Many-body Hydrodynamic Interactions Research Articles

Mechanical Slowing Down of Network-Forming Phase Separation of Polymer Solutions.

Phase separation is a fundamental phenomenon leading to spatially heterogeneous material distribution, which is critical in nature, biology, material science, and industry. In ordinary phase separation, the minority phase always forms droplets. Contrary to this common belief, even the minority phase can form a network structure in viscoelastic phase separation (VPS). VPS can occur in any mixture with significant mobility differences between their components and is highly relevant to soft matter and biomatter. In contrast to classical phase separation, experiments have shown that VPS in polymer solutions lacks self-similar coarsening, resulting in the absence of a domain-coarsening scaling law. However, the underlying microscopic mechanism of this behavior remains unknown. To this end, we perform fluid particle dynamics simulations of bead-spring polymers, incorporating many-body hydrodynamic interactions between polymers through a solvent. We discover that polymers in the dense-network-forming phase are stretched and store elastic energy when the deformation speed exceeds the polymer dynamics. This self-generated viscoelastic stress mechanically interferes with phase separation and slows its dynamics, disrupting self-similar growth. We also highlight the essential role of many-body hydrodynamic interactions in VPS. The implications of our findings may hold importance in areas such as biological phase separation, porous material formation, and other fields where network structures play a pivotal role.

Impact of Inverse Squeezing Flow on the Self-Assembly of Oppositely Charged Colloidal Particles under Electric Field

Hydrodynamic interactions (HIs) play a critical role in the self-organization of colloidal suspensions and biological solutions. However, their roles have remained elusive particularly for charged soft matter systems. Here we consider the role of HIs in the self-assembly of oppositely charged colloidal particles, which is a promising candidate for electrical tunable soft materials. We employ the fluid particle dynamics method to consider many-body HIs and the coupling between the colloid, ion, and fluid motions. We find that, under a constant electric field, oppositely charged colloidal particles form clusters and percolate into a gel network, unlike bundlelike aggregates aligned in the field direction observed by Brownian dynamics simulations neglecting HIs. We reveal that the cluster-forming tendency originates from the incompressibility-induced "inverse squeezing flow" effect that dramatically slows down the disaggregation of attached colloids. Our findings indicate that the HI selects a unique kinetic pathway to the nonequilibrium colloidal self-assembly.

Active Stokesian dynamics

Since its development, Stokesian dynamics has been a leading approach for the dynamic simulation of suspensions of particles at arbitrary concentrations with full hydrodynamic interactions. Although developed originally for the simulation of passive particle suspensions, the Stokesian dynamics framework is equally well suited to the analysis and dynamic simulation of suspensions of active particles, as we elucidate here. We show how the reciprocal theorem can be used to formulate the exact dynamics for a suspension of arbitrary active particles, and then show how the Stokesian dynamics method provides a rigorous way to approximate and compute the dynamics of dense active suspensions where many-body hydrodynamic interactions are important.

Theoretical consideration of the rheological properties of aggregated suspensions

The rheological properties of particulate dispersions containing aggregate structures were theoretically investigated in this study. Under the assumption of Stokes flow, the viscosity of fluids with fine particles was derived by a theoretical method based on the multipole expansion in reciprocal space. In this method, many-body hydrodynamic interactions were considered as the multipole-expanded moment of the force density at the surface of the particles. It is possible to calculate the viscosity of particulate suspensions by considering higher-order moments. The viscosity of monodisperse particulate suspensions was calculated under various conditions. To verify the accuracy of the calculation, the viscosity of uniformly distributed particulate suspensions was calculated, and the results were compared with the experimental results of previous studies. The calculated viscosities were in good agreement with the experimental results for a wide range of particle volumetric concentrations. The viscosity of aggregated suspensions was also calculated to examine the mechanism of viscosity change. The viscosity was systematically calculated with changing the aggregate size and particle concentration. The results indicate that the hydrodynamic effect is not significant on the viscosity change by aggregation, which is contrary to the assumption of previous viscosity models. The calculation results suggest that the increase in the viscosity of aggregated suspensions is instead caused by the direct influence of inter-particle forces.

Impact of polydispersity and confinement on diffusion in hydrodynamically interacting colloidal suspensions

We present a computational study of the equilibrium dynamics of a polydisperse hard-sphere colloidal dispersion confined in a spherical cavity. We account for many-body hydrodynamic and lubrication interactions between particles and with the confining cavity utilizing our confined Stokesian dynamics model, expanded here for size polydispersity. We find that, even though the tendency of polydispersity to homogenize structure in a suspension is still present in confinement, strong correlations induced by the cavity resist homogenization. Although seemingly opposite, these two effects have a common driver, which is to maximize configurational entropy of particles in the cavity interior. These structural effects couple with the hydrodynamics to change the particle dynamics: polydispersity weakens lubrication effects near the cavity wall, allowing small (large) particles to diffuse faster (slower) than in a monodisperse suspension. As a small (large) particle gets farther from the wall, polydispersity weakens many-body hydrodynamic couplings, driving diffusivity up (down). While the local cage dynamics dominates short-time self-diffusion, long-time dynamics is also affected. In the concentrated regime, polydispersity and confinement combine to induce radial de-mixing into size-segregated populations. The cavity becomes the most influential ‘nearest neighbour’, setting the length scale of and dynamics within these radial domains. This intermediate length-scale caging makes the angular dynamics insensitive to polydispersity but leads to radial long-time mean-square displacement that changes qualitatively with volume composition. These results hold promise for explaining colloidal-scale physics implicated in the functioning of biological cells, and the engineering of non-living confined colloids where size de-mixing could be useful in the design of encapsulated micro-reactors and therapeutic vesicles.

PyStokes: phoresis and Stokesian hydrodynamics in Python

We present a modular Python library for computing many-body hydrodynamic and phoretic interactions between spherical active particles in suspension, when these are given by solutions of the Stokes and Laplace equations. Underpinning the library is a grid-free methodology that combines dimensionality reduction, spectral expansion, and Ritz-Galerkin discretization, thereby reducing the computation to the solution of a linear system. The system can be solved analytically as a series expansion or numerically at a cost quadratic in the number of particles. Suspension-scale quantities like fluid flow, entropy production, and rheological response are obtained at a small additional cost. The library is agnostic to boundary conditions and includes, amongst others, confinement by plane walls or liquid-liquid interfaces. The use of the library is demonstrated with six fully coded examples simulating active phenomena of current experimental interest.

Numerical prediction of colloidal phase separation by direct computation of Navier\u2013Stokes equation

Numerical prediction of out-of-equilibrium processes in soft and bio matter containing liquids is highly desirable. However, it is quite challenging primarily because the motions of the components at different hierarchical levels (e.g., large colloids and small solvent molecules) are spatio-temporally coupled in a complicated manner via momentum conservation. Here we critically examine the predictability of numerical simulations for colloidal phase separation as a prototype example of self-organization of soft materials containing a liquid. We use coarse-grained hydrodynamic simulations to tackle this problem, and succeed in almost perfectly reproducing the structural and topological evolution experimentally observed by three-dimensional confocal microscopy without any adjustable parameters. Furthermore, comparison with non-hydrodynamic simulations shows the fundamental importance of many-body hydrodynamic interactions in colloidal phase separation. The predictive power of our computational approach may significantly contribute to not only the basic understanding of the dynamical behavior and self-organization of soft, bio and active matter but also the computer-aided design of colloidal materials.

Coupling of Nanoparticle Dynamics to Polymer Center-of-Mass Motion in Semidilute Polymer Solutions

We investigate the dynamics of nanoparticles in semidilute polymer solutions when the nanoparticles are comparably sized to the polymer coils using explicit- and implicit-solvent simulation methods. The nanoparticle dynamics are subdiffusive on short time scales before transitioning to diffusive motion on long time scales. The long-time diffusivities scale according to theoretical predictions based on full dynamic coupling to the polymer segmental relaxations. In agreement with our recent experiments, however, we observe that the nanoparticle subdiffusive exponents are significantly larger than predicted by the coupling theory over a broad range of polymer concentrations. We attribute this discrepancy in the subdiffusive regime to the presence of an additional coupling mechanism between the nanoparticle dynamics and the polymer center-of-mass motion, which differs from the polymer relaxations that control the long-time diffusion. This coupling is retained even in the absence of many-body hydrodynamic interactions when the long-time dynamics of the colloids and polymers are matched.

Physical foundation of the fluid particle dynamics method for colloid dynamics simulation

Colloid dynamics is significantly influenced by many-body hydrodynamic interactions mediated by a suspending fluid. However, theoretical and numerical treatments of such interactions are extremely difficult. To overcome this situation, we developed a fluid particle dynamics (FPD) method [H. Tanaka and T. Araki, Phys. Rev. Lett., 2000, 35, 3523], which is based on two key approximations: (i) a colloidal particle is treated as a highly viscous particle and (ii) the viscosity profile is described by a smooth interfacial profile function. Approximation (i) makes our method free from the solid-fluid boundary condition, significantly simplifying the treatment of many-body hydrodynamic interactions while satisfying the incompressible condition without the Stokes approximation. Approximation (ii) allows us to incorporate an extra degree of freedom in a fluid, e.g., orientational order and concentration, as an additional field variable. Here, we consider two fundamental problems associated with these approximations. One is the introduction of thermal noise and the other is the incorporation of coupling of the colloid surface with an order parameter introduced into a fluid component, which is crucial when considering colloidal particles suspended in a complex fluid. Here, we show that our FPD method makes it possible to simulate colloid dynamics properly while including full hydrodynamic interactions, inertia effects, incompressibility, thermal noise, and additional degrees of freedom of a fluid, which may be relevant for wide applications in colloidal and soft matter science.

Equilibrium structure and diffusion in concentrated hydrodynamically interacting suspensions confined by a spherical cavity

The short- and long-time equilibrium transport properties of a hydrodynamically interacting suspension confined by a spherical cavity are studied via Stokesian dynamics simulations for a wide range of particle-to-cavity size ratios and particle concentrations. Many-body hydrodynamic and lubrication interactions between particles and with the cavity are accounted for utilizing recently developed mobility and resistance tensors for spherically confined suspensions (Aponte-Rivera & Zia, Phys. Rev. Fluids, vol. 1(2), 2016, 023301). Study of particle volume fractions in the range $0.05\leqslant \unicode[STIX]{x1D719}\leqslant 0.40$ reveals that confinement exerts a qualitative influence on particle diffusion. First, the mean-square displacement over all time scales depends on the position in the cavity. Additionally, at short times, the diffusivity is anisotropic, with diffusion along the cavity radius slower than diffusion tangential to the cavity wall, due to the anisotropy of hydrodynamic coupling and to confinement-induced spatial heterogeneity in particle concentration. The mean-square displacement is anisotropic at intermediate times as well and, surprisingly, exhibits superdiffusive and subdiffusive behaviours for motion along and perpendicular to the cavity radius respectively, depending on the suspension volume fraction and the particle-to-cavity size ratio. No long-time self-diffusive regime exists; instead, the mean-square displacement reaches a long-time plateau, a result of entropic restriction to a finite volume. In this long-time limit, the higher the volume fraction is, the longer the particles take to reach the long-time plateau, as cooperative rearrangements are required as the cavity becomes crowded. The ordered dynamical heterogeneity seen here promotes self-organization of particles based on their size and self-mobility, which may be of particular relevance in biophysical systems.

Pair mobility functions for rigid spheres in concentrated colloidal dispersions: Stresslet and straining motion couplings.

Accurate modeling of particle interactions arising from hydrodynamic, entropic, and other microscopic forces is essential to understanding and predicting particle motion and suspension behavior in complex and biological fluids. The long-range nature of hydrodynamic interactions can be particularly challenging to capture. In dilute dispersions, pair-level interactions are sufficient and can be modeled in detail by analytical relations derived by Jeffrey and Onishi [J. Fluid Mech. 139, 261-290 (1984)] and Jeffrey [Phys. Fluids A 4, 16-29 (1992)]. In more concentrated dispersions, analytical modeling of many-body hydrodynamic interactions quickly becomes intractable, leading to the development of simplified models. These include mean-field approaches that smear out particle-scale structure and essentially assume that long-range hydrodynamic interactions are screened by crowding, as particle mobility decays at high concentrations. Toward the development of an accurate and simplified model for the hydrodynamic interactions in concentrated suspensions, we recently computed a set of effective pair of hydrodynamic functions coupling particle motion to a hydrodynamic force and torque at volume fractions up to 50% utilizing accelerated Stokesian dynamics and a fast stochastic sampling technique [Zia et al., J. Chem. Phys. 143, 224901 (2015)]. We showed that the hydrodynamic mobility in suspensions of colloidal spheres is not screened, and the power law decay of the hydrodynamic functions persists at all concentrations studied. In the present work, we extend these mobility functions to include the couplings of particle motion and straining flow to the hydrodynamic stresslet. The couplings computed in these two articles constitute a set of orthogonal coupling functions that can be utilized to compute equilibrium properties in suspensions at arbitrary concentration and are readily applied to solve many-body hydrodynamic interactions analytically.

A fast platform for simulating semi-flexible fiber suspensions applied to cell mechanics

We present a novel platform for the large-scale simulation of three-dimensional fibrous structures immersed in a Stokesian fluid and evolving under confinement or in free-space in three dimensions. One of the main motivations for this work is to study the dynamics of fiber assemblies within biological cells. For this, we also incorporate the key biophysical elements that determine the dynamics of these assemblies, which include the polymerization and depolymerization kinetics of fibers, their interactions with molecular motors and other objects, their flexibility, and hydrodynamic coupling. This work, to our knowledge, is the first technique to include many-body hydrodynamic interactions (HIs), and the resulting fluid flows, in cellular assemblies of flexible fibers. We use non-local slender body theory to compute the fluid–structure interactions of the fibers and a second-kind boundary integral formulation for other rigid bodies and the confining boundary. A kernel-independent implementation of the fast multipole method is utilized for efficient evaluation of HIs. The deformation of the fibers is described by nonlinear Euler–Bernoulli beam theory and their polymerization is modeled by the reparametrization of the dynamic equations in the appropriate non-Lagrangian frame. We use a pseudo-spectral representation of fiber positions and implicit time-stepping to resolve large fiber deformations, and to allow time-steps not excessively constrained by temporal stiffness or fiber–fiber interactions. The entire computational scheme is parallelized, which enables simulating assemblies of thousands of fibers. We use our method to investigate two important questions in the mechanics of cell division: (i) the effect of confinement on the hydrodynamic mobility of microtubule asters; and (ii) the dynamics of the positioning of mitotic spindle in complex cell geometries. Finally to demonstrate the general applicability of the method, we simulate the sedimentation of a cloud of semi-flexible fibers.

Active microrheology of colloidal suspensions: Simulation and microstructural theory

Discrete particle simulations by accelerated Stokesian dynamics (ASD) and a microstructural theory are applied to study the structure and viscosity of hard-sphere Brownian suspensions in active microrheology (MR). The work considers moderate to dense suspensions, from near to far from equilibrium conditions. The microscopic theory explicitly considers many-body hydrodynamic interactions in active MR and is compared with the results of ASD simulations, which include detailed near- and far-field hydrodynamic interactions. We consider probe and bath particles which are spherical and of the same radius a. Two conditions of moving the probe sphere are considered: These apply constant force (CF) and constant velocity (CV), which approximately model magnetic bead and optical tweezer experiments, respectively. The structure is quantified using the probability distribution of colloidal particles around the probe, Pb|p(r)=ng(r), giving the probability of finding a bath particle centered at a vector position r relative to a moving probe particle instantaneously centered at the origin; n is the bath particles number density, and is related to the suspension solid volume fraction, ϕ, by n=3ϕ/4πa3. The pair distribution function for the bath particles relative to the probe, g(r), is computed as a solution to the pair Smoluchowski equation (SE) for 0.2≤ϕ≤0.50, and a range of Péclet numbers, describing the ratio of external force on the probe to thermal forces and defined as Pef=Fexta/(kbT) and PeU=6πηUexta2/(kbT) for CF and CV conditions, respectively. Results of simulation and theory demonstrate that a wake zone depleted of bath particles behind the moving probe forms at large Péclet numbers, while a boundary-layer accumulation develops upstream and near the probe. The wake length saturates at Pef≫1 for CF, while it continuously grows with PeU in CV. This contrast in behavior is related to the dispersion in the motion of the probe under CF conditions, while CV motion has no dispersion; the dispersion is a direct result of many-body nonthermal interactions. This effect is incorporated in the theory as a force-induced diffusion flux in pair SE. We also demonstrate that, despite this difference of structure in the two methods of moving the probe, the probability distribution of particles near the probe is primarily set by the Péclet number, for both CF and CV conditions, in agreement with dilute theories; as a consequence, similar values for apparent viscosity are found for the CF and CV conditions. Using the microscopic theory, the structural anisotropy and Brownian viscosity near equilibrium are shown to be quantitatively similar in both CF and CV motions, which is in contrast with the dilute theory which predicts larger distortions and Brownian viscosities in CV, by a factor of two relative to CF MR. This difference relative to dilute theory arises due to the determining role of many-body interactions associated with the underlying equilibrium structure in the semidilute to concentrated regime.

Simulation of hydrodynamically interacting particles confined by a spherical cavity

In order to study diffusion and rheology within a spherical cavity, a theoretical framework is used to model the motion of an arbitrary number of hydrodynamically interacting colloidal particles confined within a solid, continuous spherical cavity. The model accurately accounts for many-body hydrodynamic interactions and lubrication interactions that occur between particles and with the cavity.

Pair mobility functions for rigid spheres in concentrated colloidal dispersions: Force, torque, translation, and rotation.

The formulation of detailed models for the dynamics of condensed soft matter including colloidal suspensions and other complex fluids requires accurate description of the physical forces between microstructural constituents. In dilute suspensions, pair-level interactions are sufficient to capture hydrodynamic, interparticle, and thermodynamic forces. In dense suspensions, many-body interactions must be considered. Prior analytical approaches to capturing such interactions such as mean-field approaches replace detailed interactions with averaged approximations. However, long-range coupling and effects of concentration on local structure, which may play an important role in, e.g., phase transitions, are smeared out in such approaches. An alternative to such approximations is the detailed modeling of hydrodynamic interactions utilizing precise couplings between moments of the hydrodynamic traction on a suspended particle and the motion of that or other suspended particles. For two isolated spheres, a set of these functions was calculated by Jeffrey and Onishi [J. Fluid Mech. 139, 261-290 (1984)] and Jeffrey [J. Phys. Fluids 4, 16-29 (1992)]. Along with pioneering work by Batchelor, these are the touchstone for low-Reynolds-number hydrodynamic interactions and have been applied directly in the solution of many important problems related to the dynamics of dilute colloidal dispersions [G. K. Batchelor and J. T. Green, J. Fluid Mech. 56, 375-400 (1972) and G. K. Batchelor, J. Fluid Mech. 74, 1-29 (1976)]. Toward extension of these functions to concentrated systems, here we present a new stochastic sampling technique to rapidly calculate an analogous set of mobility functions describing the hydrodynamic interactions between two hard spheres immersed in a suspension of arbitrary concentration, utilizing accelerated Stokesian dynamics simulations. These mobility functions provide precise, radially dependent couplings of hydrodynamic force and torque to particle translation and rotation, for arbitrary colloid volume fraction ϕ. The pair mobilities (describing entrainment of one particle by the disturbance flow created by another) decay slowly with separation distance: as 1/r, for volume fractions 0.05 ≤ ϕ ≤ 0.5. For the relative mobility, we find an initially rapid growth as a pair separates, followed by a slow, 1/r growth. Up to ϕ ≤ 0.4, the relative mobility does not reached the far-field value even beyond separations of many particle sizes. In the case of ϕ = 0.5, the far-field asymptote is reached but only at a separation of eight radii and after a slow 1/r growth. At these higher concentrations, the coefficients also reveal liquid-like structural effects on pair mobility at close separations. These results confirm that long-range many-body hydrodynamic interactions are an essential part of the dynamics of concentrated systems and that care must be taken when applying renormalization schemes.

Two dimensional colloidal crystals formed by particle self-assembly due to hydrodynamic interaction

Aggregation and crystallization of colloidal parti- cles deposited from suspensions on glass surfaces were stud- ied. Trajectories of individual particles are tracked and record- ed. Statistics over large amount of particles were made to measure the mean square displacement (MSD), , as func- tions of time, t. Isolated particles diffuse normally along the solid surface in a two dimensional random manner. A power law of ~t α is obeyed both by short and long time scale MSDs of particles with neighbors. However, the exponent values are quite different. When the particle area fraction f≤ 80%,theparticlesdiffusenormallyattheshorttimescalewith a retarded diffusion coefficient. While at the long time scale, a superdiffusive behavior of the particles is detected due to col- lective motion of particles. When f>80 %, a spatial confine- ment effect shows in addition. The retarded particle dynamics and the collective particle movements both originate from the many-body hydrodynamic interaction enhanced by the quasi- two dimensional geometric conditions due to the existence of thesubstrateandtheneighborparticles.Ifthesubstratesurface condition is favorable and the hydrodynamic interaction dom- inates, the long-range hydrodynamic interaction can lead par- ticles in dense particle aggregations to self-assemble into long particle chains. This chaining behavior finally results in a phase transition taking place gradually over a large range of the particle area fraction.

Many-body microhydrodynamics of colloidal particles with active boundary layers

Colloidal particles with active boundary layers—regions surrounding the particles where non-equilibrium processes produce large velocity gradients—are common in many physical, chemical and biological contexts. The velocity or stress at the edge of the boundary layer determines the exterior fluid flow and, hence, the many-body interparticle hydrodynamic interaction. Here, we present a method to compute the many-body hydrodynamic interaction between N spherical active particles induced by their exterior microhydrodynamic flow. First, we use a boundary integral representation of the Stokes equation to eliminate bulk fluid degrees of freedom. Then, we expand the boundary velocities and tractions of the integral representation in an infinite-dimensional basis of tensorial spherical harmonics and, on enforcing boundary conditions in a weak sense on the surface of each particle, obtain a system of linear algebraic equations for the unknown expansion coefficients. The truncation of the infinite series, fixed by the degree of accuracy required, yields a finite linear system that can be solved accurately and efficiently by iterative methods. The solution linearly relates the unknown rigid body motion to the known values of the expansion coefficients, motivating the introduction of propulsion matrices. These matrices completely characterize hydrodynamic interactions in active suspensions just as mobility matrices completely characterize hydrodynamic interactions in passive suspensions. The reduction in the dimensionality of the problem, from a three-dimensional partial differential equation to a two-dimensional integral equation, allows for dynamic simulations of hundreds of thousands of active particles on multi-core computational architectures. In our simulation of 104 active colloidal particle in a harmonic trap, we find that the necessary and sufficient ingredients to obtain steady-state convective currents, the so-called ‘self-assembled pump’, are (a) one-body self-propulsion and (b) two-body rotation from the vorticity of the Stokeslet induced in the trap.

Short-time transport properties of bidisperse suspensions and porous media: a Stokesian dynamics study.

We present a comprehensive computational study of the short-time transport properties of bidisperse hard-sphere colloidal suspensions and the corresponding porous media. Our study covers bidisperse particle size ratios up to 4 and total volume fractions up to and beyond the monodisperse hard-sphere close packing limit. The many-body hydrodynamic interactions are computed using conventional Stokesian Dynamics (SD) via a Monte-Carlo approach. We address suspension properties including the short-time translational and rotational self-diffusivities, the instantaneous sedimentation velocity, the wavenumber-dependent partial hydrodynamic functions, and the high-frequency shear and bulk viscosities and porous media properties including the permeability and the translational and rotational hindered diffusivities. We carefully compare the SD computations with existing theoretical and numerical results. For suspensions, we also explore the range of validity of various approximation schemes, notably the pairwise additive approximations with the Percus-Yevick structural input. We critically assess the strengths and weaknesses of the SD algorithm for various transport properties. For very dense systems, we discuss in detail the interplay between the hydrodynamic interactions and the structures due to the presence of a second species of a different size.

Purely hydrodynamic ordering of rotating disks at a finite Reynolds number.

Self-organization of moving objects in hydrodynamic environments has recently attracted considerable attention in connection to natural phenomena and living systems. However, the underlying physical mechanism is much less clear due to the intrinsically nonequilibrium nature, compared with self-organization of thermal systems. Hydrodynamic interactions are believed to play a crucial role in such phenomena. To elucidate the fundamental physical nature of many-body hydrodynamic interactions at a finite Reynolds number, here we study a system of co-rotating hard disks in a two-dimensional viscous fluid at zero temperature. Despite the absence of thermal noise, this system exhibits rich phase behaviours, including a fluid state with diffusive dynamics, a cluster state, a hexatic state, a glassy state, a plastic crystal state and phase demixing. We reveal that these behaviours are induced by the off-axis and many-body nature of nonlinear hydrodynamic interactions and the finite time required for propagating the interactions by momentum diffusion.

Stability of restructured non-fractal aggregates in simple shear flow

The restructuring behavior of non-fractal aggregates in simple shear flow is numerically investigated. The change in internal structure of aggregates having different packing properties is examined by Lagrangian simulation method. The many-body hydrodynamic interaction is rigorously estimated by Stokesian dynamics approach while the adhesion of aggregate is manifested via particle–particle interaction. The simulation results show that the restructuring of aggregate originates from the superimposition of rotational and extensional component of simple shear flow. The aggregate rearranges its particles so that a stable structure corresponding to the applied shear flow is obtained. The stable structure is considered as dynamic equilibrium resulting from the balance of the forming and the disintegrating of the bonds between particles. The stable structure of aggregate is dependent strongly on shear condition but weakly on initial structure of aggregate. Despite of the significant difference in the initial packing properties, the stable structure reveals only slightly different. The dependence of stable structure on high shear tress condition is similar for all aggregates. The difference in stable structure of aggregate at low shear stress arises from the irreversible behavior of particle from quasi-stable structure to static structure.