Stokesian Dynamics Research Articles

Two-body transient viscous interactions in free space

A generalization of Stokesian dynamics is formulated to describe hydrodynamic interactions between two spheres in a viscous fluid. The analysis quantifies transient mutual interactions in terms of frequency-dependent friction coefficients of both spheres as well as their temporally varying mobility response to an impulsive force. The analysis also contributes to work on many-body unsteady Brownian motions.

The Effect of the Layered Internal Structure of Fibrous Beds on the Hydrodynamic Diffusive Behavior of Microparticles.

To separate and collect microparticles such as cells, the behavior of particles in fibrous filters was investigated. It is essential to understand, in detail, the motion of particles in microscale flows, because Re is often small, and particles exhibit complex behaviors such as changes in relative position and spreading owing to hydrodynamic interactions. We calculated the motion of microparticles passing through the fibrous bed using the Stokesian dynamics method, in which hydrodynamic interaction is considered, theoretically. The fibrous bed was modeled by particles and five types of structures (a monolayer with fiber volume fractions φ of 3%, 4%, and 5%, and a bilayer with φ = 3%−5% and 5%−3%) were considered. Our numerical results showed that the particles moved in a complicated manner, and spread throughout the fibrous bed. It was found that the behavior of individual microparticles varied depending on the internal structure, although the average permeation velocity was primarily determined by the fiber volume fraction. This great dependence of the behavior of particle assemblage on the internal structure of the fibrous bed was caused by the individual particle motion under the influence of the layers in front of and behind them, owing to the hydrodynamic interaction.

A hierarchical matrix approach for computing hydrodynamic interactions

For simulations of large numbers of small, spherical particles in a Stokes flow, the long-range hydrodynamic interactions approximated by the Rotne–Prager–Yamakawa (RPY) kernel can be summed rapidly using, for example, the fast multipole method (FMM) or the particle-mesh Ewald (PME) method. In this paper, we develop new fast methods for computing these sums using the H2 hierarchical matrix representation, for open and for periodic boundary conditions. To the best of our knowledge, the method for infinite periodic sums using the H2 hierarchical matrix representation is the first such method developed. We also consider a more general RPY kernel that handles polydisperse particle radii, and show analytically and experimentally that the proxy surface method for efficiently constructing the H2 hierarchical matrix representation remains effective in this case. Numerical tests demonstrate the well-controlled accuracy of the H2 summation methods and their linear-scaling computation and storage cost. We find that the H2 matrix approach has lower cost for computing the summations compared to FMM and PME, but higher precomputation cost (required for each particle configuration). This precomputation cost can be amortized over several summations when computing Brownian displacements or forces in Brownian and Stokesian dynamics simulations with very large numbers of particles.

Numerical analysis of the wake of complex-shaped snow particles at moderate Reynolds number

Climate model parametrization relies strongly on the prediction of snow precipitation, which in turn depends upon the snowflakes falling motion in air. The falling attitudes of such particles are elaborate because of the particles' irregular shapes, which produce meandering and turbulent wakes and give rise to convoluted trajectories. This also has an impact on the drag experienced by the particle. Especially for large snow particles falling close to the ground, Stokesian dynamics is not applicable, and the dependency of drag coefficient on Reynolds number becomes non-linear. This trend arises from the complex interaction between snowflakes and the surrounding air. We investigate the wake of complex-shaped snow particles using a validated delayed-detached eddy simulation model of airflow around a fixed snowflake, combined with experimental observations of free-falling, 3D-printed snowflake analogs. This novel approach allows us to analyze the wake topology and decompose its momentum flux to investigate the influence of shape and wake flow on the drag coefficient and its implications on falling attitudes by comparison with experiments. At low Re, the presence of separated vortex rings is connected to particle porosity and produces an increase in the drag coefficient. At moderate flow regimes, the particle flatness impacts the shear layer separation and the momentum loss in the wake, while at high Re the drag coefficient has almost the same value among the tested geometries although the contribution of different momentum flux terms differs. These results represent a further step toward a deeper understanding the drag of complex-shaped particles.

Cyclic force driven colloidal self-assembly near a solid surface

HypothesisSelf-assembled colloidal mobility out of a non-equilibrium system can depend on many external and interparticle forces including hydrodynamic forces. While the driving forces guiding colloidal suspension, translation and self-assembly are different and unique, hydrodynamic forces are always present and can significantly influence particle motion. Unfortunately, these interparticle hydrodynamic interactions are typically overlooked. ExperimentsHere, we studied the collective behavior of colloidal particles (4.0 µm PMMA), located near the solid surface in a fluid medium confined in a cylindrical cell (3.0 mm diameter, 0.25 mm height) which was rotated vertically at a low rotational speed (20 rpm). The observed colloidal behavior was then validated through a Stokesian dynamics simulation where the concept of hydrodynamic contact force or lubrication interactions are avoided which is not physically intuitive and mathematically cumbersome. Rather, we adopted hard-sphere like colloidal collision or mobility model, while adopting other useful simplification and approximations. FindingsUpon particles settling in a circular orbit, they hydrodynamically interact with each other and evolve in different structures depending on the pattern of gravity forces. Their agglomeration is a function of the applied rotation scheme, either forming colloidal clusters or lanes. While evolving into dynamic structures, colloids also laterally migrate away from the surface.

Potential Investigation on Multiphase Flow of Loaded Dispersion for the Production of Metallized Paper

The current review research's main objective is to develop dispersion models in the multilayer curtain coating with the production of metallized paper. To achieve this, the curtain coating on the paper substrate is employed with respect to multilayer coating of polymers. The first layer of polymer is applied to the paper and then it is subjected to vacuum metallization with aluminum deposition. After it, another second layer of polymer is subjected on it to prevent it from oxidation. These coated polymers are different in nature. The metallized paper will be produced which has high strength will be formulated in this application of curtain coating. The instability of curtain and air entrainment will be minimized from high Weber number, low Reynolds number, Optimum web speed and Coat weights. The above demonstrated process simulation will be modelled in Ansys-CFD. The dispersion of solids in the curtain flow through substrate moving on the web will be evaluated from different numerical methods. Each method has its own characteristics to study the nature of solids dispersion. The high loaded solids dispersion will be investigated from numerical methods including Langrangian Point Particle, Coarse grained molecular dynamics, Stokesian Dynamics, Brownian Dynamics, Point Particle Method Reynolds Averaged Navier Stokes equation, Eulerian Method, Langrangian-Eulerian Point Particle, Large Eddy Simulation point particle, Combined discrete element and Large Eddy Simulation and Discrete Element Methods.

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.

Characterization of storage modulus of starch suspensions during the initial stages of pasting using Stokesian dynamics simulations

This study performs Stokesian dynamics simulations of suspensions of rigid spheres to determine the conditions under which swollen starch granules can be considered rigid for rheology measurements. The first part of the study benchmarks the numerical simulations to experimental measurements of storage modulus (G′) for monodisperse polystyrene suspensions. The second part of the study compares the simulations to experimental measurements of G′ for waxy maize and normal rice starch suspensions swollen to volume fractions 0.4 < φ < 0.6. These starch granules were fractionated before swelling to create a narrow range of swollen granule sizes. For granules with a narrow size distribution, the Stokesian dynamics simulations quantitatively match the experimental G′ for volume fractions φ ≤ 0.5, but deviate significantly when φ > 0.5. These results indicate that granule deformability plays an important role when φ > 0.5, and indicates the range where one can apply theories of rigid suspension rheology.

Nanoparticle dispersion in porous media: Effects of array geometry and flow orientation.

We investigate the effects of array geometry and flow orientation on transport of finite-sized particles in ordered arrays using Stokesian dynamics simulations. We find that quiescent diffusion is independent of array geometry over the range of volume fraction of the nanoposts examined. Longitudinal dispersion under flow depends on the direction of incident flow relative to the array lattice vectors. Taylor-Aris behavior is recovered for flow along the lattice directions, whereas a nonmonotonic dependence of the dispersion coefficient on the Péclet number is obtained for flow orientations slightly perturbed from certain lattice vectors, owing to a competition between directional locking and spatial velocity variations.

Parallel accelerated Stokesian dynamics with Brownian motion

We present scalable algorithms to simulate large-scale stochastic particle systems amenable for modeling dense colloidal suspensions, glasses and gels. To handle the large number of particles and consequent many-body interactions present in such systems, we leverage an Accelerated Stokesian Dynamics (ASD) approach, for which we developed parallel algorithms in a distributed memory architecture. We present parallelization of the sparse near-field (including singular lubrication) interactions, and of the matrix-free many-body far-field interactions, along with a strategy for communicating and mapping the distributed data structures between the near- and far field. Scaling to up to tens of thousands of processors for a million particles is demonstrated. In addition, we propose a novel algorithm to efficiently simulate correlated Brownian motion with hydrodynamic interactions. The original Accelerated Stokesian Dynamics approach requires the separate computation of far-field and near-field Brownian forces. Recent advancements propose computation of a far-field velocity using positive spectral Ewald decomposition. We present an alternative approach for calculating the far-field Brownian velocity by implementing the fluctuating force coupling method and embedding it using a nested scheme into ASD. This straightforward and flexible approach reduces the computational time of the Brownian far-field force construction from O(NlogN)1+|α| to O(NlogN).

Aggregation and breakup of colloidal particle aggregates in shear flow: A combined Monte Carlo - Stokesian dynamics approach

A method for the simulation of aggregation and breakup processes in colloidal particle suspensions is presented. The method combines a Monte Carlo algorithm to determine, on the basis of probabilistic considerations, the sequence of aggregation and breakup events, and a Discrete Element Method, built in the framework of Stokesian dynamics and contact mechanics, to accurately reproduce them. Liquid-solid suspensions subject to a uniform shear stress are investigated. The model is seen to be able to reproduce the typical dynamic steady state which is observed in colloidal suspensions under severe shearing, in which the effects of aggregation and breakup balance each other. The structural properties of the aggregates and the dynamics of the aggregation and breakup phenomena are characterized in detail. Both fragmentation and erosion are seen to contribute to the breakup process, which is characterized by an exponent similar to the one reported in the literature for compact clusters.

Numerical analysis on motion of microparticles passing through straight and tortuous fibrous layers

The behavior of microparticle assemblage moving through the saturated pores in a fibrous layer has been investigated numerically. We adopted a particle model to express the straight and tortuous fibrous layers and calculated the velocities of individual microparticles using the Stokesian dynamics approach assuming the Stokes flow. The simulation results showed that the particles spread as they moved through the layer. This is interpreted as hydrodynamic diffusion caused by the hydrodynamic interaction dominant in the Stokes flow. More pronounced diffusion was observed in the tortuous fibrous layer than in the straight one. It was found that the velocity of each particle deviated more from the ensemble average velocity of the assemblage in the tortuous fibrous layer. It was also observed that the tortuous fibrous layers exhibited greater variation in the size of the pores where particles passed. Our results quantitatively indicated that the tortuous fibrous layer consisted of a wide variety of pore sizes, which affects the velocity of the particles passing through it. Consequently, the difference in each particle velocity causes the hydrodynamic diffusion. It was also revealed that the subtle difference in the fiber shape substantially influences the hydrodynamic behavior of the particles moving inside.

Numerical Analysis on Transport of Particle Assemblage in Fibrous Media

We have simulated the motion of particle assemblage passing through fibrous media. On the assumption that the particle size is of the order of micrometers, the velocity of individual particles was calculated by use of the Stokesian dynamics that describes the Stokes flow in the presence of multiple particles. The results show that a part of particles is captured by fibers while others avoid them and permeate the media. From the velocity, traveling distance and direction of the particles which are not captured, the diffusion caused by the hydrodynamic interaction was observed. The results indicated that the motion of each particle greatly differs depending on the particle size particularly for the large fiber volume fraction, which would be closely related to the hydrodynamic diffusive behavior.

Rheology of a concentrated suspension of spherical squirmers: monolayer in simple shear flow

Abstract

Stokesian dynamics simulations of a magnetotactic bacterium

The swimming of bacteria provides insight into propulsion and steering under the conditions of low-Reynolds number hydrodynamics. Here we address the magnetically steered swimming of magnetotactic bacteria. We use Stokesian dynamics simulations to study the swimming of single-flagellated magnetotactic bacteria (MTB) in an external magnetic field. Our model MTB consists of a spherical cell body equipped with a magnetic dipole moment and a helical flagellum rotated by a rotary motor. The elasticity of the flagellum as well as magnetic and hydrodynamic interactions is taken into account in this model. We characterized how the swimming velocity is dependent on parameters of the model. We then studied the U-turn motion after a field reversal and found two regimes for weak and strong fields and, correspondingly, two characteristic time scales. In the two regimes, the U-turn time is dominated by the turning of the cell body and its magnetic moment or the turning of the flagellum, respectively. In the regime for weak fields, where turning is dominated by the magnetic relaxation, the U-turn time is approximately in agreement with a theoretical model based on torque balance. In the strong-field regime, strong deformations of the flagellum are observed. We further simulated the swimming of a bacterium with a magnetic moment that is inclined relative to the flagellar axis. This scenario leads to intriguing double helical trajectories that we characterize as functions of the magnetic moment inclination and the magnetic field. For small inclination angles (lesssim {20^{circ }}) and typical field strengths, the inclination of the magnetic moment has only a minor effect on the swimming of MTB in an external magnetic field. Large inclination angles result in a strong reduction in the velocity in direction of the magnetic field, consistent with recent observations that bacteria with large inclination angles use a different propulsion mechanism.Graphic abstract

Predictions of microstructure and stress in planar extensional flows of a dense viscous suspension

Abstract

Nanoparticle dispersion in porous media: Effects of hydrodynamic interactions and dimensionality

AbstractWe investigate the effect of steric and hydrodynamic interactions (HI) on quiescent diffusion and flow‐driven transport of finite‐sized nanoparticles through periodic 2D (two‐dimensional) and 3D (three‐dimensional) nanopost arrays using Stokesian dynamics simulations. We find that steric and HI hinder particle diffusivity under quiescent conditions and enhance longitudinal dispersion under flow. Moreover, the presence of HI leads to a power‐law increase in the longitudinal dispersion coefficient with Pe due to spatial variations in the fluid velocity. Lastly, our simulations reveal that longitudinal particle dispersion coefficients behave similarly in 2D and 3D when HI are included.

Shear-induced glass-to-crystal transition in anisotropic clay-like suspensions.

A new numerical framework based on Stokesian dynamics is used to study a shear-induced glass-to-crystal transition in suspensions of clay-like anisotropically charged platelets. The structures obtained in quiescent conditions are in agreement with previous Monte Carlo results: a liquid phase at very short interaction range (high salt concentration), phase separation and a gel without large scale density fluctuations at intermediate interaction ranges, and glassy states at very large interaction ranges. When initially glassy suspensions are sheared, hydrodynamic torques first rotate platelets so they can reach a transient quasi-nematic disordered state. These orientational correlations permit to unlock translational degrees of freedom and the platelets then form strings aligned with the velocity direction and hexagonally packed in the gradient-vorticity plane. Under steady shear, platelet orientations are correlated but the system is not nematic. After flow cessation and relaxation in quiescent conditions, positional and orientational order are further improved as the platelet suspension experiences a transition to a nematic hexagonal crystal. Energy calculations and the existence of residual stress anisotropy after relaxation show that this final structure is not an equilibrium state but rather a new ordered, arrested state. The transient, nematic, disordered state induced by shear immediately after startup and unlocking translational degrees of freedom is thought to be an initial step that may be generic for other suspensions of strongly anisotropic colloids with important translation-orientation coupling induced by long-range interactions.

Modeling particle-fluid interaction in a coupled CFD-DEM framework

In this work, we present an alternative methodology to solve the particle-fluid interaction in the resolved CFDEM ® coupling framework. This numerical approach consists of coupling a Discrete Element Method (DEM) with a Computational Fluid Dynamics (CFD) scheme, solving the motion of immersed particles in a fluid phase. As a novelty, our approach explicitly accounts for the body force acting on the fluid phase when computing the local momentum balance equations. Accordingly, we implement a fluid-particle interaction computing the buoyant and drag forces as a function of local shear strain and pressure gradient. As a benchmark, we study the Stokesian limit of a single particle. The validation is performed comparing our outcomes with the ones provided by a previous resolved methodology and the analytical prediction. In general, we find that the new implementation reproduces with very good accuracy the Stokesian dynamics. Complementarily, we study the settling terminal velocity of a sphere under confined conditions.

Modeling of non-spherical particle flows: Movement and orientation behavior

The fast advancement of existing and new functional material systems, where particulate morphology differs from traditional systems (e.g. fibers, flakes,), demands technical know-how on the processing of non-spherical particles in liquid media. There are few to no technical relevant tools available for the prediction of such particulate systems, specifically when particle-particle interactions and particle orientation are relevant, making development of such processes time consuming and expensive. Therefore, a tool is needed to support process design and further understand of non-spherical systems. On this work, a novel approach for the calculation of drag forces and drag induced torques for non-spherical particles in the context of CFD-DEM coupling is presented. The approach is inspired by Stokesian Dynamics for the computation of drag forces and torques when using the multi-sphere method for the representation of non-spherical particles.