Short-range Hydrodynamic Interactions Research Articles

Immersed boundary method for considering lubrication effects in the CFD-DEM simulations

Although the CFD-DEM simulations could predict the long-range hydrodynamic interaction with high accuracy, they face difficulty in the close distance between particles because mesh resolution is not fine enough to capture the lubrication effects. As a remedy, we used a variant of Immersed Boundary method in our CFD solver to model a problem as a fully resolved simulation. Then, we developed a second-order boundary layer reconstruction approach to increase the accuracy of the immersed boundary method. Furthermore, for the first time and in the present work, we considered how shared cells between the particles need to be treated in the simulation of two approaching particles. Moreover, we investigated the relationship between mesh resolution and time step size on the accuracy of the calculated force. We found a specific range for this ratio to capture the correct short-range hydrodynamic interactions.

The role of hydrodynamic interactions on the aggregation kinetics of sedimenting colloidal particles.

The aggregation kinetics of sedimenting colloidal particles under fully destabilized conditions has been investigated over a wide range of particle volume fractions (Φ) and Péclet numbers (Pe) using the recent PSE algorithm implementing the Rotne-Prager-Yamakawa (RPY) approximation for long-range Hydrodynamic Interactions (HI). Fast Lubrication Dynamics (FLD) and simple Brownian Dynamics (BD) methods have also been employed to assess the importance of long range hydrodynamic interactions on the resulting dynamics. It has been observed that long-range hydrodynamic interactions are essential to capture the fast aggregation rates induced by the increase in sedimentation rate of clusters with increasing mass, which manifests with an explosive-like cluster growth after a given induction time. On the contrary, simulations employing only short-range hydrodynamic interactions (such as FLD) and BD (which neglects completely hydrodynamic interactions) are incapable of predicting this very rapid kinetics, because sedimentation simply leads to all particles and clusters moving vertically with identical velocity. It has been observed that at high volume fractions and low Pe values, a gel point can be formed and a phase diagram predicting when gelation is reached has been obtained. It was also observed that, as Pe increases, the anisotropy of the resulting clusters decreases, suggesting that denser clusters with spherical-like morphology are formed due to cluster breakage and restructuring. We can conclude that long-range hydrodynamic effects are of crucial importance in understanding the aggregation dynamics of settling clusters, revealing important features of the complex interplay between sedimentation, and colloidal interactions.

Local lubrication model for spherical particles within incompressible Navier-Stokes flows.

The lubrication forces are short-range hydrodynamic interactions essential to describe suspension of the particles. Usually, they are underestimated in direct numerical simulations of particle-laden flows. In this paper, we propose a lubrication model for a coupled volume penalization method and discrete element method solver that estimates the unresolved hydrodynamic forces and torques in an incompressible Navier-Stokes flow. Corrections are made locally on the surface of the interacting particles without any assumption on the global particle shape. The numerical model has been validated against experimental data and performs as well as existing numerical models that are limited to spherical particles.

Modeling Paramecium swimming in a capillary tube

In certain types of biomimetic surgery systems, micro robots inspired by Paramecium are designed to swim in a capillary tube for gaining access to internal organs with minimal invasion. Gaining insights into the mechanics of Paramecium swimming in a capillary tube is vital for optimizing the design of such systems. There are two approaches to modeling the physics of micro swimming. In the envelope approach which is widely accepted by researchers, Paramecium is approximated as a sphere self-propelled by tangential and normal surface distortions. Not only this approach is incapable of considering the specific geometry of Paramecium, but also it neglects short range hydrodynamic interactions due to beating cilia. Thus it leads to dissimilarity between experimental data and simulation results. In this study, it is aimed to present a sub layer approach to modeling Paramecium locomotion which is capable of directly applying the hydrodynamic interactions due to beating cilia on Paramecium boundary. In this approach, Paramecium’s boundary is discretized to hydrodynamically independent elements; in each time step of swimming, a specific function is fit to Paramecium boundary. Then, element coordinates are extracted and fluid dynamic equations are solved to model the physics of micro swimming.

Collision model for fully resolved simulations of flows laden with finite-size particles

We present a collision model for particle-particle and particle-wall interactions in interface-resolved simulations of particle-laden flows. Three types of interparticle interactions are taken into account: (1) long- and (2) short-range hydrodynamic interactions, and (3) solid-solid contact. Long-range interactions are incorporated through an efficient and second-order-accurate immersed boundary method (IBM). Short-range interactions are also partly reproduced by the IBM. However, since the IBM uses a fixed grid, a lubrication model is needed for an interparticle gap width smaller than the grid spacing. The lubrication model is based on asymptotic expansions of analytical solutions for canonical lubrication interactions between spheres in the Stokes regime. Roughness effects are incorporated by making the lubrication correction independent of the gap width for gap widths smaller than ∼1% of the particle radius. This correction is applied until the particles reach solid-solid contact. To model solid-solid contact we use a variant of a linear soft-sphere collision model capable of stretching the collision time. This choice is computationally attractive because it allows us to reduce the number of time steps required for integrating the collision force accurately and is physically realistic, provided that the prescribed collision time is much smaller than the characteristic time scale of particle motion. We verified the numerical implementation of our collision model and validated it against several benchmark cases for immersed head-on particle-wall and particle-particle collisions, and oblique particle-wall collisions. The results show good agreement with experimental data.

Can we reduce debris flow to an equivalent one-phase flow?

A recent extension of the discrete element method is reported for the simulation of dense mixtures of non-colloidal particles and viscous fluids in the non-inertial regime. As an application, we examine the interplay between rate dependent dilatancy and hydro-mechanical coupling which can be expected in debris flow. The numerical model includes sphere-sphere contacts using a soft contact approach [2], short range hydrodynamic interactions defined by frame-invariant expressions of forces and torques in the lubrication approximation, and drag forces resulting from the poromechanical coupling computed with the DEM-PFV technique [3]. The bulk shear stress is decomposed into contact stress and hydrodynamic stress. Both contributions are shown to be increasing functions of a dimensionless shear rate Iv, in agreement with experimental results [4]. Statistics of microstructural variables highlight a complex interplay between solid contacts and hydrodynamic interactions. In contrast with a popular idea, the results suggest that lubrication may not necessarily reduce the contribution of contact forces to the bulk shear stress. The proposed model is general and applies directly to sheared satured granular media in which pore pressure feedback plays a key role. We argue that it can be the case for debris fow, especially during the triggering phase, when run-out include transitional phases, and when the flow is stopped. It is then concluded that debris cannot be computed by assuming solely the rheological properties of an equivalent mixture.

Microscopic origins of shear stress in dense fluid–grain mixtures

A numerical model is used to simulate rheometer experiments at constant normal stress on dense suspensions of spheres. The complete model includes sphere–sphere contacts using a soft contact approach, short range hydrodynamic interactions defined by frame-invariant expressions of forces and torques in the lubrication approximation, and drag forces resulting from the poromechanical coupling computed with the DEM-PFV technique. Series of simulations in which some of the coupling terms are neglected highlight the role of the poromechanical coupling in the transient regimes. They also reveal that the shear component of the lubrication forces, though frequently neglected in the literature, has a dominant effect in the volume changes. On the other hand, the effects of lubrication torques are much less significant. The bulk shear stress is decomposed into contact stress and hydrodynamic stress terms whose dependency on a dimensionless shear rate—the so called viscous number \(I_v\)—are examined. Both contributions are increasing functions of \(I_v\), contacts contribution dominates at low viscous number (\(I_v<0.15\)) whereas lubrication contributions are dominant for \(I_v> 0.15\), consistently with a phenomenological law infered by other authors. Statistics of microstructural variables highlight a complex interplay between solid contacts and hydrodynamic interactions. In contrast with a popular idea, the results suggest that lubrication may not necessarily reduce the contribution of contact forces to the bulk shear stress. The proposed model is general and applies directly to sheared immersed granular media in which pore pressure feedback plays a key role (triggering of avalanches, liquefaction).

Hydrodynamic simulations of self-phoretic microswimmers

A mesoscopic hydrodynamic model to simulate synthetic self-propelled Janus particles which is thermophoretically or diffusiophoretically driven is here developed. We first propose a model for a passive colloidal sphere which reproduces the correct rotational dynamics together with strong phoretic effect. This colloid solution model employs a multiparticle collision dynamics description of the solvent, and combines stick boundary conditions with colloid-solvent potential interactions. Asymmetric and specific colloidal surface is introduced to produce the properties of self-phoretic Janus particles. A comparative study of Janus and microdimer phoretic swimmers is performed in terms of their swimming velocities and induced flow behavior. Self-phoretic microdimers display long range hydrodynamic interactions with a decay of 1/r(2), which is similar to the decay of gradient fields generated by self-phoretic particle, and can be characterized as pullers or pushers. In contrast, Janus particles are characterized by short range hydrodynamic interactions with a decay of 1/r(3) and behave as neutral swimmers.

Numerical modelling of finite-size particle collisions in a viscous fluid

A general model is presented for short-range hydrodynamic interactions and head-on particle-particle/wall collisions. The model has been embedded in two distinct numerical methods for fully resolved simulation of finite-size particles in a viscous fluid. It accounts for the material properties of the particles and lubrication effects prior to collision that cannot be fully resolved on a fixed grid. We demonstrate that the model is able to reproduce experimental data for the coefficient of restitution of particle-wall collisions over a wide range of Stokes number based on the particle impact velocity. The set of model parameters we selected and more generally the modelling approach we propose can be efficiently used for fully resolved simulations of moderately dense solid-liquid suspensions.

Dynamics of Bacterial Swarming

When vegetative bacteria that can swim are grown in a rich medium on an agar surface, they become multinucleate, elongate, synthesize large numbers of flagella, produce wetting agents, and move across the surface in coordinated packs: they swarm. We examined the motion of swarming Escherichia coli, comparing the motion of individual cells to their motion during swimming. Swarming cells' speeds are comparable to bulk swimming speeds, but very broadly distributed. Their speeds and orientations are correlated over a short distance (several cell lengths), but this correlation is not isotropic. We observe the swirling that is conspicuous in many swarming systems, probably due to increasingly long-lived correlations among cells that associate into groups. The normal run-tumble behavior seen in swimming chemotaxis is largely suppressed, instead, cells are continually reoriented by random jostling by their neighbors, randomizing their directions in a few tenths of a second. At the edge of the swarm, cells often pause, then swim back toward the center of the swarm or along its edge. Local alignment among cells, a necessary condition of many flocking theories, is accomplished by cell body collisions and/or short-range hydrodynamic interactions.

Fully resolved simulations of colliding monodisperse spheres in forced isotropic turbulence

Fully resolved simulations of particles suspended in a sustained turbulent flow field are presented. To solve the Navier–Stokes equations a lattice-Boltzmann scheme was used. A spectral forcing scheme is applied to maintain turbulent conditions at a Taylor microscale Reynolds number of 61. The simulations contained between 2 and 10 vol % particles with a solid to fluid density ratio between 1.15 and 1.73. A lubrication force is used to account for subgrid hydrodynamic interaction between approaching particles. Results are presented on the influence of the particle phase on the turbulence spectrum and on particle collisions. Energy spectra of the simulations show that the particles generate fluid motion at length scales of the order of the particle size. This results in a strong increase in the rate of energy dissipation at these length scales and a decrease of kinetic energy at larger length scales.Collisions due to uncorrelated particle motion are observed (primary collisions), and collision frequencies are in agreement with theory on inertial particle collisions. In addition to this, a large number of collisions at high frequencies is encountered. These secondary collisions are due to the correlated motion of particles resulting from short-range hydrodynamic interactions and spatial correlation of the turbulent velocity field at short distances. This view is supported by the distribution of relative particle velocities, the particle velocity correlation functions and the particle radial distribution function.

Investigations of bubble–particle interactions

Bubble–particle interaction during flotation comprises of collision, attachment and detachment. This paper presents a review of our investigations into these microprocesses. Analysis of collision phenomenon focuses on the physicochemical hydrodynamics of water flow passing the rising bubbles. The influence of the fore-and-aft asymmetry of water streamlines and of the mobility of the bubble surface on collision efficiency is quantified. In the case of attachment, the analysis considers contact and attachment times and reveals that the available models for contact times are far from satisfactory. It may be necessary to include short-range hydrodynamic interactions for the modeling of contact times. At present, the actual attachment time is difficult to predict from first principles. Finally, the examination of detachment focuses on models for predicting the tenacity of attached particles. The influence of the bubble size on tenacity is also analyzed. Simplified equations describing the maximum particle size for stable attachment to air bubbles are derived.

On the theory of concentrated hard-sphere suspensions

A systematic theory for the dynamics of hard-sphere suspensions of interacting Brownian particles with both hydrodynamic and direct interactions is presented. A generalized diffusion equation is derived for concentrated suspensions. The volume fraction (φ) dependence of the short- and long-time self-diffusion coefficients are thus explored from a unifying point of view. The long-range hydrodynamic interactions due to the Oseen tensor are shown to play a crucial role in both coefficients, while the short-range hydrodynamic interactions just lead to corrections. The importance of the correlation effects between particles due to the long-range hydrodynamic interactions is also stressed. The nonlocal correlation effect is an important factor, leading to the behavior of the long-time self-diffusion coefficient ( D S L) as D S L ∼ (1 − φ/ φ 0) 2 near the volume fraction of φ 0 = 0.5718. The direct interactions are also found to be drastically reduced by the short-range hydrodynamic interactions.

Trajectory Modeling of Non-Brownian Particle Flotation Using an Extended Derjaguin-Landau-Verwey-Overbeek Approach

Pressure flotation of nitrocellulose (NC) fines was quantified by tralectory analysis. A model was formulated that incorporates recently developed extended DLVO (ExDLVO) theory and the short-range hydrodynamic interactions of a particle near a bubble surface. A repulsive Lifshitz-van der Waals (LW) force was found to exist between particle and bubble. Attractive long-range hydrophobic forces between NC particles and bubbles were responsible for particle adhesion. Model predictions of flotation efficiency compared well with experimental results

Picosecond rotational reorientation of cresyl violet in polymer solution

Picosecond absorption spectroscopy has been used to study the rotational reorientation of cresyi violet in methanol solutions containing poly(ethylene oxide). The increase in the rotational reorientation time with increasing polymer concentration can be attributed to the short-range hydrodynamic interactions between the dye and entangled polymer chains.