matter. We find that mostly smooth particles formed compact structures with large number of neighbors with weak connection strength and higher fractal dimension. Microplastics with sharper edges and corners aggregated into more fractal structures with fewer neighbors, but with stronger connections. We investigated the behavior of aggregates under shear flow. The critical shear rate at which the aggregates break up is much larger for spherical and rounded cube microplastics, the compact aggregate structure outweighs their weaker connection strength. The rounded cube aggregate exhibited unexpectedly high resistance against breakup under shear. We attribute this to being fairly compact due to weaker, flexible neighbor connections, which are still strong enough to prevent particles to break off during shear flow. Irrespective of stronger connections between neighbouring microplastics, fractal aggregates of cubes break up at lower shear rates. We find that cube aggregates reduced their radius of gyration significantly, indicating restructuring during shear, while most neighbor connections were kept intact. Sphere aggregates, however, kept their overall size while undergoing local rearrangements, breaking a significant portion of their neighbor interactions.

Aggregation of amphiphilic nanocubes in equilibrium and under shear

We investigate the self-assembly of amphiphilic nanocubes into finite-sized aggregates in equilibrium and under shear, using molecular dynamics (MD) simulations and kinetic Monte Carlo (KMC) calculations. These patchy nanoparticles combine both interaction and shape anisotropy, making them valuable models for studying folded proteins and DNA-functionalized nanoparticles. The nanocubes can self-assemble into various finite-sized aggregates ranging from rods to self-avoiding random walks, depending on the number and placement of the hydrophobic faces. Our study focuses on suspensions containing multi- and one-patch cubes, with their ratio systematically varied. When the binding energy is comparable to the thermal energy, the aggregates consist of only few cubes that spontaneously associate/dissociate. However, highly stable aggregates emerge when the binding energy exceeds the thermal energy. Generally, the mean aggregation number of the self-assembled clusters increases with the number of hydrophobic faces and decreases with increasing fraction of one-patch cubes. In sheared suspensions, the more frequent collisions between nanocube clusters lead to faster aggregation dynamics but also to smaller terminal steady-state mean cluster sizes. The results from the MD and KMC simulations are in excellent agreement for all investigated two-patch cases, whereas the three-patch cubes form systematically smaller clusters in the MD simulations compared to the KMC calculations due to finite-size effects and slow aggregation kinetics. By analyzing the rate kernels, we are able to identify the primary mechanisms responsible for (shear-induced) cluster growth and breakup. This understanding allows us to tune nanoparticle and process parameters to achieve desired cluster sizes and shapes.

Self-Assembly of Amphiphilic Cubes in Suspension

We study the self-assembly of amphiphilic cubic colloids using molecular dynamics as well as rejection-free kinetic Monte Carlo simulations. We vary both the number and location of the solvophobic faces (patches) on the cubes at several colloid volume fractions and determine the resulting size and shape distributions of the self-assembled aggregates. When the binding energy is comparable to the thermal energy of the system, aggregates typically consist of only few spontaneously associating/dissociating colloids. Increasing the binding energy (or lowering the temperature) leads to the emergence of highly stable aggregates, e.g., small dimers in pure suspensions of one-patch cubes or large (system-spanning) aggregates in suspensions of multipatch colloids. In mixtures of one- and multipatch cubes, the average aggregation number increases with increasing number of solvophobic faces on the multipatch cubes as well with increasing fraction of multipatch cubes. The resulting aggregate shapes range from elongated rods over fractal objects to compact spheres, depending on the number and arrangement of solvophobic patches on the cubic colloids. Our findings establish the complex self-assembly pathways for a class of building blocks that combine both interaction and shape anisotropy, with the potential of forming hierarchically ordered superstructures.

Diffusion and sedimentation in colloidal suspensions using multiparticle collision dynamics with a discrete particle model

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 experimental data and 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 solvent at short times. However, the long-time self-diffusion coefficient in MD+MPCD is comparable to that in experiments, and the sedimentation coefficient in MD+MPCD is in good agreement with that in experiments and BD+RPY, suggesting that MD+MPCD gives a reasonable description of hydrodynamic interactions in colloidal suspensions. The discrete-particle MD+MPCD approach is convenient and readily extended to more complex shapes, and we determine the long-time self-diffusion coefficient in suspensions of nearly hard cubes to demonstrate its generality.

Multi-ciliated microswimmers-metachronal coordination and helical swimming

The dynamics and motion of multi-ciliated microswimmers with a spherical body and a small number N (with [Formula: see text]) of cilia with length comparable to the body radius, is investigated by mesoscale hydrodynamics simulations. A metachronal wave is imposed for the cilia beat, for which the wave vector has both a longitudinal and a latitudinal component. The dynamics and motion is characterized by the swimming velocity, its variation over the beat cycle, the spinning velocity around the main body axis, as well as the parameters of the helical trajectory. Our simulation results show that the microswimmer motion strongly depends on the latitudinal wave number and the longitudinal phase lag. The microswimmers are found to swim smoothly and usually spin around their own axis. Chirality of the metachronal beat pattern generically generates helical trajectories. In most cases, the helices are thin and stretched, i.e., the helix radius is about an order of magnitude smaller than the pitch. The rotational diffusion of the microswimmer is significantly smaller than the passive rotational diffusion of the body alone, which indicates that the extended cilia contribute strongly to the hydrodynamic radius. The swimming velocity is found to increase with the cilia number N with a slightly sublinear power law, consistent with the behavior expected from the dependence of the transport velocity of planar cilia arrays on the cilia separation.

Smoothed profile method for direct numerical simulations of hydrodynamically interacting particles

A general method is presented for computing the motions of hydrodynamically interacting particles in various kinds of host fluids for arbitrary Reynolds numbers. The method follows the standard procedure for performing direct numerical simulations (DNS) of particulate systems, where the Navier-Stokes equation must be solved consistently with the motion of the rigid particles, which defines the temporal boundary conditions to be satisfied by the Navier-Stokes equation. The smoothed profile (SP) method provides an efficient numerical scheme for coupling the continuum fluid mechanics with the dispersed moving particles, which are allowed to have arbitrary shapes. In this method, the sharp boundaries between solid particles and the host fluid are replaced with a smeared out thin shell (interfacial) region, which can be accurately resolved on a fixed Cartesian grid utilizing a SP function with a finite thickness. The accuracy of the SP method is illustrated by comparison with known exact results. In the present paper, the high degree of versatility of the SP method is demonstrated by considering several types of active and passive particle suspensions.

Flagellar arrangements in elongated peritrichous bacteria: bundle formation and swimming properties

The surface distribution of flagella in peritrichous bacterial cells has been traditionally assumed to be random. Recently, the presence of a regular grid-like pattern of basal bodies has been suggested. Experimentally, the manipulation of the anchoring points of flagella in the cell membrane is difficult, and thus, elucidation of the consequences of a particular pattern on bacterial locomotion is challenging. We analyze the bundle formation process and swimming properties of Bacillus subtilis-like cells considering random, helical, and ring-like arrangements of flagella by means of mesoscale hydrodynamics simulations. Helical and ring patterns preferentially yield configurations with a single bundle, whereas configurations with no clear bundles are most likely for random anchoring. For any type of pattern, there is an almost equally low probability to form V-shaped bundle configurations with at least two bundles. Variation of the flagellum length yields a clear preference for a single major bundle in helical and ring patterns as soon as the flagellum length exceeds the body length. The average swimming speed of cells with a single or two bundles is rather similar, and approximately [Formula: see text] larger than that of cells of other types of flagellar organization. Considering the various anchoring patterns, rings yield the smallest average swimming speed independent of the type of bundle, followed by helical arrangements, and largest speeds are observed for random anchoring. Hence, a regular pattern provides no advantage in terms of swimming speed compared to random anchoring of flagella, but yields more likely single-bundle configurations.

Structure and Shear Response of Janus Colloid-Polymer Mixtures in Solution

We investigate the structure and rheological properties of dilute colloid-polymer mixtures at rest and under shear via molecular simulations that take into account hydrodynamic interactions. Mixtures of amphiphilic Janus colloids (JCs) and hydrophobic/amphiphilic polymers are considered for various solvent qualities and polymer concentrations. Free polymers, small polymer droplets, and hybrid aggregates coexist in mixtures with slightly hydrophobic homopolymers. As the solvent quality worsens, all polymers aggregate into small droplets, covered and stabilized by the JCs. In mixtures with amphiphilic polymers, we observe the coexistence of free polymers, purely polymeric micelles, and hybrid aggregates. At low shear rates, all mixtures exhibit a Newtonian-like response with intrinsic shear viscosities that are up to 2 times as large as of pure suspensions of nonadsorbing colloids at the same concentration. Furthermore, the mean aggregation number increases slightly due to the flow-enhanced collision of aggregates. At larger shear rates, however, the aggregates break up, the polymers align in the flow direction, and the mixtures exhibit shear-thinning. This shear-induced breakup occurs at stronger shear compared to pure JC suspensions, indicating that the adsorbed polymers reinforce the hybrid aggregates.

Wall entrapment of peritrichous bacteria: a mesoscale hydrodynamics simulation study

Microswimmers such as E. coli bacteria accumulate and exhibit an intriguing dynamics near walls, governed by hydrodynamic and steric interactions. Insight into the underlying mechanisms and predominant interactions demand a detailed characterization of the entrapment process. We employ a mesoscale hydrodynamics simulation approach to study entrapment of an E. coli-type cell at a no-slip wall. The cell is modeled by a spherocylindrical body with several explicit helical flagella. Three stages of the entrapment process can be distinguished: the approaching regime, where a cell swims toward a wall on a nearly straight trajectory; a scattering regime, where the cell touches the wall and reorients; and a surface-swimming regime. Our simulations show that steric interactions may dominate the entrapment process, yet, hydrodynamic interactions slow down the adsorption dynamics close to the boundary and imply a circular motion on the wall. The locomotion of the cell is characterized by a strong wobbling dynamics, with cells preferentially pointing toward the wall during surface swimming.

Hydrodynamics of polymers in an active bath

The conformational and dynamical properties of active polymers in solution are determined by the nature of the activity. Here, the behavior of polymers with self-propelled, active Brownian particle-type monomers differs qualitatively from that of polymers with monomers driven externally by colored-noise forces. We present simulation and theoretical results for polymers in solution in the presence of external active noise. In simulations, a semiflexible bead-spring chain is considered, in analytical calculations, a continuous linear wormlike chain. Activity is taken into account by independent monomer or site velocities, with orientations changing in a diffusive manner. In simulations, hydrodynamic interactions (HIs) are taken into account by the Rotne-Prager-Yamakawa tensor or by an implementation of the active polymer in the multiparticle-collision-dynamics approach for fluids. To arrive at an analytical solution, the preaveraged Oseen tensor is employed. The active process implies a dependence of the stationary-state properties on HIs via the polymer relaxation times. With increasing activity, HIs lead to an enhanced swelling of flexible polymers, and the conformational properties differ substantially from those of polymers with self-propelled monomers in the presence of HIs, or free-draining polymers. The polymer mean-square displacement is enhanced by HIs. Over a wide range of timescales, hydrodynamics leads to a subdiffusive regime of the site mean-square displacement for flexible active polymers, with an exponent of 5/7, larger than that of the Rouse (1/2) and Zimm (2/3) models of passive polymers.

Structure and dynamics of amphiphilic Janus spheres and spherocylinders under shear

We study the structure formation and flow properties of colloidal dispersions comprised of Janus spheres, Janus spherocylinders, and their mixtures, using hybrid molecular dynamics simulations that take into account hydrodynamic interactions. We systematically vary the Janus balance and the shape anisotropy of the particles, and explore a range of colloid volume fractions in the liquid regime of the phase diagram. At rest, Janus spheres with small hydrophobic patches form spherical micelles for all investigated colloid concentrations. In contrast, Janus spheres with an entirely hydrophobic hemisphere aggregate to larger worm-like micelles and network-like structures. Janus spherocylinders exhibit a similar self-assembly behavior. At small and intermediate shear, we observe deformation and rearrangement of the micelles, accompanied by a Newtonian-like rheology with slightly higher shear viscosity compared to homoparticle dispersions at the same concentration. As the shear rate is increased further, the micelles eventually break up into small dimers and free particles, causing a distinct shear-thinning of the dispersions. The network-like structures exhibit a similar flow behavior at high shear rates, but for weak shear we find an almost threefold increase of the shear viscosity and a distinct shear-thinning behavior due to the fracturing of the intertwined networks. In general, we identify a strong correlation between the size of the aggregates and the rheology of the dispersions, allowing for the determination of dynamic properties solely based on structural information.

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.

Colloidal swimmers near curved and structured walls

We present systematic numerical simulations to understand the behavior of colloidal swimmers near a wall. We extend previous theoretical calculations based on lubrication theory to include walls with arbitrary curvature, and show how to extract from simulations a set of parameters crucial to accurately estimate the leading hydrodynamic contributions associated with the curvature of a wall. Our results show explicitly how introducing curvature to the wall not only affects the average incident angle the swimmer acquires when swimming near it, but it also leads to much broader angular distributions. This suggests an increasingly leading role of thermal fluctuations with curvature, which in turn results in significantly different motility of the swimmers. We also show how the backwards motion previously reported for pushers also extends to puller-like swimmers under the appropriate conditions. Finally, aiming at understanding the behavior of colloidal swimmers near a colloidal crystal, we also considered the case of a wall built from colloidal particles that are either free to rotate, representing a crystal held together by isotropic forces, or have their rotational degrees of freedom locked-in, representing a crystal held together by directional interactions. In both cases, we find that puller-like swimmers follow a stochastic run-and-tumble-like dynamics.

Bridging the gap between molecular dynamics and hydrodynamics in nanoscale Brownian motions

Through molecular dynamics simulations, we examined the hydrodynamic behavior of the Brownian motion of fullerene particles based on molecular interactions. The solvation free energy and velocity autocorrelation function (VACF) were calculated by using the Lennard-Jones (LJ) and Weeks-Chandler-Andersen (WCA) potentials for the solute-solvent and solvent-solvent interactions and by changing the size of the fullerene particles. We also measured the diffusion constant of the fullerene particles and the shear viscosity of the host fluid, and then the hydrodynamic radius aHD was quantified from the Stokes-Einstein relation. The aHD value exceeds that of the gyration radius of the fullerene when the solvation free energy exhibits largely negative values using the LJ potential. In contrast, aHD is similar to the size of bare fullerene when the solvation free energy is positive using the WCA potential. Furthermore, the VACF of the fullerene particles is directly comparable with the analytical expressions utilizing the Navier-Stokes equations both in incompressible and compressible forms. A hydrodynamic long-time tail t-3/2 is demonstrated for timescales longer than the kinematic time of the momentum diffusion over the particle size. However, the VACF at shorter timescales deviates from the hydrodynamic description, particularly for smaller fullerene particles and for the LJ potential. This occurs even though the compressible effect is considered when characterizing the decay of the VACF around the sound-propagation timescale over the particle size. These results indicate that the nanoscale Brownian motion is influenced by the solvation structure around the solute particles originating from the molecular interaction.

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.

Clustering and dynamics of particles in dispersions with competing interactions: theory and simulation

Dispersions of particles with short-range attractive and long-range repulsive interactions exhibit rich equilibrium microstructures and a complex phase behavior. We present theoretical and simulation results for structural and, in particular, short-time diffusion properties of a colloidal model system with such interactions, both in the dispersed-fluid and equilibrium-cluster phase regions. The particle interactions are described by a generalized Lennard-Jones-Yukawa pair potential. For the theoretical-analytical description, we apply the hybrid Beenakker-Mazur pairwise additivity (BM-PA) scheme. The static structure factor input to this scheme is calculated self-consistently using the Zerah-Hansen integral equation theory approach. In the simulations, a hybrid simulation method is adopted, combing molecular dynamics simulations of colloids with the multiparticle collision dynamics approach for the fluid, which fully captures hydrodynamic interactions. The comparison of our theoretical and simulation results confirms the high accuracy of the BM-PA scheme for dispersed-fluid phase systems. For particle attraction strengths exceeding a critical value, our simulations yield an equilibrium cluster phase. Calculations of the mean lifetime of the appearing clusters and the comparison with the analytical prediction of the dissociation time of an isolated particle pair reveal quantitative differences pointing to the importance of many-particle hydrodynamic interactions for the cluster dynamics. The cluster lifetime in the equilibrium-cluster phase increases far stronger with increasing attraction strength than that in the dispersed-fluid phase. Moreover, significant changes in the cluster shapes are observed in the course of time. Hence, an equilibrium-cluster dispersion cannot be treated dynamically as a system of permanent rigid bodies.

Static and dynamic light scattering by red blood cells: A numerical study

Light scattering is a well-established experimental technique, which gains more and more popularity in the biological field because it offers the means for non-invasive imaging and detection. However, the interpretation of light-scattering signals remains challenging due to the complexity of most biological systems. Here, we investigate static and dynamic scattering properties of red blood cells (RBCs) using two mesoscopic hydrodynamics simulation methods—multi-particle collision dynamics and dissipative particle dynamics. Light scattering is studied for various membrane shear elasticities, bending rigidities, and RBC shapes (e.g., biconcave and stomatocyte). Simulation results from the two simulation methods show good agreement, and demonstrate that the static light scattering of a diffusing RBC is not very sensitive to the changes in membrane properties and moderate alterations in cell shapes. We also compute dynamic light scattering of a diffusing RBC, from which dynamic properties of RBCs such as diffusion coefficients can be accessed. In contrast to static light scattering, the dynamic measurements can be employed to differentiate between the biconcave and stomatocytic RBC shapes and generally allow the differentiation based on the membrane properties. Our simulation results can be used for better understanding of light scattering by RBCs and the development of new non-invasive methods for blood-flow monitoring.

Dramatic influence of patchy attractions on short-time protein diffusion under crowded conditions

In the dense and crowded environment of the cell cytoplasm, an individual protein feels the presence of and interacts with all surrounding proteins. While we expect this to strongly influence the short-time diffusion coefficient D_s of proteins on length scales comparable to the nearest-neighbor distance, this quantity is difficult to assess experimentally. We demonstrate that quantitative information about D_s can be obtained from quasi-elastic neutron scattering experiments using the neutron spin echo technique. We choose two well-characterized and highly stable eye lens proteins, bovine α-crystallin and γ_B-crystallin, and measure their diffusion at concentrations comparable to those present in the eye lens. While diffusion slows down with increasing concentration for both proteins, we find marked variations that are directly linked to subtle differences in their interaction potentials. A comparison with computer simulations shows that anisotropic and patchy interactions play an essential role in determining the local short-time dynamics. Hence, our study clearly demonstrates the enormous effect that weak attractions can have on the short-time diffusion of proteins at concentrations comparable to those in the cellular cytosol.

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.

The raspberry model for hydrodynamic interactions revisited. I. Periodic arrays of spheres and dumbbells

The so-called "raspberry" model refers to the hybrid lattice-Boltzmann and Langevin molecular dynamics scheme for simulating the dynamics of suspensions of colloidal particles, originally developed by Lobaskin and Dünweg [New J. Phys. 6, 54 (2004)], wherein discrete surface points are used to achieve fluid-particle coupling. This technique has been used in many simulation studies on the behavior of colloids. However, there are fundamental questions with regards to the use of this model. In this paper, we examine the accuracy with which the raspberry method is able to reproduce Stokes-level hydrodynamic interactions when compared to analytic expressions for solid spheres in simple-cubic crystals. To this end, we consider the quality of numerical experiments that are traditionally used to establish these properties and we discuss their shortcomings. We show that there is a discrepancy between the translational and rotational mobility reproduced by the simple raspberry model and present a way to numerically remedy this problem by adding internal coupling points. Finally, we examine a non-convex shape, namely, a colloidal dumbbell, and show that the filled raspberry model replicates the desired hydrodynamic behavior in bulk for this more complicated shape. Our investigation is continued in de Graaf et al. [J. Chem. Phys. 143, 084108 (2015)], wherein we consider the raspberry model in the confining geometry of two parallel plates.

Hydrodynamic correlations in shear flow: Multiparticle-collision-dynamics simulation study

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 wave 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 simulations reveal the directional dependence of the frequency and attenuation of the longitudinal velocity correlation function. Furthermore, the velocity autocorrelation functions of a tagged fluid particle in shear flow are determined. The simulation results for various hydrodynamic correlations agree very well with the theoretical predictions.

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.

Multi-particle collision dynamics algorithm for nematic fluids

Research on transport, self-assembly and defect dynamics within confined, flowing liquid crystals requires versatile and computationally efficient mesoscopic algorithms to account for fluctuating nematohydrodynamic interactions. We present a multi-particle collision dynamics (MPCD) based algorithm to simulate liquid-crystal hydrodynamic and director fields in two and three dimensions. The nematic-MPCD method is shown to successfully reproduce the features of a nematic liquid crystal, including a nematic-isotropic phase transition with hysteresis in 3D, defect dynamics, isotropic Frank elastic coefficients, tumbling and shear alignment regimes and boundary condition-dependent order parameter fields.

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.